Airport Under Control

Airport under Control
Multiagent Scheduling for Airport Ground Handling
Airport under Control

Multiagent Scheduling for Airport Ground Handling
PROEFSCHRIFT
ter verkrijging van de graad van doctor

aan de Universiteit van Tilburg,
op gezag van de rector magnificus,
Prof. dr. Ph. Eijlander,
in het openbaar te verdedigen ten overstaan van een
door het college voor promoties aangewezen commissie
in de aula van de Universiteit
op woensdag 25 mei 2011 om 10:15 uur
door
Xiaoyu Mao
geboren op 6 december 1980 te Xian, P.R. China
Promotores:
Prof. dr. H.J. van den Herik
Prof. dr. E.O. Postma
Copromotores:
Dr. ir. N. Roos
Dr. A.H. Salden
Beoordelingscommissie:
Prof. dr. A.P.J. van den Bosch
Prof. dr. G. van Oortmerssen
Prof. dr. A.J. van Zanten
Prof. dr. C.M. Jonker
Prof. dr. C. Witteveen
Dutch Ministry of Economic Affairs

The research reported in this thesis has been funded by the Dutch Ministry of Economic
Affairs in the framework of the Casimir Project program (Project No. CSI4006).
SIKS Dissertation Series No. 2011-13

The research reported in this thesis has been carried out under the auspices of SIKS, the
Dutch Research School for Information and Knowledge Systems.
TiCC Ph.D. Series No. 16

Cover design: Chris Eichberger
ISBN 978-90-5335-401-8
c
2011
Xiaoyu Mao
All rights reserved. No part of this publication may be reproduced, stored in a retrieval
system, or transmitted, in any form or by any means, electronically, mechanically, photocopying, recording or otherwise, without prior permission of the author.
Preface
The classical decision theory in project management with a single decision maker soon
becomes inapplicable because of the large-scale informational and managerial decentralisation. The rapid change in both technology and the structure of the market place in
recent years has called for new paradigms for managing large and distributed projects.
Within the field of distributed artificial intelligence, the research area of multiagent systems provide a natural way to model and solve problems with inherent complexity that
is caused by large-scale decentralisation.
Our research starts from a practical problem of such a decentralised setting scheduling airport ground handling (AGH) operations. At an airport, many aircraft are turning
around at the same time. Each of the aircraft turnaround processes can be seen as a
project involving a multitude of organisations working simultaneously on diverse activities. The general goal of our research is to investigate the characteristics of the AGH
scheduling problem and provide an adequate solution model that can solve the problem
efficiently and robustly. Our proposed multiagent scheduling system, that is discussed in
this thesis, may be used to solve a wider range of real-world scheduling problems.
One of the advantages of doing a PhD at both a university and a research-oriented
industrial company is receiving guidance not only from experts in academia, but also from
experts in industries. In the academic world, I have had the honour to receive guidance
from Jaap van den Herik and Eric Postma, my two supervisors from Tilburg Center for
Cognition and Communication (TiCC) at Tilburg University. I owe many thanks to Jaap
for his great enthusiasm and support for my research, in particular, for teaching me how
to write scientific topics in understandable and attractive texts. A special gratitude goes
to Eric for the inspirations he brought into my research. During the early phase of my
research, I have had the pleasure to be guided by Nico Roos from Maastricht University.
I owe Nico my sincere gratitude for many things. In the industrial world, I am grateful to
my daily advisor Alfons Salden from Almende. Alfons always brings me a broader scope
of research interests, from fundamental physics to industrial robotics.
Similar to the guidance I received, throughout the whole process of performing research, I received supports and encouragement from many colleagues from Almende,
Maastricht University, and Tilburg University. I mention Adriaan ter Mors, Jeroen
Valk, Tam
as M
ahr, Duco Ferro, Anne van Rossum, Andries Stam, Steven de Jong, Jahn
Takeshi-Saito, and Laurens van der Maaten. I would like to recognise my Almende colleague Adriaan ter Mors in particular. I have had the pleasure to cooperate with Adriaan
in the same research project for four years. Along the way we have built up not only an
vi
Preface
enjoyable working partnership but also a life-long valuable friendship.

Moreover, I also wish to acknowledge gratefully the excellent support and help by the
management team at Almende and the staff members at Tilburg University. I mention
Hans Abbink, Peet van Tooren, Jan Peter Larsen, Judith Engelsman, Janny Ramakers,
Joke Hellemons and Olga Houben. I thank Janny in particular for her generous help of
translating the english summary into a dutch samenvatting.
In addition, I would like to thank Tony Wauters from KaHo Sint-Lieven for his kindness of sharing his research results in multi-project scheduling.
In conclusion to these acknowledgements, I particularly would like to express my
sincere gratitude to my parents. I owe my father eight years of company throughout my
oversea life. I thank him for his life-saving financial supports for my Master studies and
his weekly moral supports sent from 8, 000 kilometres away.
Finally, love to Xiaochen.
Xiaoyu Mao
Rotterdam, May 2011
Contents
Preface
Contents
ix
Glossary
xi
List of Figures
xvii
List of Tables
xix
1 Introduction
1.1 Airport Ground Handling . . . . . . . . . . . . .
1.2 Problem Statement and Research Questions . . .
1.3 Research Methodology . . . . . . . . . . . . . . .
1.3.1 Problem Generalisation and Formulation
1.3.2 Literature Review . . . . . . . . . . . . .
1.3.3 Agent-based Model Design . . . . . . . .
1.3.4 MAS Solutions Development . . . . . . .
1.3.5 Empirical Evaluation . . . . . . . . . . . .
1.4 Structure of the Thesis . . . . . . . . . . . . . . .
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2 AGH Scheduling Problem

2.1 Resource-constrained Project Scheduling Problem . . . .
2.1.1 Activity and Activity Network . . . . . . . . . .
2.1.2 Temporal Relations and Constraints . . . . . . .
2.1.3 Resources and Constraints . . . . . . . . . . . . .
2.1.4 Schedules and Performance Measures . . . . . . .
2.2 AGH Scheduling Problem . . . . . . . . . . . . . . . . .
2.2.1 Scheduling Multiple Projects . . . . . . . . . . .
2.2.2 Informational and Managerial Decentralisation .
2.2.3 Decision Making under Uncertainty . . . . . . .
2.2.4 A DRCMPSP/u Formulation of AGH Scheduling
2.3 Chapter Summary . . . . . . . . . . . . . . . . . . . . .
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viii
Contents
3 A Review of Existing Solution Methods

3.1 Solution Methods for RCMPSP . . . . . . . . . . .
3.1.1 Exact Methods . . . . . . . . . . . . . . . .
3.1.2 Priority-rule-based Heuristics . . . . . . . .
3.1.3 Meta-heuristics . . . . . . . . . . . . . . . .
3.1.4 Constraint Satisfaction and Optimisation .
3.1.5 Beyond Centralised Solution Methods . . .
3.2 Solution Methods for DRCMPSP . . . . . . . . . .
3.2.1 Multiagent Systems and Mechanism Design
3.2.2 MAS Solutions to DRCMPSP . . . . . . . .
3.2.3 Towards a New MAS Solution . . . . . . .
3.3 Project Scheduling under Uncertainty . . . . . . .
3.3.1 Proactive-reactive Scheduling . . . . . . . .
3.3.2 Stochastic Scheduling . . . . . . . . . . . .
3.3.3 Fuzzy Scheduling . . . . . . . . . . . . . . .
3.3.4 Contingent Scheduling . . . . . . . . . . . .
3.3.5 Sensitivity Analysis . . . . . . . . . . . . .
3.4 Chapter Summary . . . . . . . . . . . . . . . . . .
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4 A Lease-based Multiagent Model

4.1 Agents, Schedules, and Utilities . . . . . . . . . . . . . . . . . .
4.1.1 Resource Agent, Schedule, and Utility . . . . . . . . . .
4.1.2 Project Agent, Schedule, and Utility . . . . . . . . . . .
4.1.3 A Conflict-free and Feasible Agent-based AGH Schedule
4.2 Lease-based Market Mechanism . . . . . . . . . . . . . . . . . .
4.2.1 Utility Decomposition . . . . . . . . . . . . . . . . . . .
4.2.2 Lease-based Slot Negotiation . . . . . . . . . . . . . . .
4.3 Answer to Research Question 1 . . . . . . . . . . . . . . . . . .
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5 Online Iterative Scheduling

5.1 Clairvoyant Online Schedule Generation Scheme
5.1.1 Clairvoyant Online Scheme . . . . . . . .
5.1.2 Schedule Generation Schemes . . . . . . .
5.1.3 An Example . . . . . . . . . . . . . . . .
5.1.4 A Discussion of Employing COSGS . . . .
5.2 Iterative Schedule-improvement Method . . . . .
5.2.1 ISIM by Secure-time-window Update . . .
5.2.2 ISIM by Resource-type-profile Update . .
5.3 Experiments . . . . . . . . . . . . . . . . . . . . .
5.3.1 Experimental Setup . . . . . . . . . . . .
5.3.2 Results and Analysis . . . . . . . . . . . .
5.4 Answer to Research Question 2 . . . . . . . . . .
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ix
6 Stable Proactive Scheduling
6.1 Stability: Solution Robustness . . . . . . . . . . . . . . . . . .
6.1.1 Stability Measures . . . . . . . . . . . . . . . . . . . .
6.1.2 Stability in Proactive-reactive Scheduling Procedures .
6.1.3 Solution Models for Stable Proactive Scheduling . . .
6.1.4 Towards an Agent-based Stable Scheduling . . . . . .
6.2 Agent-based Stable Proactive Scheduling . . . . . . . . . . . .
6.2.1 Constructive Heuristic Procedures by Resource Agents
6.2.2 Coevolving Slack Time Windows by Project Agents .
6.3 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.3.1 Experimental Setup . . . . . . . . . . . . . . . . . . .
6.3.2 Results and Analysis . . . . . . . . . . . . . . . . . . .
6.4 Answer to Research Question 3 . . . . . . . . . . . . . . . . .
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7 Conclusions
7.1 Answers to the Research Questions . . . . . . . . . . . . . . .
7.1.1 Agent-based Model for AGH Scheduling Problem . . .
7.1.2 Efficiency and Robustness under Partial Observability
7.1.3 Efficiency and Robustness under Nondeterminism . .
7.2 Answer to the Problem Statement . . . . . . . . . . . . . . .
7.3 Recommendations for Future Research . . . . . . . . . . . . .
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111
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113
113
114
References
117
Appendices
127
A Airport Ground-Handling Operations
127
B Properties of the 80 Chosen MPSPLib Instances
131
Summary
135
Samenvatting
139
Curriculum Vitae
143
List of Publications
145
SIKS Dissertation Series
147
TiCC Ph.D. Series
155
Glossary
List of Abbreviations
The list below contains all technical abbreviations used in the thesis. Normal lexical abbreviations, for instance, e.g. and i.e., are not listed. Similar considerations apply for
organisations, such as BNVKI. Abbreviations used only in tables or figures are explained
in the corresponding table or figure.
ADSTW
AGH
AI
AoA
AoN
APD
APDP
BPR
BSS
Co-EAs
COP
COS
COSGS
CPF
CSP
DAI
Dec-POMDP
DRCMPSP/u
DRCMPSP
EFPF
Activity-dependent Slack Time Window

Airport Ground Handling
Artificial Intelligence
Activity on Arc
Activity on Node
Minimising the Average Project Delay
Minimising the Average Project Delay Penalty
Backward Pass Recursion
Basic Simple Strategy
Coevolutionary Algorithms
Constraint Optimisation Problem
Clairvoyant Online Scheme
Clairvoyant Online Schedule Generation Scheme
Cohabited Predecessor First
Constraint Satisfaction Problem
Distributed Artificial Intelligence
Decentralised Partially Observable Markov Decision Process
Decentralised Resource-constrained Multi-project Scheduling Problem
under Uncertainty
Decentralised Resource-constrained Multi-project Scheduling Problem
Earliest Finished Predecessor First
xii
EGT
ES
FPR
GT-MAS
ISIM
LFT
MABO
MAS
MaxPF
MinEA
MinED
MIP
MPSPLib
MRCPSP
OI-MAS
OR
p-SGS
PD
PERT
PM
PSPLib
PS
RCMPSP
RCPSP
RES
RfQ
RPF
RQ
s-SGS
SPD
SPM
TCPSP
TPM
TRCPSP
TRPC
TSRUC
TSRU
Glossary
Evolutionary Game Theory
Evolutionary Strategy
Forward Pass Recursion
Game-theoretic MAS Scheduling Approach
Iterative Schedule-improvement Method
Minimum Latest Finish Time First
Myopic Activity-based Optimisation
Multiagent System
Maximise the Sum of Pairwise Floats
Minimise the Number of Extra Arcs
Minimise the Estimated Disruption
Mixed Integer Programming
Library for Multi-project Scheduling Problems
Multi-mode Resource-constrained Project Scheduling Problem
Online Iterative MAS Scheduling Approach
Operations Research
Parallel Schedule Generation Scheme
Minimising the Project Delay
Program Evaluation and Review Technique
Minimising the Project Makespan
Library for Project Scheduling Problems
Problem Statement
Resource-constrained Multi-project Scheduling Problem
Resource-constrained Project Scheduling Problem
Restart Evolution Strategy
Request for Quotation
Richest Predecessor First
Research Question
Serial Schedule Generation Scheme
Minimising the Summed Project Delay
Minimising the Summed Project Makespan
Time-constrained Project Scheduling Problem
Minimising the Total Project Makespan
Time- and Resource-constrained Project Scheduling Problem
Minimising the Total Resource Procurement Cost
Minimising the Total Squared Resource Utilisation Cost
Minimising the Total Squared Resource Utilisation
xiii
List of Symbols
Single-project
ai
a0
an+1
A
A+
dl
dmax
ij
Scheduling Problem
ith activity of a project
Dummy start activity of a project
Dummy completion activity of a project
Complete set of project (real) activities
Complete set of project (real and fictitious) activities
Project deadline
Maximum time lag between the start of activity ai and aj
dmin
ij
Minimum time lag between the start of activity ai and aj
dt
tef
i
tes
i
fi
fi
Ai
Ai
I
te
ts
tlf
i
tls
i
n
pi
rl
si
S
si
Ai
Ai
i
Project due time

Earliest possible finish time of activity ai
Earliest possible start time of activity ai
Scheduled finish time of activity ai
Actual finish time of activity ai
Set of immediate predecessors of activity ai
Set of immediate successors of activity ai
A time interval
End time of a time interval
Start time of a time interval
Latest possible finish time of activity ai
Latest possible start time of activity ai
Total number of real activities in a project
Estimated processing time of activity ai
Expected project release time
Scheduled start time of activity ai
A complete set of activity start times, a.k.a., a project schedule
Actual start time of activity ai
Set of transitive predecessors of activity ai
Set of transitive successors of activity ai
Operating mode of activity ai
Length of the project critical path
Simple finish-start precedence relation
xiv
Glossary
Multi-project Scheduling Problem

ai,j
j th activity of project Pi
ai,0
Dummy start activity of project Pi
ai,ni +1
Dummy completion activity of project Pi
Ai
Complete set of all (real) activities in project Pi
+
Ai
Complete set of all (real and fictitious) activities in project Pi
dli
Deadline of project Pi
Dl
Super deadline
dti
Due time of project Pi
fi,j
Scheduled finish time of activity ai,j
fi,j
Actual finish time of activity ai,j
i,j
Operating mode of activity ai,j
ni
Total number of real activities of project Pi
pi,j
Estimated processing time of activity ai,j
pi,j
Actual processing time of activity ai,j
Pi
P
rli
rli
Rl
si,j
si,j
ith project in an RCMPSP

Set of all projects in an RCMPSP
Expected release time of project Pi
Actual release time of project Pi
Super release time
Scheduled start time of activity ai,j
Actual start time of activity ai,j
cdl
i
i
Delay cost per time unit for project Pi

Length of the critical path of project Pi
Resources
ck
cpk
cuk
rik
k
ri,j
R
Rk
uk (S, t)
Maximum capacity of resource type Rk

Procurement cost per resource unit of resource type Rk
Utilisation cost per resource unit of resource type Rk
The amount of resources needed by activity ai from resource type Rk
The amount of resources needed by activity ai,j from resource type Rk
Set of all (renewable) resource types
k th type of resources
Scheduled amount of resource of type Rk to be used at time point t
Agent-based Model for AGH Scheduling

i,j
Schedule of activity ai,j
xv
oi,j,l
i,j
O
lth aggregated offer for scheduling ai,j
dli (i )
Project delay time given a schedule i
Ek
Set of edged in resource flow network Gk
Set of aggregated offers for scheduling ai,j
fvi,j
k v k
0
i ,j 0
Resource quantity of Rk passing on from activity ai,j to activity ai0 ,j 0
Gk
Resource flow network of resource type Rk
dlimg (i,j
)
i
mg
i,j
UPAi (i )
mg
URA
(ki,j )
k
oki,j,l
k
Oi,j
Marginal delay caused by the scheduling of activity ai,j

Marginal project-agent utility of PAi given a partial schedule i,j
i
Marginal resource-agent utility of RAk given a partial schedule ki,j
lth offer sent by RAk for scheduling ai,j
Set of offers sent by RAk for scheduling ai,j
PAi
Project agent representing project Pi
Project-agent schedule of project Pi
Complete set of all project-agent schedules
UPAi (i )
Project-agent utility given project-agent schedule i and project unit

delay cost cdl
i
R
Pr (i,j,k,l
)
R
Price of given resource-agent slot i,j,k,l
P
i,j,k
Project-agent slot
RAk
Resource agent representing resource type Rk
Resource-agent schedule of resource type Rk
R
c(i,j,k
)
R
R
Capacity of resource-agent slot i,j,k
Complete set of all resource-agent schedules
URAk ( )
Resource-agent utility given resource-agent schedule k and resource

unit utilisation cost cuk
P
rc(i,j,k
)
P
Resource cost of project-agent slot i,j,k
(k , t)
Resource load of Rk at time t given a resource-agent schedule k
RfQ ki,j
R
i,j,k
s
Ii,j
Request for quotations
TC (
oi,j,l )
Total cost of aggregated offer oi,j,l
tslk
i,j
slk
ti
Length of slack time window inserted after activity schedule i,j
Resource-agent slot
Secure time window of ai,j
Vector of ni lengths of slack time windows inserted after activities of

project Pi
uk (k , t)
Amount of Rk scheduled to be used at time t
k
vi,j
Vertex representing activity ai,j in resource flow network Gk
Vk
Set of vertices in resource flow network Gk
xvi
vtk
vsk
i,j
i,j
Glossary
Sink vertex of resource flow network Gk
Source vertex of resource flow network Gk
Object variable in (1,1)-ES for activity ai,j
Strategy variable in (1,1)-ES for activity ai,j
Vector of object variables
Vector of strategy variables
List of Figures
1.1
An example of Boeing 747 turnaround schedule in Gantt chart . . . . . .
2.1
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AoN representation of a project . . . . . . . . . . . . . . . . . . . . . . .

Allen (1983)s interval algebra for possible temporal relations . . . . . .
Possible temporal relations between a time point t and a time interval I
max
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dmax
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Generalised precedence relations by min/max time lags . . . . . . . . .
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An example of super AoN network for RCMPSP . . . . . . . . . . . . . .
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Agent encapsulation approaches . . . . . . . . . . . . . . . . . . . . . . . .

R
A resource-agent slot i,j,k
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An example of a resource-agent schedule with six slots . . . . . . . . . . .
An activity schedule i,j . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Lease-based slot negotiation, step 1 Sending RfQs . . . . . . . . . . . .
Lease-based slot negotiation, step 2 Receiving slot offers . . . . . . . .
Lease-based slot negotiation, step 3 Aggregating and evaluating slot offers
Lease-based slot negotiation, step 4 Sending leases requests . . . . . .
Lease-based slot negotiation, step 5 Making leases . . . . . . . . . . . .
AoN network of an example project P1 . . . . . . . . . . . . . . . . . . . .
Schedule of ai,j on the timeline of PA1 . . . . . . . . . . . . . . . . . . . .
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AoN network of an example project P1 . . . . . . . . . . . . . . . . . . .

Project-agent schedule 1 made by the COSGS . . . . . . . . . . . . .
s
of a1,1 in iteration 1 . . . . . . . . . . . . .
The secure time window I1,1
s
of a1,2 in iteration 1 . . . . . . . . . . . . .
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of a1,3 in iteration 1 . . . . . . . . . . . . .
Improves project-agent schedule 1 using the ISIM . . . . . . . . . . . .
Schedule improvement of a1,2 when R2 profile changes . . . . . . . . . .
Project-agent schedule 1 in iteration 2 . . . . . . . . . . . . . . . . . .
Schedule improvement by ISIM for the 10 projects in I90/10/1 . . . . .
Trade-offs between project-agent objective and resource-agent objective
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The AoN networks of two projects (left) and the project schedules (right)
92
xviii
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
6.10
6.11
6.12
6.13
6.14
6.15
6.16
List of Figures
A resource flow network of R1 and the corresponding resource profile . . .

An alternative resource flow network of R1 and the resource profile . . . .
The AoN network of a project P1 with a disrupted activity a1,1 . . . . . .
Schedule 1 without slack time . . . . . . . . . . . . . . . . . . . . . . . .
Schedule 01 with a slack time . . . . . . . . . . . . . . . . . . . . . . . . .
Two options of obtaining resources for ai,j in a resource flow network . .
Two options of obtaining resources for ai,j in a resource-profile diagram .
The resource flow network and the resource profile diagram of RAk . . . .
Two options of allocating resources for ai,j in resource flow networks . . .
Two options of allocating resources for ai,j in resource-profile diagrams . .
Two options of allocating resources for ai,j in resource flow networks . . .
Two options of allocating resources for ai,j in resource-profile diagrams . .
Probability density function of a beta ( = 2, = 5) distribution . . . . .
1000 samples of actual activity processing duration pi,j (pi,j = 10) . . . .
(1,1)-ES learning curves of the 10 projects in I90/10/1 with a particular
instance of incidents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6.17 (1,1)-ES learning curves of the 10 projects in I90/10/1 with random instances of incidents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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List of Tables
3.1
3.2
Priority-rule-based heuristics . . . . . . . . . . . . . . . . . . . . . . . . .
MAS-based solution methods for DRCMPSP . . . . . . . . . . . . . . . .
33
39
4.1
4.2
4.3
4.4
4.5
k
A list of slot offers Oi,j
for scheduling ai,j from RAk
Evaluating the aggregated offers for scheduling ai,j .
List of slot offers sent by RA1 . . . . . . . . . . . . .
List of slot offers sent by RA2 . . . . . . . . . . . . .
Aggregated offers for scheduling a1,1 . . . . . . . . .
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5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
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5.10
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Offers sent by RA1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Aggregated offer for scheduling a1,1 . . . . . . . . . . . . . . . . . . . . . .
Offers sent by RA2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Aggregated offers for scheduling a1,2 . . . . . . . . . . . . . . . . . . . . .
Offers sent by RA3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Aggregated offers for scheduling a1,3 . . . . . . . . . . . . . . . . . . . . .
Slot offers sent by RA1 in the first iteration of the ISIM . . . . . . . . . .
Aggregated offers for scheduling a1,1 in the first iteration of the ISIM . . .
Slot offers by RA2 in the first iteration of the ISIM . . . . . . . . . . . . .
Aggregated offers for scheduling a1,2 in the first iteration of the ISIM . . .
Old offers sent by RA2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
New offers sent by RA2 . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ISIM - Resource offers update . . . . . . . . . . . . . . . . . . . . . . . . .
Simulated AGH Scheduling Problems . . . . . . . . . . . . . . . . . . . . .
Average improvement ratios by ISIM on the 80 MPSPLib problem instances
Average improvement ratios by ISIM on the simulated AGH instances . .
Project-by-project improvement ratios by ISIM on 10 I90/10 instances . .
Minimal, maximal, and average numbers of iterations to achieve a stable
schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.19 Comparison of four methods on average project delay (APD) . . . . . . .
5.20 Comparison of four methods on total squared resource utilisation (TSRU)
5.21 Comparison of APD and TSRU on simulated AGH instances . . . . . . .
6.1
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Comparison of three heuristics on total project stability over 100 simulations106
xx
LIST OF TABLES
B.1 Properties of the chosen 80 problem instances from MPSPLib . . . . . . . 131
Chapter 1
Introduction
In the past decades, globalisation and economic growth have resulted in a worldwide continuous boost of air-traffic demands. Nowadays, the rising flight demands are exceeding
the capacities of most existing airports1 . However, the existing airports cannot expand as
much as required, because of two significant constraints: spatial limitations and environmental protection regulations (cf. Graham and Guyer, 1999; Gualandi et al., 2006). Given
the constraints, one of the solutions to handle the growing number of flights would be
the construction of new major airports and medium-sized airports (EuroControl, 2008).
Next to the long-term plan of constructing new airports, making airport operations more
efficient also plays an important part to increase current airports throughputs. Among
all airport operations, we are interested in the ground-handling operations that are carried
out during aircraft turnaround processes. Other areas of interest that may increase airport
throughputs by supporting reliable turnarounds are the domain of aircraft taxi planning
(see ter Mors, 2010) and collaborative operations in improving maintenance contracts (see
de Jong, 2010).
An aircraft turnaround process often involves a multitude of organisations working
simultaneously on diverse operations. The simultaneous operations are carried out in an
environment with a high degree of uncertainty. This makes an aircraft turnaround process
time critical. A minor delay in a single operation with respect to one aircraft can create
many changes in related work schedules of other operations or even in the schedules of
other aircraft. So, a minor delay may lead to a substantial waste of resources. If the
occurrence is not anticipated, it may even lead to a large delay of the entire airport.
In addition to the time criticality, the exchange of relevant information is also critical.
Different parties involved in a turnaround process have different and often conflicting
interests, there will be a limit (possibly legally enforced) to what extent the parties are
willing to accommodate their schedules and those of others. A question of a different
nature is how much information the parties are willing to exchange.
1 The
research for this thesis started in 2005. The economic crisis of 2007-2009 has affected some of
our statements in this introductory chapter. In contrast, the commotion with the volcanic ash cloud
in April-May 2010 has emphasised the importance of intelligent scheduling and adequate control at
airports. All in all, we believe that the economic crisis is temporary. Therefore, we have decided to
maintain the original statements, although they should sometimes be read as ideas in the long run.
Introduction
Scheduling of all aircraft turnaround processes at an airport is a complex task. The

inherent problem complexity and environmental uncertainty highlight the challenge of
designing a system that can make efficient and robust schedules. In this thesis, we
investigate approaches within a multiagent-system solution framework for designing such
a scheduling system.
This introductory chapter starts by providing some background knowledge on the
problem domain of our research the airport ground handling (see Section 1.1). Subsequently, in Section 1.2, the problem statement and three research questions are formulated. This is followed, in Section 1.3, by a description of the research methodology that
will be applied to address the research questions and the problem statement. Finally, the
structure of the thesis is presented in Section 1.4.
1.1
Airport Ground Handling
Delay is an experience shared by almost anyone who ever travelled. Arguably, it is an

inevitable feature of any system in the real and often unpredictable world. However,
identifying the causes of delays can help the system managers in developing strategies to
cope with the disruptions to their plans, and thus improve the system performance.
The Central Office of Delay Analysis2 (CODA) within the European Organisation for the Safety of Air Navigation (EuroControl) is responsible for
collecting and analysing information with regard to air-traffic delays in Europe. A recent
study of CODA revealed that amongst all causes of aircraft departure delays, airlinerelated delays are the primary cause; and during 2009, airline-related delays accounted
for around 49% of all aircraft departure delays (EuroControl, 2010). Amongst all sources
of airline-related delays occurring at airports, ground handling plays a significant role
worth to be investigated in more depth (cf. van Leeuwen and Witteveen, 2009). Below,
we define airport ground handling.
Definition 1.1 Airport Ground Handling (AGH). Airport ground handling refers
to the management of all aircraft turnaround processes at an airport.
The turnaround process of an aircraft starts when the aircraft lands at an airport
and ends when the aircraft takes off for the next flight. During this period of time,
which is known as turnaround time, a series of ground-handling operations are required
for serving the aircraft. Examples of the operations are (re)fuelling, cleaning, catering,
passengers handling, and baggage handling. A comprehensive list of aircraft groundhandling operations can be found in Appendix A: Airport Ground-handling Operations.
Figure 1.1 is extracted from the Airport Handling Manual (IATA, 2009) published
by International Air Transport Association (IATA). It shows an example of the
turnaround schedule of a Boeing 747 aircraft in Gantt chart (cf. Gantt, 1974). As we see
from this chart, such a turnaround process involves diverse ground-handling operations.
Trying to carry out the ground-handling operations simultaneously would reduce
turnaround time. This is preferable for three groups: (i) airline companies, (ii) airport
authority, and (iii) air passengers. For airline companies, reducing turnaround time will
2 In
the thesis, we indicate organisation names with small capitals.
1.1. Airport Ground Handling

Minutes (e.g., B747)
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Positioning Pass. Steps/Jet Bridges

Disembarking
Cleaning
Boarding
Removal Pass. Steps/Jet Bridges
Forward: Positioning Highloader
Forward: Door opening/Closing
Forward: Loading
Rear: Positioning High Loader
Rear: Door Opening/Closing
Rear: Loading
Lower Deck: Loading/Unloading
Positioning Fuel truck
Refuelling
Positioning Catering Trucks
Catering
Start Engines/Pushback
Main Deck: Positioning High Loader
Main Deck: Door Opening/Closing
Main Deck: Loading
Figure 1.1: An example of Boeing 747 turnaround schedule in Gantt chart

subsequently increase the total flying time of the aircraft and provide the airline companies the opportunity of handling more flights a day, thereby increasing their revenues.
Short turnaround time is also advantageous to airport authority, as the use of terminal
gates is maximised if turnaround time is kept as short as possible. For air passengers who
enjoy punctual aircraft departure and arrival, the efficiency of aircraft turnarounds is the
basis of on-time arrival and smooth transit.
However, not all ground-handling operations can be carried out simultaneously. Some
of them have to be recorded in a workflow (a sequence of operations) with precedence
constraints between one another. A short aircraft turnaround is determined by an efficient
planning and scheduling of the ground-handling operations.
Nowadays, planning and scheduling of ground-handling operations in a turnaround
process can not be done by one organisation. It is generally not the case that airline
companies themselves perform the ground-handling operations for their own aircraft, in
particular not when an aircraft is turning around at a remote airport (e.g., an aircraft of
Emirates Airline turning around at Amsterdam Schiphol Airport). Many airlines prefer
to outsource their remote ground-handling operations either to their alliance partners or
to authorised third-party ground-handling parties. In other words, the ground-handling
operations are carried out as services provided to the airlines.
In 1996, the European Union Council issued a council directive European Union
Ground Handling Council Directive (EU Council, 1996), henceforth the 1996 EU Directive. The objective of the 1996 EU Directive is to encourage the competitive provision
of ground-handling services at European airports, in order to (i) reduce airline costs, (ii)
improve quality of service, and (iii) provide airlines with the possibility to choose their
ground-handling service providers.
The opening up of the AGH market led to a significant increase in the number of
Introduction
third-party ground-handling service providers at the European airports. Furthermore, it

led to free competition on the European AGH market, which lowered the ground-handling
prices to the benefit of the airline companies (Airport Research Center, 2009). However,
the 1996 EU Directive also led to an ever higher level of complexity and sophistication of
AGH management, in particular in relation to the following two aspects.
1. Coordinated decision making across multiple organisations.
The liberalisation of the AGH market has resulted in a multitude of organisations
involved in a single aircraft turnaround process. Preferably, the ground-handling
operations are performed simultaneously to decrease turnaround time. This high
degree of simultaneous execution of ground-handling operations requires a high interoperability amongst ground-service providers. The efficiency of such operations
relies on (i) the capacity of the staff and technology-advanced equipments of each
ground-service provider, and (ii) the coordination amongst the different subcontractors with their own interests and different information support systems. Coordination amongst the different organisations in AGH is in practice carried out
by human operators, often connected via (radio) telephones. With the growth
of air-transportation volume and the number of organisations, human operators
can quickly become overwhelmed by the increased communication and coordination
load. The increased need for coordination is a result of the dependencies amongst
the plans of the individual organisations, each of which has to adapt its own plans
to the joint plan. The limited capacities in inter-human communication and coordination mean that opportunities are missed, and operations slow down, as crucial
information does not reach the right actor or planning system or emerges in time.
2. Dealing with environmental uncertainty.
The environment of AGH operations is well-known for its large number of disturbances. For instance, the actual arrival time of an aircraft is often different from
the one foreseen in the original flight timetable. Uncertainties about the departure
time from the departure airport and the duration of a flight result in the uncertainty of the aircrafts arrival time. Moreover, there are uncertainties during the
execution of ground-handling operations due to unforeseeable events such as noshow of passengers, breakdown of machinery, and bad weather conditions. As a
result, ground-handling operations may take longer time than expected, invalidating the baseline schedule, i.e., a schedule that optimally assigns time and resources
to operations under normal conditions. Nowadays, most airports are operating over
their normal capacities. This makes the already tightly coupled inter-organisational
schedules much tighter. A disturbance by a minor incident may cause a slight
change in one aircrafts schedule. However, this slight change may cause a chain of
schedule repairs in other aircrafts turnaround schedules, involving a large number
of other organisations. Failing to meet the schedule requirements may induce additional costs, which may include resource resetup cost, inventory cost, and various
organisational costs.
In summary, the coordinated management of inter-dependent plans and schedules
amongst different organisations under uncertainty is an important and complex prob-
1.2. Problem Statement and Research Questions
lem. We have chosen to investigate this problem in our research. The general problem
statement and research questions are formulated in the following section.
1.2
Problem Statement and Research Questions
As described in Section 1.1, scheduling AGH operations involves the coordination of

multiple organisations. A global AGH schedule contains all pieces of individual schedules
of different organisations. These schedules should respect the individual interests of those
organizations.
So far, the scheduling research literature in both operations research (OR) and artificial intelligence (AI) deals mostly with centralised scheduling problems (cf. Nuijten, 1994;
Brucker, 2003; Blazewicz et al., 2007). They assume a central authority in the scheduling
system with top-down approaches. However, when designing an AGH scheduling system,
one has to take into consideration that the information environment and the managerial
decision making are distributed over multiple self-interested organisations.
The conventional centralised scheduling approaches are no longer applicable. The
modern way is to distribute the solution process across multiple organisations, following
a distributed artificial intelligence (DAI) approach (Russell and Norvig, 2003). In particular, multiagent systems (MASs), built on the basis of DAI principles, offer a way to
understand, manage, and use distributed, large-scale, dynamic, open, and heterogeneous
computing and information systems involved in decentralised AGH scheduling.
Some attempts in MAS scheduling have been investigated (see Wellman et al., 2001;
Confessore et al., 2007; Homberger, 2007; Wauters et al., 2010). However, these attempts
all assume a static and deterministic scheduling environment. The decentralised, dynamic,
and nondeterministic scheduling environment in AGH leads us to the following problem
statement (PS).
PS: Can a number of self-interested agents, by coordinating their local scheduling decisions, achieve a global AGH schedule that is both efficient and
robust?
From the problem statement above we may derive three specific research questions
(RQs). First of all, employing a multiagent system as our solution framework calls for an
agent-based model of the AGH scheduling problem. Thus, we formulate our first research
question as follows.
RQ1: How can an AGH scheduling problem be represented in an agent-based
model?
In general, an agent-based model is composed of (1) a collection of autonomous agents,
and (2) inter-agent interactions that lead to emergent properties. Therefore, in order to
answer RQ1, two steps have to be taken. First, the roles, characteristics and goals of
individual agents have to be specified. Second, the language, protocol, and decision
process for inter-agent interactions have to be designed.
The primary objective of coordinating individual agents decisions through agent interactions is to achieve a global conflict-free and feasible schedule3 . A global schedule
3 Definitions
of a global conflict-free schedule and a global feasible schedule can be found in 4.1.3.
Introduction
that is both conflict free and feasible might neither be efficient in terms of social welfare,
nor be robust under uncertainty. In the context of AGH scheduling, uncertainty may
encompass many different aspects. In this thesis, we will investigate two classes of uncertainty. They are (i) partial observability and (ii) nondeterminism (see detailed analyses
in 2.2.3). The two different classes of uncertainty lead us to the second and the third
research questions.
RQ2: How can agents make and coordinate their local decisions in order to
achieve a globally efficient and robust schedule in a partially observable
environment?
achieve a globally efficient and robust schedule in a nondeterministic
environment?
In the subsequent chapters, we answer the three research questions mentioned above.
The answers to the three research questions will allow us to formulate an answer to the
problem statement. Below we provide our overall research methodology. The subsequent
chapters will describe our approaches in detail.
1.3
Research Methodology
In order to answer the three research questions stated above, we employ an empirical
research methodology in which we perform the following five main steps: (1) problem
generalisation and formulation, (2) literature review, (3) agent-based model design, (4)
MAS solutions development, and (5) empirical validation.
1.3.1
Problem Generalisation and Formulation
The thesis aims to design and develop a decentralised scheduling solution framework that
not only solves the scheduling problem in AGH, but also covers a wider range of real-world
scheduling applications. So, in the first main step, we try (i) to identify the characteristics
of the AGH scheduling problem, (ii) to analyse the characteristics of this domain-specific
scheduling problem and place the problem in a much broader perspective, and (iii) to
reformulate the AGH scheduling problem from a more generic scheduling perspective.
1.3.2
Literature Review
With a generic problem formulation at our disposal, we may conduct a literature review
by studying scholarly articles, books, and other sources (e.g., dissertations, industrial
reports). We are interested in various techniques and approaches that attempt to solve
the generalised scheduling problem. For this purpose we make a description, summary,
and critical evaluation of each of a selected number of proposed solution methods in both
OR and AI literature. Our goal is to offer an overview of significant contributions from the
literature (also articles published on related topics are included) and provide convincing
reasons for developing MAS solution methods.
1.4. Structure of the Thesis
1.3.3
Agent-based Model Design
We model the generic scheduling problem in a heterogenous MAS solution framework

and design a market-based mechanism in which agents are categorised as either consumer
agents or producer agents. All consumer agents have a need of goods produced by the
producer agents, and trade or bid for goods at various prices. All agents exchange goods
so as to maximise either their profits or their utility. Local decision making amongst
agents is coordinated to generate a globally feasible and conflict-free schedule.
1.3.4
MAS Solutions Development
MAS scheduling under uncertainty requires individual agents to make strategic decisions
that take into account the dynamics in the environment. In a heterogenous MAS, different types of agents require different approaches to deal with uncertainty. In addition, we
consider two classes of uncertainty partial observability and nondeterminism. These
two uncertainty classes require different scheduling schemes. Accordingly, we design various scheduling schemes and approaches for different types of agents in supporting the
efficiency and robustness of the agent decision-making process.
1.3.5
Empirical Evaluation
The last step of our methodology consists of performing a series of experiments. These
experiments provide the empirical results that can be used to evaluate the performance of
our proposed MAS solution methods within various settings. In general, we conduct two
main categories of experiments: (i) scheduling experiments under partial observability
and (ii) scheduling experiments under nondeterminism. In each of these two categories,
we implement the proposed market-based mechanism in a MAS. The obtained experimental results are used for evaluating the system performance of our solution methods
with respect to the conventional OR solution methods (e.g., priority-rule-based heuristic
approaches) and centralised AI search methods.
1.4
Structure of the Thesis
The structure of the thesis is as follows.

Chapter 1: Introduction. The chapter introduces the application domain of our research airport ground handling. A problem statement is formulated and
three research questions are derived from the problem statement. In addition, a five-step research methodology is presented.
Chapter 2: AGH Scheduling Problem. In this chapter we identify the characteristics of an AGH scheduling problem and reformulate the problem into a more
generic problem definition, viz. that of a project scheduling problem. A formal description of the project scheduling problem is presented and a range of
extensions and variations are discussed. We reformulate the AGH scheduling problem as a decentralised resource-constrained multi-project scheduling
problem under uncertainty.
Introduction
Chapter 3: A Review of Existing Solution Methods. The chapter reviews the existing solution methods in the literature of project scheduling problems in
both OR and AI research. We focus on presenting the state-of-the-art solution methods in solving (1) multi-project scheduling problems, (2) decentralised scheduling problems, and (3) project scheduling under uncertainty. We discuss the limitations of the reviewed solution methods and
their (in)applicabilities for solving the AGH scheduling problem. The discussion leads us to a new agent-based model.
Chapter 4: A Lease-based Multiagent Model. In this chapter, we propose a novel
agent-based model for the AGH scheduling problem. The model adopts
a coarse-grained physical-entity-oriented modelling approach. It consists
of the roles, schedules, and utilities of two classes of agents. We design a
market-based coordination mechanism in which the scheduling decisions of
the individual agents are coordinated in a lease-based negotiation scenario.
The chapter addresses our first research question RQ1.
Chapter 5: Online Iterative Scheduling. The chapter focuses on the first class of
AGH scheduling uncertainty partial observability. We propose an online
iterative scheduling approach in the multiagent setting. This approach is
composed of (1) a clairvoyant online schedule-generation scheme and (2) an
iterative schedule improvement method. By employing this approach, we
aim at achieving a globally efficient and robust schedule. Experiments are
conducted and empirical analyses are provided to answer RQ2.
Chapter 6: Stable Proactive Scheduling. In this chapter, we focus on dealing with
the nondeterministic aspect of AGH scheduling problems. We investigate
proactive scheduling procedures for constructing stable baseline schedules.
In the proactive procedure, two classes of agents employ different approaches
(heuristics and evolutionary learning approaches) to construct stable baseline schedules. The constructed schedules should be robust, i.e., being able
to tolerate and absorb minor disruptions that may occur during the project
execution. A scheduling environment is simulated where the processing
times of activities are nondeterministic. The environment is used for evaluating the proposed approaches in dealing with nondeterminism. RQ3 is
answered by empirical results.
Chapter 7: Conclusions. The chapter concludes the thesis by summarising the answers to the individual research questions and relating them. Moreover, it
gives an answer to the problem statement. We also provide a short discussion on potential future research lines.
Chapter 2
AGH Scheduling Problem

The turnaround process of an aircraft consists of a series of ground-handling operations
carried out under both temporal and resource constraints. The process can be seen as an
instance of a project defined in the field of project management (Dorndorf, 2002). Project
is a broad concept that for different people can refer to many different things. We adopt
the concept of project used in the context of AGH as follows.
Definition 2.1 Project. A project is a unique process, consisting of a set of coordinated
intermediate activities (or tasks), each of which requires time and resources for its completion. The process is undertaken to achieve one or multiple objectives, while conforming
to specific temporal and resource constraints.
From the project definition above, we may derive the following definition of project management.
Definition 2.2 Project Management. Project management is a set of principles,
methods, and technologies applied for the purpose of accomplishing a project (i) on-time,
(ii) under budget, and (iii) up to specification.
Managing a project during its life cycle often involves three phases, namely the phases of
planning, scheduling, and control (cf. Lewis, 2005; Kerzner, 2006).
Planning involves defining the project scope (e.g., stakeholders, objectives, and
deadline), identifying a work breakdown structure (i.e., a list of intermediate activities and their interdependencies), and estimating the processing duration as well
as the resource requirement for each of the intermediate activities.
Scheduling concerns specifying the start times (or the finish times) of all the
intermediate activities and allocating the given resources to the activities during
their specified time windows.
Control focuses on the difference between the schedule and actual execution once
the project has started. During the control phase, project execution is monitored so
10

that potential problems can be identified in a timely manner and corrective actions
can be taken, when necessary.
Our main focus on managing an aircraft turnaround process is the creation of an

adequate schedule that establishes start and finish times of the individual operations
as well as resource assignment that leads to a successful accomplishment of turnaround
process. Therefore, we are interested in the problems that arise in the scheduling phase
of the project management and we focus on the development of novel techniques for
generating an efficient and robust schedule.
In this chapter, we identify the characteristics of an AGH scheduling problem and
reformulate the problem within a project-scheduling framework. In Section 2.1, we introduce the classic resource-constrained project scheduling problem (RCPSP) and describe
the fundamental concepts within RCPSP. Section 2.2 identifies and discusses the characteristics of the AGH scheduling problem, and formulates the problem as a generalised
RCPSP a decentralised resource-constrained multi-project scheduling problem under
uncertainty (DRCMPSP/u). Finally, the chapter is summarised in Section 2.3.
2.1
Resource-constrained Project Scheduling Problem
During the last decades, the resource-constrained project scheduling problem has attracted an ever-growing attention and has become a standard problem for project scheduling in the literature (see Neumann and Zimmermann, 1999; Demeulemeester and Herroelen, 2002). Let us introduce the problem by providing a descriptive definition.
Definition 2.3 Resource-constrained Project Scheduling Problem (RCPSP).
An RCPSP involves the construction of a project schedule that specifies for each activity
the start (or finish) time in such a way that the prescribed precedence constraints and
resource constraints are satisfied and the objective function(s) is/are optimised.
In the remainder of the section, we introduce the basic concepts in RCPSP. These
include activity and activity network in 2.1.1, precedence relations and constraints in
2.1.2, resources and resource constraints in 2.1.3, and schedules and performance measures in 2.1.4.
2.1.1
Activity and Activity Network
Activities are the essential components of a project. Finishing all activities brings about
the completion of the entire project. We assume that a project consists of a set A of n
N real activities: A = {a1 , . . . , an }, where activity ai (ai A) is to be carried out
without interruption1 . Two fictitious activities (a dummy start activity a0 and a dummy
completion activity an+1 ) are added to represent project start and project completion,
respectively. Let A+ denote the set of all activities including the fictitious activities, thus
A+ = A {a0 , an+1 }. Each activity ai has an estimated processing time (or duration) pi
1 We
assume non-preemptive activity execution, meaning that once the activity has started, it cannot be
interrupted and resumed again. Preemptive activities are not the subject of this thesis.
11
2.1. Resource-constrained Project Scheduling Problem
and normally requires resources (except for the dummy activities that consume neither)
for execution.
Activities are usually coupled by given dependencies between each other. It is the
representation of the dependencies that distinguishes an activity network from other
ways of representing a project, such as Gantt chart, track planning, and line of balance
(Demeulemeester and Herroelen, 2002). There are two possible modes of representing
a project using an activity network the activity-on-arc (AoA) representation and the
activity-on-node (AoN) representation. The latter is more often used since it can represent
generalised precedence relations (Neumann et al., 2001). More details on generalised
activity-to-activity precedence relations are discussed in 2.1.2.
4
1
10
11
5
2
Legend
activity
ai
precedence relation
Figure 2.1: AoN representation of a project

The AoN network is a project-network technique often used in project management (cf.
Lockyer and Gordon, 2005). In an AoN network, a project is depicted as an acyclic graph,
consisting of a set of nodes representing activities, and a set of directed arcs representing
precedence relations between a pair of activities. The best known precedence relation is
simple finish-start precedence relation, which tells that for an activity pair (ai , aj ), the
successor activity aj can only start (and immediately start) when the predecessor activity
ai has finished. The simple finish-start precedence relation is denoted by ai aj .
Figure 2.1 shows an example of an AoN network representing a project consisting
of 10 real activities. The arcs in Figure 2.1 represent the simple finish-start precedence
relations. In an AoN network, nodes are numerically labelled such that the successor
nodes always have higher numbers (labels) than all their predecessors.
Below, we define the set of immediate predecessors and the set of immediate successors
of activity ai . These two sets of activities are denoted by A i and A i , respectively.
A i = {aj A+ | aj ai }
A i = {aj A+ | ai aj }
In addition, A i and A i denote the set of transitive predecessors and the set of transitive
12
successors of activity ai , respectively.
Ai = Ai Aj,
Ai = Ai Aj,
aj A+ , aj ai
aj A+ , ai aj
For instance, in the example project of Figure 2.1, A 5 = {a1 , a3 }, A 5 = {a7 , a8 }, A 5 =
{a0 , a1 , a2 , a3 }, and A 5 = {a7 , a8 , a9 , a10 , a11 }.
2.1.2
Temporal Relations and Constraints
In this subsection, we deal with the temporal aspects of project scheduling. We start
by (a) introducing some basic temporal concepts used in RCPSP. These includes time
points, time intervals, and possible temporal relations among them. Then, we (b) discuss
how to represent generalised precedence relations between a pair of activities in RCPSP.
Finally, we (c) discuss several additional temporal constraints.
A: Time Points and Time Intervals
Names
Symbols
Ij
1.
Ii before Ij
<
2.
Ii meets Ij
3.
Ii overlaps Ij
4.
Ii finished-by Ij
fi
Ii contains Ij
di
Ii
6.
Ii starts Ij
Ii
7.
Ii equals Ij
Ii started-by Ij
si
Ii during Ij
5.
8.
9.
10. Ii finishes
Ij
11. Ii overlapped-by Ij
12. Ii met by
13. Ii after Ij
Ij
f
oi
mi
>
Ii
Ii
Ii
Ii
Ii
Ii
Ii
Ii
Ii
Ii
Ii
Figure 2.2: Allen (1983)s interval algebra for possible temporal relations
An important distinction in temporal concepts is that between time points and time
intervals (cf. Vila, 1994). The distinction coincides with the distinction between events
and activities in project-scheduling terms. In project scheduling, an event occurs at a
point of time, and an activity is occurring over a time interval. Let t denote a time point
13
and I = [ts , te ) denote a time interval that starts at time point ts (inclusive) and ends at
time point te (non-inclusive).
According to Allen (1983)s interval temporal logic, there are thirteen possible temporal relations between a pair of time intervals. These relations are shown in Figure 2.2.
By swapping the positions of such a time-interval pair, the number of interval-to-interval
relations is reduced to seven (see Dorndorf, 2002).
Different from Allen who treated a time point as an indivisible time interval, thus
eliminating the need for time points, we opt to maintain the concept of time point in
order to address some of the temporal constraints in RCPSP. Since a time interval I
is defined by two time points: ts and te , the possible temporal relations between a time
point t and a time interval I = [ts , te ) (i.e., point-to-interval relations) comprise five cases,
which is illustrated in Figure 2.3.
Names
1.
Formula
t before I
t < ts
I
t
2.
t = ts
t starts I
I
t
3.
t during I
ts < t < t e
I
t
4.
t met-by I
t = te
5.
t after I
te < t
I
t
I
t
Figure 2.3: Possible temporal relations between a time point t and a time interval I
In addition, we say t is included by I (denoted by t I), when ts t < te .
B: Generalised Precedence Relations
In RCPSP, processing an activity requires a time interval. Accordingly, the number of
possible temporal relations between a pair of activities (ai , aj ) is also thirteen. When activity processing times are known and deterministic, we can formulate any of the thirteen
temporal relations by using a start-start relation with minimum and maximum time lags.
aj
ai
pi
si
pj
sj
max
min
Figure 2.4: Minimum (dmin
dmax
ij ) and maximum (dij ) time lag: dij
ij
Let si denote the start time of activity ai . A given minimum time lag dmin
N
ij
between the start of two different activities ai and aj says that
dmin
sj si .
ij
(2.1)
14
That is, activity aj cannot start earlier than dmin

time units after the start of activity ai
ij
(see Figure 2.4).
If activity aj can start as soon as activity ai has finished, i.e., dmin
= pi , inequality
ij
2.1 then represents a simple finish-start precedence constraint as depicted in Figure 2.1.
Moreover, a given maximum time lag dmax
N between the start of two different
ij
activities ai and aj says that
(2.2)
sj si dmax
ij .
That is, activity aj cannot start later than dmax

time units after the start of activity ai .
ij
(see Figure 2.4).
We note that other possible relations, such as start-finish, finish-start, and finishfinish can be trivially transformed into start-start relations when activity processing times
are known and deterministic (cf. Dorndorf, 2002). Therefore, a start-start relation with
minimum and maximum time lags can represent a generalised precedence relation between
two different activities (cf. Elmaghraby and Kamburowski, 1992).
Taking relation 2 (i.e., ai meets aj ) in Figure 2.2 as an example, this relation can be
enforced by imposing two constraints pi sj si and sj si pi . Thus, ai meets aj
can be represented by start-start relation, where dmin
= dmax
= pi .
ij
ij
dmin
ij
-dmax
ij
Figure 2.5: Generalised precedence relations by min/max time lags

In an AoN network, one can use bi-directional arrows with minimum and maximum
time lags to represent generalised precedence relations, where positive arc weights represent minimum time lags and negative arc weights represent maximum ones (see Figure 2.5). In the thesis, we choose to investigate a simplified precedence relation simple
finish-start precedence relation, and will use one arrow to represent the relation (as shown
in Figure 2.1).
C: Additional Temporal Constraints
Apart from activity-to-activity precedence constraints, scheduling a project often has to
take into account various additional temporal constraints. In the following, we discuss
three of them, in which we face two hard constraints: (i) the project-release-time constraint, and (ii) the project-deadline constraint; and one soft constraint: (iii) the projectdue-time constraint. The hard constraints sometimes are also referred to as strict
constraints. Violating any of these constraints will cause a project failure. In contrast,
soft constraints such as the project-due-time constraint can be violated, although it is not
a favourable event. Therefore, violating soft constraints often comes with some sort of
punishment. Below we discuss all three types of constraints.
15
i) project-release-time constraint
Project release time is also known as project arrival time or project ready time. It defines
the moment from which the project can be started. Let rl denote the project release
time. A project-release-time constraint prescribes that no activity of the project can
start earlier than rl. Since s0 stands for the start time of the project and all activities
start no earlier than s0 , we may state that
rl s0 .
(2.3)
ef
Let tes
i be the earliest possible start time and ti be the earliest possible finish time of
ef
+
es
activity ai (ai A ), respectively (ti = ti + pi ). Therefore, the earliest possible start
time tes
0 of the dummy start activity a0 corresponds to the project release time (i.e., rl).
During the initialisation step, the earliest possible start times and the earliest possible
finish times of all remaining activities can be computed by using the following Forward
Pass Recursion (FPR) algorithm (see Algorithm 2.1). We recall that A i denotes the set
of immediate predecessors of activity ai (ai A+ ).
Algorithm 2.1 Forward Pass Recursion (FPR)

1:
2:
3:
4:
5:
ef
Initialisation: tes
0 := rl, t0 := rl
for j := 1 to n + 1 do
ef
tes
j := max{ti |ai A j }
es
tef
j := tj + pj
end for
The FPR algorithm results in the earliest possible start time tes
n+1 and the earliest
ef
es
possible finish time tef
of
the
dummy
completion
activity
a
.
t
n+1
n+1 is identical to tn+1
n+1
since pn+1 is equal to 0. Once tef
n+1 is known, the shortest project duration or the length
of the project critical path (denoted by ) can be obtained:
ef
es
= tef
n+1 t0 = tn+1 rl.
ef
We note that tes
i and ti are variables during the course of scheduling process. Their
values are updated whenever the schedule of a (transitive) predecessor of ai is decided or
changed.
ii) project-deadline constraint

When a project is given a strict deadline dl, there is an upper bound on the latest possible
project completion time. We note that the project deadline should be greater than the
end time of the project critical path: dl rl + , otherwise no feasible schedule exists. A
project-deadline constraint can be formulated as follows:
sn+1 dl.
(2.4)
16
A Backward Pass Recursion (BPR) algorithm yields the latest possible start and finish
times of all project activities (see Algorithm 2.2). For activity ai , the latest possible start
lf
ls
time is denoted by tls
, and the latest possible finish time is denoted by tlf
i (ti = ti + pi ).
i
+
We recall that A i denotes the set of immediate successors of activity ai (ai A ).
Algorithm 2.2 Backward Pass Recursion (BPR)
ls
Initialisation: tlf
n+1 := dl, tn+1 := dl
for j := n to 0 do
ls
3:
tlf
j := min{ti |ai A j }
lf
4:
tls
j := tj pj
5: end for
1:
2:
ef
lf
ls
Similar to tes
i and ti , ti and ti are also variables that are updated in the course of
lf
the scheduling process, the value of tls
i and ti are updated whenever the schedule of a
(transitive) successor of ai is decided or changed.
An RCPSP with also a project-deadline constraint is often referred to as the time- and
resource-constrained project scheduling problem (TRCPSP2 ) (cf. Neumann et al., 2001).
iii) project-due-time constraint

The project due time or due date is often set by the project manager(s) during the
tactical planning phase of the project management (Hans et al., 2007). A project-duetime constraint is a soft temporal constraint which means that the completion time of
a project can go beyond its due time, even though this is not favourable. To prevent
this from happening, project completion time over its due time is often punished with a
penalty referred to as project delay penalty.
Let dt denote the project due time. dt should be set equal to or greater than the end
of the project critical path (i.e., rl + ). Thus,
rl + dt dl.
2.1.3
Resources and Constraints
Project activities require time as well as resources for their executions (the exception
being the dummy activities, which are assumed to require no time and no resources). In
this subsection, we discuss the resource aspects of project scheduling. These include (a)
resource categories, (b) activity operating modes, and (c) resource-capacity constraints.
A: Resource Categories
The resources for carrying out project activities may be of different categories. In general, resources can be divided into three categories: renewable resources, non-renewable
2 Guldemond
et al. (2008) use the term TCPSP for a class of project-scheduling problems, where additional
temporal constraints are introduced on the activity level, such as a release time or a deadline for each
activity.
17
resources, and doubly-constrained resources (Blazewicz et al., 1983). Below we define

them.
Definition 2.4 Renewable resource. Renewable resources are those resources available on a period-by-period basis. The amount of resources is renewable from period to
period, only the total resource used at every time instant is constrained.
Typical examples of renewable resources include manpower, machines, tools, equipment,
space, etc.
Definition 2.5 Non-renewable resource. Non-renewable resources are those resources
available on a total project basis, with a limited consumption availability for the entire
project.
The best examples of non-renewable resources are money and energy.
Definition 2.6 Doubly-constrained resource. Doubly-constrained resources are those
resources constrained per period as well as for the overall project.
Doubly-constrained resources can be incorporated by a combination of renewable and
non-renewable resources. Examples are: (i) capitals with a restricted period of cash flow
and a limited total of cash amount, and (ii) man-hours per day in combination with a
constraint on the total number of man-hours for the entire project.
In this thesis, we focus on the study of renewable resources in RCPSP, and refrain
from studying non-renewable resources and doubly-constrained resources. For more information on the latter topics, we refer the readers to Servakh and Shcherbinina (2007).
B: Activity Operating Modes
Within the category of renewable resources, there are also various resource types. In order
to carry out a project, different types of renewable resources are often needed. We assume
that a set R of K renewable resource types, R = {R1 , . . . , RK }, is required for carrying
out the activities of the project in question. In the project planning phase, the project
manager must decide for each activity ai , (i) the resource requirement, which includes the
required resource type(s) and
the corresponding amount of each type needed for carrying
out the activity3 : {(k : rik )k {1, . . . , K} rik N}; (ii) the estimated processing time
needed in order to finish the activity: pi .
The combination of the resource requirement and the estimated processing time would
permit the activity ai to be finished with the given resources in the given processing time.
We call such a combination an activity operating mode or simply a mode. Let i be a
mode of activity ai , and
3 We

i = h{(k : rik )k {1, . . . , K} rik N}, pi i.
(2.5)
note that each activity may require more than one resource type for execution. In case an activity
requires 0 unit of resource type Rk , the item (k : 0) in the resource requirement set is omitted for brevity
purpose. One exception is for the dummy activities, of which the resource requirement of dummy
activities are written as {(0 : 0)}.
18
An activity may sometimes be carried out by using more than one mode. Problems
with multiple mode options for executing activities are termed multi-mode RCPSP (MRCPSP). MRCPSP are not the subject of this research; for an impression, the readers are
referred to the survey work on this subject by Lova et al. (2006).
20
12
1:2
1
0
2:6
15
0
0:0
15
12
10
1:1
2:2
20
11
5
4
1:3
2:2
1:2
12
2:3
1:2
0:0
Legend
pi
pj
1:2
k : rik
k : rjk
Figure 2.6: Refined AoN representation of a project

The AoN network in Figure 2.6 details the AoN network of the project (as given in
Figure 2.1) by associating with each activity a mode i . For simplicity, in the given
example, we assume that performing an activity requires only one of the two resource
types (R = {R1 , R2 }). For instance, the mode of activity a5 in the project depicted in
Figure 2.6 is h{(1 : 2)}, 15i, meaning that the execution of activity a5 requires 2 units of
resource type R1 and lasts 15 time units.
C: Resource-capacity Constraints
Traditionally, resource constraints in scheduling problems refer to the resource-capacity
constraint. When resources are capacity constrained, it means that for each resource
type Rk (Rk R), at most ck N units of the resource type can be used at the same
time, where ck N is the maximum capacity of resource type Rk . We recall that rik
is the amount of resource type Rk used by activity ai (ai A). We assume that the
given quantity ck is constant throughout the scheduling horizon. The same holds for rik
throughout the processing duration of ai .
Given a complete set of activity start times S = {si }ai A+ of the project, let
A(S, t) = {ai A|si t < si + pi }
(t 0)
(2.6)
be the set of activities of which the processing times contain the time point t, also called
the active set at time t. Let uk (S, t) be the amount of resource type Rk used at time t
by all activities. So,
X
uk (S, t) =
rik (Rk R, t 0).
(2.7)
ai A(S,t)
19
Moreover, the resource-capacity constraint can be formulated as

uk (S, t) ck
2.1.4
(Rk R, t 0).
(2.8)
Schedules and Performance Measures
A sequence of scheduled start times S = (s0 , . . . , sn+1 ) for all activities of a project, is
called a project schedule. A project schedule is a solution to an RCPSP. In this subsection,
we first define the concept of feasibility of a schedule and then discuss several scheduling
objectives, i.e., different ways of measuring the performance of a schedule.
A schedule to an RCPSP is called feasible if all precedence constraints and resource
constraints are satisfied. We define a feasible schedule as follows.
Definition 2.7 Feasible schedule. A feasible schedule S to an RCPSP should satisfy
the following constraints simultaneously.
rl s0
si + pi sj
uk (S, t) ck
(ai aj )
(2.9)
(Rk R, t 0)
A feasible schedule S to a TRCPSP should satisfy an additional constraints: sn+1 dl.

In the scheduling phase of project management, finding a feasible project schedule is
essential. However, when a project has more than one feasible schedule, in most cases
the project manager will try to find the best schedule amongst all feasible schedules using
suitable objective functions. In the following subsection, we discuss various projectscheduling objectives.
The quality of a feasible schedule can be measured by a utility function (a.k.a. objective
function) f (S), which represents a particular scheduling objective. A scheduling problem
with a utility function becomes an optimisation problem in which f (S) is to be maximised
(or minimised). We describe an RCPSP in the following linear programming formulation.
Find
S = arg min f (S)

S
subject to
si + pi sj
(ai aj )
uk (S, t) ck
(Rk R, t 0)
rl s0
(2.10)
Motivated by real-world situations, a wide variety of objectives for RCPSP have

been studied. We distinguish two classes of objectives: (a) time-based objectives and
(b) resource-based objectives. In addition, most real-world applications consider a third
class, i.e., (c) a combination of multiple objectives as a joint objective. In the sequel, we
will discuss and formulate these three classes of project-scheduling objectives.
20
A: Time-based Objectives
One of the most common objectives in project scheduling is to find the schedule that
minimises the project makespan (a.k.a. the project throughput time). Project makespan
is defined as the elapsed time between the project release and the project completion.
Let PM denote the objective of (1) minimising the project makespan. We formulate the
objective of PM as follows.
PM :
(2.11)
f (S) = sn+1 rl
Minimising the project makespan is important in many practical situations: it leads to a

timely release of resource capacities for future projects; it reduces the risk of violating a
deadline; it generates timely incoming cash flows, etc. (cf. Demeulemeester and Herroelen,
2002).
When a project due time dt is given, a representation variation of minimising the
project makespan, considered as the second time-based objective, is (2) minimising the
project delay (denoted by PD). Project delay is often referred to as the elapsed time
between the project due time and the project completion time.
PD :
f (S) = max(sn+1 dt, 0)
(2.12)
B: Resource-based Objectives
In many real-world situations resource-based objectives are considered next to time-based
objectives. Below, we introduce two often-used resource-based objectives.
If the resources necessary to carry out the activities have to be purchased (e.g., expensive machinery), then we speak of the resource investment problem. Project managers
in resource investment problems often want to minimise the total resource procurement
cost (denoted by TRPC). The objective function for minimising the total resource procurement cost is defined as follows.
TRPC :
f (S) =
Rk R
cpk max uk (S, t),

t0
(2.13)
where cpk 0 is the procurement cost per unit of resource type Rk R and uk (S, t) is the
amount of resource Rk used at time t given a schedule S.
The second resource-based objective involves generating a schedule where the utilisation of resources is as flat as possible, without violating the project-deadline constraint. In
this case, we speak of the resource levelling problem. The degree to which the resource
usage is levelled can be expressed in various ways (cf. Neumann et al., 2001). A typical
resource-levelling measurement considers the total squared resource utilisation cost. The
objective of minimising the total squared resource utilisation (denoted by TSRU) given a
schedule S can be formulated as follows.
21
2.2. AGH Scheduling Problem
TSRU :
f (S) =
X X
u2k (S, t)
(2.14)
Rk R t0
When utilisation resources of different resource types is charged with different cost,
we speak of minimising the total squared resource utilisation cost (denoted by TSRUC),
and it can be formulated as follows.
TSRUC :
f (S) =
Rk R
cuk
u2k (S, t)
(2.15)
t0
where cuk 0 is the utilisation cost per unit of resource type Rk R per unit of time.
C: A Combination of Multiple Objectives
From the discussion above, we have seen that a project schedule can be weighted against
a variety of performance measures. These measures may pertain to the makespan of the
project, the delay of the project, the resource procurement, the levelling of resource utilisation, etc. In many situations, these objective functions may be more or less equally
relevant. A solution that is optimal with respect to one single objective might be arbitrarily bad with respect to other criteria, and thus unacceptable for a project manager
(Tkindt and Billaut, 2006). In general, there will be a trade-off amongst schedules. This
forces a project manager to decide a weight distribution for each of the measures in such
situations.
This gives rise to the problem of scheduling projects under multiple objectives (cf.
Slowi
nski et al., 1994; Tkindt and Billaut, 2006). The problem is also sometimes referred
to as multi-goal problem or multicriteria problem. The analysis involves the use of different objectives which are combined with weight factors. A weight factor that is assigned
to each of the considered objectives, determines the importance of one objective vis-`a-vis
that of other objectives. We note that these weight factors should be context dependent
and they need to be empirically modelled.
Below we give an example of a combination of two objectives: minimising the project
delay (PD) and minimising the total squared resource utilisation cost (TSRUC).
PD + TSRUC : f (S) = w1 max(sn+1 dt, 0) + w2
Rk R
cuk
u2k (S, t)
(2.16)
t0
In Equation 2.16, the two weight factors w1 and w2 are used to represent the relative
importance of one objective compared to the other.
2.2
The AGH scheduling problem has been brought up only recently, namely since the liberalisation of ground-handling market (cf. Schmidbergera et al., 2009). Models such as job
22
shop scheduling (see Xue and Fan, 2007) and simple temporal network (see van Leeuwen
and Witteveen, 2009) are employed to formulate the problem. In this section, we identify
and analyse the characteristics of an AGH scheduling problem from a project-scheduling
perspective.
In the research field of project scheduling, the RCPSP addressed in Section 2.1 is a
well-known problem. However, it is a rather basic model with assumptions that are too
restrictive for many practical applications (Hartmann and Briskorn, 2010). In practice,
project-scheduling problems can be of various variations and extensions of the classic
RCPSP model4 .
In this section, we focus on three extensions of classic RCPSP with considering the
characteristics of the studied AGH scheduling domain. They are scheduling multiple
projects (see 2.2.1), (2) informational and managerial decentralisation (see 2.2.2), and
uncertainty in scheduling (see 2.2.3). Following the discussion of the three extensions of
RCPSP, we model the AGH scheduling problem as an instance of a generalised RCPSP
a decentralised resource-constrained multi-project scheduling problem under uncertainty
(see 2.2.4).
2.2.1
Scheduling Multiple Projects
In real-life applications, it is rarely the case that a single organisation carries out a single
project at a time. Instead, an increasing number of organisations tend towards an organisational structure in which multiple projects are performed simultaneously, and with
collaboration of a number of partners (cf. Pennypacker and Dye, 2002; Tobis and Tobis,
2002; Turner, 2008).
As introduced in Section 1.1, an aircraft turnaround process consists of a series of
ground-handling operations. The operations can be seen as the intermediate activities
in the scope of a project. Therefore, scheduling a turnaround process can be seen as
an instance of an RCPSP. Consequently, AGH scheduling, which aims at scheduling all
aircraft turnarounds at an entire airport, requires an extended model of RCPSP with
multiple projects.
In a multi-project scheduling context, assuming that the activities of each project
require only local (non-shared) resources, the problem of scheduling multiple projects
can be decomposed into scheduling a set of independent (single) projects (Confessore
et al., 2007). However, most of the projects carried out in a multi-project environment do
not have the luxury of dedicated resources. A number of researchers (e.g., Payne, 1995;
Pennypacker and Dye, 2002) explicitly pointed out that most projects that are run in
parallel by a company make use of shared and often limited resources. Frequent conflicts
of interest arise when more than one project requires the same type of resource at the
same time. Therefore, scheduling multiple projects with shared resources is much more
complicated than scheduling in single-project cases.
We define the problem of scheduling multiple projects sharing limited resources as a
resource-constrained multi-project scheduling problem.
4 While
we are composing this thesis, Hartmann and Briskorn (2010) published a survey work on variants
and extensions of the classic RCPSP. The survey provides an exhaustive overview over the extensions
studied in the last decades (restricted to deterministic problems though), and classifies the extensions
according to the structure of the RCPSP.
23
Definition 2.8 Resource-constrained Multi-project Scheduling Problem

(RCMPSP). A resource-constrained multi-project scheduling problem is the problem of
simultaneous scheduling two or more projects, each of which has its own set of activities
constituting different network structures. A common pool of resources is provided to execute the activities of different projects. Precedence relations between two activities are
defined only within the same project.
Formally, we can describe an RCMPSP as follows.
An RCMPSP consists of a set P of m projects (P = {P1 , . . . , Pm }, m N2 ),
sharing a set R of K types of (renewable) resources (R = {R1 , . . . , RK }, K N1 ).
Each project Pi (i {1, . . . , m}) has a release time rli , and consists of a set Ai of
ni N real activities ai,j with j {1, . . . , ni }. Two fictitious activities ai,0 and
ai,ni +1 are added for representing the start and the completion of project Pi .
Each resource type Rk has a maximum capacity ck .

k
Each activity ai,j has only one activity operating mode i,j = h{(k : ri,j
)k
k
{1, . . . , K} ri,j
N}, pi,j i
Simple finish-start precedence relations describe execution orders for pairs of
activities of the same project: ai,j ai,l .
A feasible solution to an RCMPSP is a schedule S = {si,j | 1 i m, 0 j ni + 1}

specifying the start times of all project activities and satisfying the following constraints.
rli si,0
si,j + pi,j si,l

uk (S, t) ck
(i {1, . . . , m})
(ai,j ai,l )
(2.17)
(Rk R, t 0)
We recall that function uk (S, t) stands for the amount of resource type Rk used at time
t by all project activities {ai,j }. It can be derived as follows.
uk (S, t) =
XX
i
k
ri,j
, where si,j t < si,j + pi,j
(2.18)
A variety of objective functions differing from those for RCPSP have to be considered
when solving an RCMPSP. We mention in the following several widely used examples
of these objective functions: (1) TPM: minimising the total project makespan, (2) SPM:
minimising the summed project makespan, and (3) SPD: minimising the summed project
delay, (4) APD: minimising the average project delay, (5) APDP: minimising the average
project delay penalty.
TPM is an objective function on the top management level regardless of the relative
importance of different projects. It concerns the time difference between the completion
time of the last project and the release time of the first project. The formulation of TPM
is as follows.
24
TPM :
f (S) = max(sni +1 ) min(rli ),

i
i {1, . . . , m}
(2.19)
The objective function of SPM is defined as follows.
SPM :
f (S) =
m
X
i=1
(si,ni +1 rli )
(2.20)
Assuming due time dti of each project Pi is introduced, we define the objective function
of SPD as follows.
SPD :
f (S) =
m
X
i=1
max(si,ni +1 dti , 0)
(2.21)
We recall that project makespan is defined as the elapsed time between project release
time and project completion (see Equation 2.11). Accordingly, we have the objective
function of APD as follows.
APD :
f (S) =
m
X
max(si,n
i=1
i +1
dti , 0)
(2.22)
The APD objective less accurately represents the reality, as it implicitly assumes
equal delay penalties for all projects (cf. Kurtulus, 1985). APDP is introduced as a more
realistic objective, where each project is associated with a time-unit delay cost (i.e., cdl
i
for Pi ).
APDP :
f (S) =
m
X
cdl max(si,n
i
i=1
2.2.2
i +1
dti , 0)
(2.23)
Informational and Managerial Decentralisation
In the AGH environment, having a centralised authority that makes the scheduling decisions for all aircraft on each individual ground-handling operation is impractical and
undesirable. First, aggregating all aircraft-turnaround information to a central hub is
a heavy task with respect to both computation and communication. Second, aircraft
are operated by different airline companies that may have different interests and preferences. Third, ground-handling operations are carried out by a number of self-interested
third-party ground-service providers.
The informational and managerial decentralisation in AGH scheduling problem coincide with many real-world project-scheduling situations where project environments are
becoming more distributed both geographically and organisationally (cf. Confessore et al.,
25
2007). In this case, the multiple projects in an RCMPSP usually will no longer belong
to the same company. Each project may have its own manager, who is self-interested
and tries to optimise the performance of its own project. Information about the precedence relations among activities as well as the resource requirement of one project is
only known to the project manager himself5 . Moreover, resources shared by the multiple
projects in an RCMPSP may be provided by various resource providers. We assume that
each resource type is associated with a resource provider who is also self-interested and
tries to maximise its own utility function with regard to the utilisation of the resources
it provides.
The decentralisation of decision-making processes in practice urges us to study a
decentralised scheduling problem. We define a decentralised resource-constrained multiproject scheduling problem as follows.
Definition 2.9 Decentralised Resource-constrained Multi-project Scheduling
Problem (DRCMPSP). A decentralised resource-constrained multi-project scheduling
problem is an RCMPSP in which each project is managed by a self-interested project
manager, and each resource type is managed by a self-interested resource manager. All
different types of managers make scheduling decisions based on their own objectives.
We note that the DRCMPSP definition given in Definition 2.9 extends the decentralised problem definition introduced by Confessore et al. (2007) and Homberger (2007)
by introducing the self-interested resource managers.
2.2.3
Decision Making under Uncertainty
Uncertainty is inevitable in real-life project environment. Project-management uncertainty may have a variety of sources. These include imprecise, outdated or incomplete
information, inability to accurately model the impact of expected or unexpected events,
imprecision in estimation and judgement, and so on.
An attempt to categorise uncertainty in project management was made by BonfillTeixidor (2006) from a hierarchical decision-making process point of view. She divided
uncertainty into three categories: strategic uncertainty, tactical uncertainty, and operational uncertainty. Project scheduling involves decisions on the operational level of project
management. Therefore, we focus on studying the operational uncertainty. Below we give
several examples of uncertainty6 with respect to projects and activities, respectively.
Uncertainty with respect to projects
1. A project may have a delayed or advanced release time.
2. A project deadline may be postponed or advanced.
3. New arriving project(s) may have to be incorporated.
4. Certain projects may be cancelled before the projects start or during the course
of the project executions.
5 For
brevity, we use he or his whenever he or she and his or her are meant.
the sake of readability, we abbreviate the term operational uncertainty to uncertainty here and
for the rest of the thesis, too.
6 For
26

Uncertainty with respect to activities
1. The processing time and resource requirement of an activity may be inaccurately estimated.
2. Resources for carrying out an activity may become unavailable or arrive behind
schedule.
3. Staff/operators may encounter problems that cause productivity drops.
4. New activities may have to be incorporated during the course of a project.
5. Certain activities may have to be dropped due to changes in the project scope.
As it is clear from the given examples, uncertainty lies at the very heart of projectscheduling problems. Below, we define a DRCMPSP under uncertainty.
Definition 2.10 Decentralised Resource-constrained Multi-project Scheduling
Problem under Uncertainty (DRCMPSP/u). A decentralised multi-project scheduling problem under uncertainty is a DRCMPSP in which projects executions are subject
to various uncertainty.
Similar to most practical project-scheduling environments, the AGH scheduling environment is well known for its large number of disturbances stemming from various
sources. The disturbances cause a high degree of uncertainty in the AGH schedules. In
this thesis, we focus on investigating scheduling solutions under the following two classes
of uncertainty: (a) partial observability and (b) nondeterminism. Below, we discuss them
briefly in the context of AGH scheduling.
A: Partial Observability
Partial observability in AGH scheduling can be interpreted as variable aircraft arrival
times. The actual arrival time of an aircraft at the airport is often different from (most
of the times, it is later than) the one foreseen in the original flight plan. The uncertainty
in aircraft arrival time may be caused by different reasons, for instance, (i) bad weather
conditions at the arrival airport for aircraft landing, (ii) the delayed departure from the
departure airport, and (iii) longer en-route flying time because of head wind or air traffic
control. In project-scheduling terms, partial observability is interpreted as variable project
release times7 .
7A
recent work of investigating decentralised decision making in partial observable environments can
be found in Oliehoek (2010), in which the author investigated the decentralised partially observable
Markov decision process (Dec-POMDP). The research scope and focus of Oliehoek (2010) are different
from ours in three distinct aspects. First, Oliehoek (2010) studies planning problem, whereas we study
scheduling problem. Second, Oliehoek (2010) studies cooperative agents, whereas we study competitive
agents. Third, in Oliehoek (2010) the uncertainty resides in both the outcome of agent actions and the
perception of the state of the environment, whereas in our research we consider the uncertainty in the
perception of the state of the environment only.
27
B: Nondeterminism
Nondeterminism in AGH scheduling can be interpreted as variable ground-handling operational times. During the scheduling phase of AGH, each of the ground-handling operations has an estimated processing duration. However, during the execution phase, the
actual processing durations may differ from the original estimations. There can be various
reasons for this variation, for instance, (i) bad weather conditions will extend the baggage
loading/unloading duration, (ii) breakdown of maintenance machinery will require extra
time for aircraft maintenance, and (iii) no-show of passengers will delay the passenger
boarding process. In project-scheduling terms, nondeterminism is interpreted as variable
activity processing times.
2.2.4
A DRCMPSP/u Formulation of AGH Scheduling Problem
Based on the analyses above, we can formulate the AGH Scheduling problem as an instance of a DRCMPSP/u. A formal definition of an AGH scheduling problem is given
below.
Definition 2.11 AGH Scheduling Problem. An AGH scheduling problem is the
problem of scheduling a set P of m aircraft turnaround processes (P = {P1 , . . . , Pm },
m N2 ), where
Pi (i {1, . . . , m}) consists of a set Ai of ni N ground-handling operations ai,j
with j {1, . . . , ni };
Two fictitious operations ai,0 and ai,ni +1 are added for representing the start and
the completion of Pi ;
Each aircraft is managed by a manager who makes scheduling decisions for the
aircrafts ground-handling operations;
Each aircraft has an expected arrival time rli and an expected departure time dti
according to the flight timetable;
All aircraft share a set R of K types of (renewable) resources (R = {R1 , . . . , RK },
K N+ ), each of which is provided by a self-interested ground-service provider;

k
k
Operation ai,j has only one operating mode i,j = h{(k : ri,j
) k {1, . . . , K} ri,j
N}, pi,j i;
Simple finish-start precedence relations describe execution orders for pairs of operations in Pi : ai,j ai,l , and it is only known to the manager of Pi ;
The actual arrival time rli of an aircraft Pi may be different from the expected one;
The actual processing time pi,j of a ground-handling operation ai,j may be different
from the estimated one;
The last two items in Definition 2.11 represent partial observability and nondeterminism, respectively.
28
2.3
Chapter Summary
In this chapter we formulated the AGH scheduling problem into a well-studied schedulingproblem framework the project scheduling problem. We provided the definition of the
classic project scheduling problem RCPSP, as well as some extensions of RCPSP.
The RCMPSP as a first extension of RCPSP is defined as a problem in which two
or more projects are concurrently active at a point in time. Each project, usually represented by means of a network, contains a finite set of activities which are ordered by
precedence relations. These projects can have different and often conflicting properties,
such as different release times, different urgencies represented by deadlines, and different
objectives.
The DRCMPSP further extends the RCMPSP by addressing multiple self-interested
decision makers. In a decentralised setting, not only the project managers, but also the
resource-type managers make strategic decisions to fulfil their own goals.
Moreover, we investigate the DRCMPSP with the existence of uncertainty, making
it a DRCMPSP/u. We identify two classes of uncertainty partial observability and
nondeterminism that appear in AGH scheduling problems as variable aircraft arrival
times and variable ground-handling operational times, respectively.
Finally, the AGH scheduling problem is formulated as an instance of a DRCMPSP/u.
Different aircraft managers being project managers have different and independent objectives, and ground-service providers being resource managers of different resource types
also have their own objective with respect to the utilisation of their resources.
Chapter 3
A Review of Existing Solution

Methods
The field of project-management theory and practice has taken tremendous strides forward in the past few decades (Demeulemeester and Herroelen, 2002). Over the years,
the project-scheduling problems occurring in practice exhibit more and more complex
structure, evolving from scheduling a static and deterministic small-scale single project
to scheduling dynamic and nondeterministic large-scale multiple projects. The development of solution procedures over the years for their resolution transcend the project
management area.
In this chapter, we provide a literature review on the latest development of projectscheduling research with emphasis on the problems where (1) multiple projects have to
be scheduled using shared resources, (2) information about projects and resources is
asymmetric and decision-making processes are decentralised (3) projects are executed in
an environment with various uncertainties.
We start this chapter by investigating the existing approaches to RCMPSPs (see
Section 3.1). Subsequently, we provide an extensive survey on the latest development of
solution methods to DRCMPSPs (see Section 3.2). Furthermore, we review some of the
methods that have been proposed in the literature for scheduling under uncertainty (see
Section 3.3). Section 3.4 summarises this chapter by discussing to which extent we go
beyond state of the art concerning the solution methods and thus contribute to the field.
3.1
Solution Methods for RCMPSP
In the past, various methods from both operations research and artificial intelligence
were proposed to handle RCMPSP in a centralised manner (cf. Lova and Tormos, 2001;
Hans et al., 2007). In the case all projects were managed by a single authority, a centralised scheduling method would be applied to find an integrated schedule. Two classes
of approaches have been used in centralised scheduling (cf. Lova and Tormos, 2001): (a)
single-project approaches and (b) multi-project approaches. Below, we briefly discuss the
30
A Review of Existing Solution Methods
difference between these two classes of approaches and focus on investigating solution
methods using multi-project approaches.
A: Single-project Approaches
In a single-project approach, the individual projects of an RCMPSP is aggregated into
a single mega-project, which can then be represented by a super AoN network (see Figure 3.1). The super AoN network combines all projects activity networks and adds
two super-dummy activities a super-dummy start activity (node 0 in Figure 3.1)
and a super-dummy completion activity (node n + 1 in Figure 3.1). Both of the two
super-dummy activities are associated with mode h{(0 : 0)}, 0i.
01
Project P1
dl1
rli
rl1
n1 + 1
0i
Project Pi
ni + 1
rlm
0m
Project Pm
dli
n+1
dlm
nm + 1
Figure 3.1: An example of super AoN network for RCMPSP

When release-time constraints exist, a super release time Rl of the mega-project is
defined as the earliest release time among all project release times, and
Rl = min(rli ),
i
i {1, . . . , m}.
Similarly, when project-deadline constraints exist, a super deadline Dl for the megaproject is defined as the latest deadline among all project deadlines, and
Dl = max(dli ),
i
i {1, . . . , m}.
In a super AoN network, the release time and the deadline of an individual project Pi
can be imposed by inserting two additional fictitious activities, ai,rl and ai,dl , where
pi,rl = rli Rl,
pi,dl = Dl dli .
(3.1)
Therefore, the mode of dummy activity ai,rl is h{(0 : 0)}, pi,rl i, and the mode of dummy
activity ai,dl is h{(0 : 0)}, pi,dl i.
3.1. Solution Methods for RCMPSP
31
Aggregating multiple projects into a mega-project reduces an RCMPSP to an RCPSP,

which can be subsequently solved by an RCPSP solver. For the literature of solving
RCPSP, readers are referred to the survey work by Ozdamar

and Ulusoy (1995) and
Herroelen et al. (1998), as well as to two handbooks by Neumann et al. (2001) and
Demeulemeester and Herroelen (2002).
Employing a single-project approach for solving RCMPSP is not always applicable.
First, aggregating multiple projects into a mega-project implicitly assumes equal delay
penalties for all projects, which is rarely the case in practice. Second, independent project
analysis becomes difficult when all projects are bound together. Third, single-project approaches cannot address the different importance of the projects in an RCMPSP. Fourth,
aggregating multiple projects into a mega-project significantly increases the network complexity and consequently increases the computational effort of the solution procedures.
Therefore, solution methods that can solve an RCMPSP while maintaining a separate
critical path per project are needed. These solution methods are often referred to as
multi-project approaches or parallel scheduling approaches (cf. Lova and Tormos, 2001;
Kr
uger and Scholl, 2007).
B: Multi-project Approaches
Solution methods for RCMPSPs based on the multi-project approach fall into four categories: (1) exact methods, (2) priority-rule-based heuristics, (3) meta-heuristics, and (4)
constraint satisfaction and optimisation.
3.1.1
Exact Methods
Exact methods aim at finding the optimal solution to a problem. Therefore, they are
often referred to as optimal procedures. Optimal procedures for solving RCMPSP have
been proposed since the early days of project management research. Examples of such
procedures include zero-one linear programming (e.g., Pritsker et al., 1969; Deckro et al.,
1991), and the branch-and-bound algorithm (e.g., Vercellis, 1994).
The pioneering work on multi-project scheduling by Pritsker et al. (1969) proposed
a zero-one linear programming formulation for RCMPSP. A three-project, eight-activity
(in total), three-resource-type example RCMPSP is used to test the optimal solutions
obtained by the zero-one programming code with respect to solutions obtained by two
heuristic approaches1 : first come first served, and minimum project slack time first. They
compared the scheduling results with respect to three different scheduling objectives:
SPM, TPM, and SPD (see 2.2.1).
Deckro et al. (1991) have formulated RCMPSP as a block angular general integer
programming model, and employed a decomposition approach to solve such integer programming problems. The scheduling problem instance they used (which is a problem
consisting of eight projects) is slightly larger and more complex than the one used by
Pritsker et al. (1969). However, the solution scalability is still limited.
Vercellis (1994) described a Lagrangian decomposition technique for solving multimode RCPSP. The decomposition can be useful in several ways, such as providing bounds
1A
more detailed discussion on heuristic approaches can found in the 3.1.2.
32
on the optimum so that the quality of approximate solutions can be evaluated. Furthermore, in the context of branch-and-bound algorithms, it can be used for more effective
fathoming of the tree nodes. In the modelling perspective, the Lagrangian optimal multipliers can provide insight to the prices for assigning the resources to different projects.
The RCMPSP is a generalisation of the RCPSP with multiple projects. It has been
shown by Blazewicz et al. (1983) that the RCPSP, as a generalisation of the classical job
shop scheduling problem, belongs to the class of NP-hard optimisation problems. The
RCMPSP problem, as a generalisation of the RCPSP, is therefore also NP-hard, meaning
that there are no known algorithms for finding optimal solutions in polynomial time (cf.
Garey and Johnson, 1979). Complexity analysis for the RCMPSP is not encouraging,
especially because the actual project scheduling problems in real-world applications are
often of large-scale. Problems become intractable when using exact methods. Hence,
most research has sought (1) efficient heuristics, and (2) meta-heuristics. In the following
two subsections, we will discuss the state of the art on priority-rule-based heuristics and
meta-heuristics for RCMPSP.
3.1.2
Priority-rule-based Heuristics
Most of the heuristic methods used for solving RCMPSP belong to the class of priorityrule-based methods (see Kurtulus and Davis, 1982; Kurtulus and Narula, 1985; Lova and
Tormos, 2001; Browning and Yassine, 2010). In general, priority-rule-based heuristics
assign different priority values to the activities that request the same resource at the
same time. The activity with the highest priority value will make use of the resource
first. These methods are also sometimes referred to as X-pass methods, including singlepass methods and multi-pass methods. The difference between single-pass and multi-pass
methods is the number of schedules they generate for each problem. Single-pass methods
generate a single schedule; while multi-pass methods generate more than one schedule and
select the one that optimises the objective function (cf. Kolisch and Hartmann, 1999).
Examples of multi-pass methods are: (a) forward-backward scheduling methods (cf. Lova
et al., 2000) and (b) sampling methods (cf. Lova et al., 2000; Lova and Tormos, 2002).
Priority rules can be classified on the basis of the information they use: (1) activityrelated , (2) project-related , and (3) resource-related (Kolisch and Hartmann, 1999).
Activity-related rules assign a priority value to an activity based on a parameter
or characteristic of the activity itself, such as its processing time (e.g., shortest
processing time first) or slack time (e.g., minimum slack time first).
Project-related rules assign priorities to activities based on the project they belong
to, or characteristics of that project (e.g., shortest activity from shortest project
first).
Resource-related rules assign priority in terms of an activitys resource demands,
scarcity of resources used, or some combination. High priorities are usually assigned
to potential bottleneck activities. An example is the maximum-total-work-content
rule).
33
Some rules combine elements of information about the activity, the project, and the
resources (cf. Kolisch and Hartmann, 1999).
Kurtulus and Davis (1982) developed six priority rules for the multi-project environment, and along with three single-project priority rules. They analysed these rules with
the objective of SPD; they found that shortest-processing-time-first heuristic was the best
under most conditions. Browning and Yassine (2010) have extended the work by Kurtulus
and Davis (1982) and conducted experiments with 20 priority rules on in total 12, 320
test problems. We summarise twenty priority rules mainly studied by Kurtulus and Davis
(1982) and Browning and Yassine (2010) in Table 3.1.
Table 3.1: Priority-rule-based heuristics
1.
2.
3.
4.
5.
6.
7.
8.
9.
Priority
Rules
FCFS First Come
First Served
LCFS Last Come
First Served
RAN Random
SPT Shortest
Processing
Time
LPT Longest
Processing
Time
MINSLK Minimum
Slack time
MAXSLK Maximum
Slack time
SASP Shortest
Activity from
the Shortest
Project
LALP Longest
Activity from
the Longest
Project
Basis
Description and Formula
Activity
es
min(tes
i,j ), where ti,j is the earliest start
time of ai,j
Activity
max(tes
i,j )
Activity
Activities selected randomly
Browning
(2010)
and
Yassine
Activity
min(pi,j ) where pi,j is the processing

time of ai,j
Kurtulus
(1982)
and
Davis
Activity
max(pi,j )
Kurtulus
(1982)
and
Davis
Activity
sl
ls
es
min(tsl
i,j ) where ti,j = ti,j ti,j is the
slack time of ai,j
Fendley (1968); Lova and

Tormos (2001); Kurtulus
and Davis (1982)
Activity
max(tsl
i,j )
Kurtulus
(1982)
Activity,
Project
min(i + pi,j ), where i is the length of

critical path of project Pi
Kurtulus
and
Davis
(1982); Deckro et al.
(1991); Lova and Tormos
(2001)
Activity,
Project
max(i + pi,j )
Kurtulus
(1982)
0
MINTWK Minimum
10.
Total Work
content
Activity,
Resource
min @
K X
X
k
pi,j ri,j
k=1 jAs
i
where Asi is the
+ pi,j
References
K
X
Kurtulus
and
Davis
(2001)
Browning and Yassine
(2010)
and
and
Davis
Davis
1
k A
ri,j
,
k=1
set of activities already

scheduled in project Pi
Kurtulus
and
Davis
(2001)
34

Table 3.1 continued from previous page
11.
12.
13.
14.
Priority
Rules
MAXTWK Maximum
Total Work
content
MINLST Minimum
Latest Start
Time
MINLFT Minimum
Latest Finish
Time
MAXSP Maximum
Schedule
Pressure
Basis
Description and Formula

0
K
X
X
16.
17.
18.
19.
20.
MINWCS Minimum
Worst Case
Slack
WACRU Weighted
Activity
Criticality and
Resource
Utilisation
TWK-LST Maximum
Total Work
content &
earliest Latest
Start Time
first (2-phase
rule)
TWK-EST Maximum
Total Work
content &
earliest
Earliest Start
Time first
(2-phase rule)
MTS Maximum
Total
Successors
MCS Maximum
Critical
Successors
K
X
Kurtulus
and
Davis
(2001)
Activity,
Resource
max @
Activity
min(tls
i,j )
Browning
(2010)
Activity
min(tlf
i,j )
Lova and Tormos (2001);

(2010)
+ pi,j
k=1 jASi
max
Activity
k
pi,j ri,j
lf
tti,j
pi,j Wi,j
k A
ri,j
k=1
, where Wi,j is the
percentage of the activity remaining to

be done at time t
0
15.
References
Browning
(2010)
and
Yassine
and
Yassine
and
Yassine
and
Yassine
i ,j
p
min (tls
i,j max (Ei,j |(ai,j , ai0 ,j 0 ) At )),
Activity,
Resource
i ,j
where Ei,j
is the earliest time to
Browning
schedule activity ai0 ,j 0 if ai,j is started
(2010)
p
at time t, and At is the set of all feasible
pairs of eligible, un-started activities at
time t
max(wCt(ai,j ) + (1 w)
K rk
X
i,j
Activity,
Resource
), where Browning
Rk
(2010)
Ct(ai,j ) is the criticality of activity ai,j
Activity,
Resource
MAXTWK first, tie broken by tls

i,j
Lova and Tormos (2001);

(2010)
Activity,
Resource
MAXTWK first, tie broken by tes

i,j
Browning
(2010)
and
Yassine
Activity
max(| A i,j |), where | A i,j | is the total

number of transitive successors of ai,j
Browning
(2010)
and
Yassine
Activity
c
max(| A i,j |), where A i,j is the set of
critical successors of ai,j
Browning
(2010)
and
Yassine
k=1
35
It is important to note that single-project approaches and multi-project approaches

often produce different schedules with the same priority rule (Lova and Tormos, 2001),
especially if the rule depends on the critical path (e.g., minimum slack time first). While
the single-project approach is more efficient for minimising a single projects processing
time, priority rules based on the multi-project approach perform better when minimising
the average delay in several projects (cf. Kurtulus and Davis, 1982).
RCMPSP studies disagree about which rule performs best and under which conditions.
This disagreement is mainly caused by the fact that problem instances that are used
to test the heuristic performance have different characteristics. The recent empirical
study conducted by Browning and Yassine (2010) provides a comprehensive analysis on
the performance of various priority rules subject to various project-, activity-, resourcerelated problem characteristics. They have developed a decision table to guide project
managers in choosing among the best priority rules based on (1) network complexity and
(2) resource-requirement characteristics.
3.1.3
Meta-heuristics
Since the last decade, meta-heuristic solution methods for RCMPSP such as (1) genetic
algorithms, (2) simulated annealing, and (3) swarm intelligence started to draw research
attention. In general, meta-heuristic methods are used to improve the (preliminary)
schedules obtained by priority-rule-based heuristics. We briefly discuss the three bestknown meta-heuristics for RCMPSP below.
Genetic Algorithms
Genetic algorithms, inspired by the process of biological evolution, have been introduced
by Holland (1975). In contrast to local search strategies, a genetic algorithm simultaneously considers a set or population of solutions instead of only one. Having generated an
initial population, new solutions are produced by combining two existing ones (crossover)
and/or by altering an existing one (mutation). After producing new solutions, the fittest
solutions survive and make up the next generation while the others are deleted. The
fitness value measures the quality of a solution, usually based on the objective function
value of the optimisation problem to be solved. RCMPSP solvers based on genetic algorithms are described by Kim et al. (2005), Kumanan et al. (2006), Yassine et al. (2007),
and Goncalves et al. (2008).
Simulated Annealing
Simulated annealing, introduced by Kirkpatrick et al. (1983), originates from the physical
annealing process in which a melted solid is cooled down to a low-energy state. Starting
with some initial solution, a so-called neighbour solution is generated by slightly perturbing the current one. If this new solution is better than the current one, it is accepted, and
the search proceeds from this new solution. Otherwise, if it is worse, the new solution is
only accepted with a probability that depends on the magnitude of the deterioration as
well as on a parameter called temperature. As the algorithm proceeds, this temperature
is reduced in order to lower the probability to accept worse neighbours. Clearly, simulated
36
annealing can be viewed as an extension of a simple greedy procedure, sometimes called

first fit strategy, which immediately accepts a better neighbour solution but rejects any
deterioration. RCMPSP solvers based on simulated annealing are described by Shankar
and Nagi (1996) and Bouleimen and Lecocq (2000).
Swarm Intelligence
Swarm intelligence is an AI approach based on the collective behaviour of decentralised,
self-organised systems. The expression was first introduced by Beni and Wang (1989),
in the context of cellular robotic systems. Swarm intelligence is typically made up of
a population of simple agents interacting locally with one another and with their environment. The agents follow simple rules, and although there is no centralised control
structure dictating how individual agents should behave, local interactions (which are
to a certain degree random) between such agents lead to the emergence of intelligent
global behaviour, mostly unknown to the individual agents. Natural examples of swarm
intelligence include ant colonies, bird flocking, animal herding, bacterial growth, and fish
schooling. The application of swarm principles to robots is called swarm robotics, while
swarm intelligence refers to the more general set of algorithms. Deng and Lin (2007)
and Gonsalves et al. (2008) have developed two particle swarm optimisation methods to
solve RCMPSP.
3.1.4
Constraint Satisfaction and Optimisation
The constraint satisfaction problem (CSP) (Kumar, 1992; Tsang, 1993) is a general framework for problems that requires finding states or objects that satisfy a number of constraints or criteria. Here we see that scheduling problems in general are concerned with
finding feasible schedules with respect to temporal and/or resource constraints. Therefore, they can be modelled in a CSP framework and solved by CSP solving techniques
(Lorterapong and Rattanadamrongagsorn, 2001).
A CSP may have multiple solutions. Any solution to a CSP that models a scheduling
problem provides a feasible schedule. In scheduling problems with desired objectives, some
solutions are often better than others. In these cases, the tasks of scheduling are to find
optimal (or near-optimal) solutions. By adding optimisation criteria, we can model the
scheduling problems into a so-called constraint optimisation problem (COP) framework
whereby the scheduling objective functions are included into a set of constraints.
The generality of the CSP has motivated the development of the constraint programming languages and related software systems. These constraint-based systems offer builtin functions for describing common types of constraints and often include CSP-solving
techniques developed in CSP research (Ran, 2003). Several constraint programming
systems include extensions specifically designed for scheduling applications, e.g., ILOG
Scheduler (Nuijten, 1994; Nuijten and Le Pape, 1998) and CHIP (Aggoun and Beldiceanu,
1993). More recent CSP/COP-based solutions for RCPSP are found in the work by Cesta
et al. (2002) and Dorndorf (2002).
3.2. Solution Methods for DRCMPSP
3.1.5
37
Beyond Centralised Solution Methods
Nowadays, centralised scheduling approaches to RCMPSPs are losing value due to the fact
that projects and resources are managed by independent managers (see 2.2.2). These
managers often have different and sometimes conflicting interests and objectives. However, the managers may be independent, the local decision-making processes are not. A
coordination mechanism among them is necessary to solve possible conflicts and to allocate the resources in an appropriate way. In Section 3.2, we investigate the solution
methods for solving a class of RCMPSP where both the problem information and the
decision process are decentralised (i.e., DRCMPSP).
3.2
Solution Methods for DRCMPSP
In decentralised scheduling procedures, scheduling decisions are performed by autonomous

decision makers, such as individual resource managers and project managers, taking into
account asymmetric information. Information asymmetry is assumed to mean that the
problem data of an individual resource type or of an individual project is private. For
a resource type, the information privacy means that resource capacity of the resource
type, resource allocation over time of the resource type are only known to the resource
manager who make scheduling decisions about the resource type. For a project, the
information privacy means that the activity network of the project, the processing times
of all activities of the project, and information with regard to calculated schedules for the
project are only known to the project manager, who makes the scheduling decisions for
the project.
The decentralised decision-making process calls for models and techniques that take
into account the strategic behaviour of individual decision makers. Therefore, a multiagent system, which can be used to solve problems that are difficult or impossible for
an individual agent or monolithic system to solve, is a suitable means for modelling a
solution framework to DRCMPSPs. In the following, we provide a brief introduction
to multiagent systems and mechanism design (3.2.1). Four recent agent-based solution
methods for solving the DRCMPSP are discussed in 3.2.2.
3.2.1
Multiagent Systems and Mechanism Design
The modern approach to AI is centred around the concept of an agent. An agent is anything that can perceive its environment through sensors and act upon that environment
through actuators. Such a notion of an agent is fairly general and can include human
agents (having eyes/ears/etc. as sensors, hands/legs/etc. as actuators), robotic agents
(having cameras as sensors, wheels as actuators), and software agents (having a graphical
user interface as sensor and as actuator). From this perspective, AI can be regarded as
the study of the principles and the design of artificial agents (Russell and Norvig, 2003).
Three key features are identified while designing an artificial agent. They are autonomy, intelligence, and interaction.
An agent being autonomous means that it is capable of independent action on
behalf of its user or owner. In other words, an agent can figure out for itself what
38

it needs to do in order to satisfy its designed objectives, rather than having to be
told explicitly what to do at any given moment.
Intelligence indicates that an agent pursues its goal(s) and executes its tasks in
such a way that it tries to optimise some given performance measures. An intelligent
agent is sometimes also referred to as a rational agent.
Agents are seldom stand-alone systems. In many situations they coexist and interact with other agents in several different ways. Interaction can take place both
directly (through a shared language and a communication protocol) and indirectly
(through the environment in which they are embedded).
A system that consists of a group of agents that have the potential to interact with
each other is called a multiagent system (MAS) (cf. Weiss, 2000; Shoham and LeytonBrown, 2009; Wooldridge, 2009). In a MAS, agents are assumed to act rationally on
behalf of their own interests, and it is generally assumed that their selfish behaviour
results in a situation that can be characterised by some sort of system equilibrium (cf.
Heydenreich et al., 2006). From a global perspective, such an equilibrium may of course
lead to suboptimal system performance.
The following two issues arise in such MAS settings.
Given a fixed decentralised setting in which agents selfishly act on behalf of their
own interests, try to characterise and analyse the quality of the resulting system
equilibria from the perspective of the overall system performance.
Try to design the decentralised setting in such a way that selfish agents are encouraged to show behaviour that results in system equilibria that nevertheless exhibit a
good overall system performance.
In economics and game theory, mechanism design is the study of designing rules of
a game or system to achieve a specific outcome, even though each agent may be selfinterested. This is done by setting up a structure in which agents have an incentive to
behave according to the rules. The resulting mechanism is then said to implement the
desired outcome. The solution concept is related to meta-game analysis, which uses the
techniques of game theory to develop rules for a game (cf. Shoham and Leyton-Brown,
2009).
3.2.2
MAS Solutions to DRCMPSP
There is a variety of suitable methods for solving decentralised manufacturing scheduling

problems (see Wellman et al. (2001) and Heydenreich et al. (2006)). However, in contrast
to the multi-project problem considered here, which is based on a complex and large
activity network, the manufacturing scheduling problems are frequently based on simple
and few precedence relations between the tasks that are to be planned (cf. Lee, 2002).
Therefore, the majority of these methods are merely marginally suitable for solving largescale and complex project-scheduling problems. For solving decentralised multi-project
scheduling problems, only a few methods are available (cf. Lee, 2002; Confessore et al.,
39
2007; Homberger, 2007; Wauters et al., 2010). Each of these four groups of researchers
proposed a MAS solution, in which multiple agents corresponding to the decision
makers (such as project managers) in the real multi-project environment collaborate,
guided by some coordination mechanism, to construct and select viable schedules2 .
Below, we discuss briefly the four existing MAS solutions, and compare the solution
methods in Table 3.2.
Agent Model
Intra-project
project
Authors
resource mediator scheduling
(activity)
agents
agents method
agents
fineLee (2002)
yes
yes
grained
Confessore
coarseno
yes
p-SGS & LFT
et al. (2007) grained
Homberger
coarseno
yes
RES
(2007)
grained
Wauters
coarselearning
no
yes
et al. (2010) grained
automata
Coordination mechanism
combinatorial auction
iterative combinatorial auction
negotiation
dispersion game & s-SGS
Table 3.2: MAS-based solution methods for DRCMPSP
Lee (2002)
Lee (2002) developed a MAS for decentrally planning a dynamic variant of the DRCMPSP
(see also Lee et al., 2003). The model is based on the assumption that several companies
or decision makers have to distribute their locally available resources to projects, which
appear dynamically during the planning horizon (i.e., equivalent to the variable-projectrelease-time problem, see 2.2.3). The core of the MAS scheduling framework is formed
by three types of agents: (1) resource agents, (2) activity agents, and (3) a coordinator
agent. A resource agent manages a single resource of a type in one department. An
activity agent is responsible for scheduling an individual activity. The coordinator agent
creates a marketplace where the resource-agent-managed resource capacities can be offered
for sale to the activity agents. The sale is handled through combinatorial auctions. We
note that the approach of modelling a resource agent for a single resource and modelling
an activity agent for an individual activity is fine-grained.
2A
recent work by Ara

uzo et al. (2009) also claims to have found a MAS solution for multi-project
scheduling problems. However, the problem they study is not quite a project-scheduling problem.
Below, we list three properties of their problem which clearly show the difference with our problem.
First, an activity in their problem only requires a single unit of resource. Second, the activities of a
project in their problem is arranged in a sequence, rather than in a network. Third, each resource type
defined in their problem only has a single unit. These three properties render their problem a machinescheduling problem. In addition, their objective is on project portfolio level rather than on operational
level.
40
Confessore et al. (2007)

Confessore et al. (2007) modelled two types of agents to deal with DRCMPSPs. The two
agent types are (1) project agents and (2) a coordinator agent. A project agent is responsible for scheduling one project comprising more than one activity. There are as many
project agents as projects. This modelling approach is coarse-grained compared to the
fine-grained model proposed by Lee (2002). For scheduling a project, the corresponding project agent uses a plain construction heuristic that consists of a parallel schedule
generation scheme (p-SGS) and a minimum latest finish time first (LFT) priority rule.
The coordinator agent is responsible for allocating the shared resources to the project
agents. The resource allocation is carried out via a combinatorial auction. Instead of
using a common objective, each project agent aims at minimising its makespan while
the coordinator agent declares the auction winners when the project agents compete for
the shared resources. The evaluations of MAS solution quality are carried out on several
multi-project instances, with up to 5 projects and 18 activities.
Homberger (2007)
In conformity with Confessore et al. (2007), Homberger (2007) adopted a coarse-grained
decomposition of the multi-project problem over agents (i.e., there are as many scheduler
agents as projects). Each scheduler agent is responsible for making schedules for one
project and a mediator agent is created to coordinate the resource allocations amongst
the scheduler agents. The scheduling procedure is carried out as follows. (1) The mediator
agent initially allocates resource capacities to each of the projects in a way that every
single project is feasibly solvable. (2) Each scheduler agent adopts a restart evolution
strategy (RES) (i.e., an evolutionary strategy that adaptively learns a better project
schedule, and a restart procedure that helps to escape from local optima) to construct
and learn a (near) optimal schedule based on the allocated resource capacities. (3) The
resource capacities allocated but unused by a project are sent back to the mediator agent.
(4) The mediator agent collects and aggregates all the unused resource capacities and
makes them observable to all scheduler agents. (5) Scheduler agents calculate possible
schedule improvement by RES, based on the current schedule plus the unused resource
capacities. (6) Improvements are sent to the mediator agent, who then selects the biggest
improvement and updates the pool of unused capacities. Steps 5 and 6 are repeated until
no improvement can be found. The solution methods that Homberger (2007) proposed
are capable of solving problems with up to 20 projects and 120 activities each, and the
performances are claimed to be competitive with a central solution using the RES.
Wauters et al. (2010)
Similar to the model proposed by Homberger (2007), the MAS model introduced by
Wauters et al. (2010) consists of two classes of agents project agents and one mediator
agent. Instead of making schedules for individual activities, the project agents construct
an activity list. They do so by employing a network of straightforward reinforcement
learning devices called learning automata. Coordination is achieved by a sequence game
(i.e., a dispersion game) in which each project agent submits its activity list and learns a
41
suitable place in the overall sequence of activity lists of all projects. The sequence game is
played using a probabilistic version of the basic simple strategy (BSS). The overall schedule
of all project activities is built by the mediator agent using a serial schedule generation
scheme (s-SGS). Wauters et al. (2010) use GT-MAS to denote their solution method. GTMAS stands for a game-theoretic MAS scheduling approach. GT-MAS produces so far
the best results in terms of average project delay (APD) in the Multi-project Scheduling
Problem Library (MPSPLib).
3.2.3
Towards a New MAS Solution
Multiagent systems offer many desirable properties (cf. Durfee and Rosenschein, 1994;
Weiss, 2000), such as (1) self-interestedness, (2) flexibility, (3) scalability, (4) efficiency, (5)
robustness, (6) reliability, (7) cost effectiveness, and (8) reusability. Within these desirable
properties, properties 1 to 3 are related to agent model and mechanism design, properties
4 and 5 involve the scheduling approaches employed by the agents, and properties 6 to 8
apply to the software development of the system3 .
In this subsection, we review the agent models and mechanisms in the aforementioned
four existing MAS solution methods and discuss their shortcomings with respect to the
three properties (a) self-interestedness, (b) flexibility and (c) scalability. The discussion
will lead to a new agent-based model for the AGH scheduling problem. The desired
properties 4 and 5 will be further investigated in Chapter 5 and 6.
A: Self-interestedness
Self-interestedness indicates that an agent concerns for its own advantage and well-being
in a multiagent system.
Three out of the four MAS models (i.e., the models proposed by Confessore et al.
(2007), Homberger (2007), and Wauters et al. (2010)) ignore totally the self-interestedness
of resource managers. In many modern industrial project-scheduling environments, resources shared by the projects are managed by third-party resource providers (or resource managers). The resource managers often have objectives different from those of
the project managers with respect to the resource allocations. In addition, within all
resource managers in a scheduling problem, one may have different objective(s) from the
others. Therefore, a more realistic MAS model has to take into account the self-interested
nature of resource managers in a project-scheduling environment.
B: Flexibility
Flexibility means the ability of incorporating new agents into the system without affecting
the operationality of the other agents.
Agent coordinations in all of the four MAS solution methods (auction (2), negotiation, dispersion game) are achieved in large-scale synchronous manners. The three
coordination mechanisms can be characterised as follows. (1) In the auction mechanisms
proposed by Lee (2002) and Confessore et al. (2007), an auction calls for a collection
3 In
this thesis, we focus on the desired properties 1 to 5 of a MAS system. Software development is
beyond the scope of this thesis.
42
of bids from a large number of agents. (2) In the negotiation mechanism proposed by
Homberger (2007), a schedule improvement requires a collection of improvement proposals from a large number of agents. (3) In the dispersion game for coordination proposed
by Wauters et al. (2010), the participation of all project agents takes place at the same
time. Large-scale synchronisation restricts new agents from easily joining in the system.
In order to increase flexibility, asynchronous coordination should be explicitly taken
into account in agent-based models (Boer et al., 2007).
C: Scalability
Scalability refers to the ability of accommodating an increased number of agents in the
system.
Thanks to the coarse-grained modelling approach, three out of the four MAS solutions (i.e., the solutions by Confessore et al. (2007), Homberger (2007), and Wauters
et al. (2010)) are able to scale to large problem instances. Although Lee (2002) models resource managers as self-interested agents, the proposed fine-grained model, where
each activity is modelled as an agent, creates easily a large number of agents when the
multi-project problem concerns a large number of activities. This increases significantly
inter-agent communication loads and synchronisation efforts especially when using auction as coordination mechanism. Methods in a fine-grained model can only solve small
problem instances (with up to 9 projects and 15 activities in their experiments). Therefore, a more scalable MAS model has to employ a coarse-grained model in order to scale
up with a large problem instance.
To summarise, designing an effective agent-based model for DRCMPSP requires for (1)
a coarse-grained modelling approach to encapsulate the agents, (2) a model that reflects
the self-interestedness of all agents, (3) an asynchronous coordination mechanism that
involves only a small number of agents at a time. In Chapter 4, we design an novel agentbased model for decentralised multi-project scheduling problem. The model includes
two classes of self-interested agents, as well as an asynchronous lease-based coordination
mechanism.
3.3
Project Scheduling under Uncertainty
In this section we survey approaches for scheduling projects under uncertainty. In general, we distinguish five classes of such approaches: (1) proactive-reactive scheduling, (2)
stochastic scheduling, (3) fuzzy scheduling, (4)contingent scheduling, and (5) sensitivity
analysis. The survey of each class is by no means exhaustive. It only intends to give the
reader a feeling of the research directions up to date.
3.3.1
Proactive-reactive Scheduling
Proactive-reactive scheduling is a two-stage scheduling approach. First, prior to the

project start, proactive scheduling constructs a baseline schedule (a.k.a. predictive schedule or pre-schedule) by employing an exact or a heuristic method. Then, while executing
3.3. Project Scheduling under Uncertainty
43
the baseline schedule, reactive scheduling revises or reoptimises the baseline schedule at
hand when an unexpected event occurs.
In case a proactive baseline schedule is developed using a deterministic scheduling
method without any anticipation of variability, the obtained optimal or sub-optimal baseline schedule will account for intensive reactive scheduling efforts. Every time a tiny
schedule disruption occurs, the proactive baseline schedule might be invalidated. To reduce the effort of reactive scheduling, robust proactive scheduling aims at constructing
a baseline schedule that incorporates anticipated project-execution variability prior to
the project start. Generating a robust proactive schedule prior to the project start may
significantly reduce the reactive-scheduling efforts. However, it should be observed that
a proactive scheduling will always require a reactive component to deal with schedule
disruptions that cannot be absorbed by the baseline schedule.
An exhaustive investigation and empirical study of proactive-reactive project scheduling can be found in van de Vonder et al. (2007).
3.3.2
Stochastic Scheduling
Stochastic scheduling is concerned with modelling operational uncertainty by a probabilistic random distribution of activity processing times. The stochastic scheduling methodology basically views the project scheduling problem as a multi-stage decision process.
Scheduling policies are used to define which activities are to be started at random decision
points over time, based on the observed and the a priori knowledge about the processing
time distribution.
The literature on stochastic project scheduling with resource constraints is rather
sparse. The larger body of theoretical work has been produced by a limited number of researchers (cf. Demeulemeester and Herroelen, 2002; Bonfill-Teixidor, 2006). By stochastic
project scheduling it is understood that (renewable) resource constraints are imposed;
this is to be contrasted with the Program Evaluation and Review Technique problem
(PERT-problem), which is resource-unconstrained and to which a large amount of literature has been devoted.
3.3.3
Fuzzy Scheduling
An alternative of modelling operational uncertainty into a probabilistic random distribution of activity processing times is to use a possibility-based model (fuzzy model).
There are several ways to fuzzify scheduling problems. Two important approaches are
(1) fuzzy activity processing time, and (2) fuzzy due time (Slowi
nski and Hapke, 1999).
The researchers advocating the fuzzy activity processing time approach argue that probability distributions for the activity processing times are unknown due to the lack of
historical data. As activity processing times have to be estimated by human experts,
in a non-repetitive or even unique setting, project management is often confronted with
judgements that are rather vague and imprecise. For example, the processing time of
an activity is clearly more than two days and less than five days; about three days is
usual. In those situations, which involve imprecision rather than uncertainty, the fuzzy
set scheduling literature recommends the use of fuzzy numbers for modelling activity processing times, rather than stochastic variables. Instead of probability distributions, these
44
quantities make use of membership functions, based on possibility theory (Herroelen and
Leus, 2005).
3.3.4
Contingent Scheduling
The contingent scheduling approach is based on the generation of multiple baseline schedules or baseline schedule fragments before and/or during project execution that either
optimally respond to anticipated disruptive events or are equivalent in performance (cf.
Herroelen and Leus, 2005). If a disruption effectively takes place, an adequate reaction
is simply to switch to the applicable schedule (fragment), or to shift to an equivalent
schedule compatible with the disruption. This approach focuses on flexibility rather than
robustness and is especially valuable for time-critical reactive scheduling (cf. Herroelen
and Leus, 2005).
3.3.5
Sensitivity Analysis
A number of recent research efforts focus on the sensitivity analysis of machine-scheduling

problems (Mauroy et al., 1997; Hall and Posner, 2004). Sensitivity analysis is the study
of how the uncertainty in the output of a mathematical model can be apportioned, qualitatively or quantitatively, to different sources of variation in the input of the model.
Sensitivity analysis addresses What if . . . ? types of questions that arise from parameter changes. The authors Hall and Posner (2004) study polynomially solvable and
intractable machine-scheduling problems and try to provide answers to a number of fundamental questions. Below we list six of them.
1. What are the limits to the change of a parameter such that the solution remains
optimal?
2. Given a specific change of a parameter, what is the new optimal cost?
3. Given a specific change of a parameter, what is a new optimal solution?
4. When does the objective function value remain optimal?
5. What types of sensitivity analysis are useful to evaluate the robustness of optimal
solutions?
6. What types of sensitivity analysis can be performed without using the full details of
the solution?
The use of sensitivity analysis for general decision-making under uncertainty has been
the subject of critique. We refer the reader to Wallace (2000), who stresses that flexibility
options are not appropriately recognised when using deterministic models with sensitivity
analysis. Wallace (2000) points out that the technique is appropriate only when analysing
an allowable variation in controllable parameters.
3.4
Chapter Summary
Numerous techniques have been employed to address the problems of project scheduling.
In this chapter, we reviewed the existing solution methods with emphases on the problems
3.4. Chapter Summary
45
in which (1) multiple projects are presented, (2) resources and projects are managed by
different autonomous decision makers, and (3) project executions are carried out in an
environment with various uncertainty. For clarity, we summarise them below together
with our conclusions.
First, we discussed centralised solution methods that deal with RCMPSP in a deterministic setting (see Section 3.1). The investigations have shown that (1) RCMPSPs are
strongly NP-hard problems and exact methods are impractical to be deployed for solving
real-world problems, and (2) heuristics and meta-heuristics are widely used in practice.
Second, we focused on investigating decentralised solution methods for problems with
decentralised decision makers (see Section 3.2). We discussed in detail four recent investigations (see Lee, 2002; Confessore et al., 2007; Homberger, 2007; Wauters et al., 2010)
and outlined the drawbacks of each of them in dealing with problems with autonomous
resource managers. The main issue here is that the managers are self interested.
Third, we discussed existing solution models that deal with uncertainty in scheduling problems (see Section 3.3). We listed five classes of approaches and discussed their
applicabilities in AGH scheduling problems.
Chapter 4
A Lease-based Multiagent
Model
AGH scheduling problems fall into a category of scheduling problems with information
asymmetry and decentralised decision-making processes (see Section 2.2). Solving such
a category of scheduling problems requires models and techniques that take into account
the strategic behaviour of individual decision makers (cf. Heydenreich et al., 2006). In
DAI, multiagent systems are known for being capable of dealing with problems with
inherent informational and managerial decentralisation (cf. Bonabeau, 2002; Shoham and
Leyton-Brown, 2009). Hence, it is appropriate to model an AGH scheduling problem in
an agent-based model and to solve it by a multiagent system. This chapter addresses our
first research question, which reads as follows.
model?
In Section 3.2, we listed several earlier attempts of employing agent-based systems for
modelling and solving DRCMPSPs (Lee et al. (2003), Confessore et al. (2007), Homberger
(2007), and Wauters et al. (2010)). We have shown that the agent-based models in
their systems cannot adequately represent an AGH scheduling problem. The inadequateness stems from potential communication overload caused by the fine-grained model to
non-self-interested resource-type managers. This means that the associated multiagent
scheduling systems are inappropriate for solving AGH scheduling problems (see 3.2.3). In
this chapter, we propose a novel agent-based model that serves as the solution framework
for dealing with AGH scheduling problems.
The proposed agent-based model comprises two modelling components: (1) modelling
agent representations, which involves choosing a proper agent-encapsulation approach to
model agents, and (2) modelling agent interactions, which involves designing a mechanism
that coordinates the agent decisions. In the first two sections of the chapter we address
the two components, respectively.
In Section 4.1, we propose a role-based agent model that adopts a physical-entityoriented encapsulation approach. Herein, we distinguish between two classes of agents,
48
A Lease-based Multiagent Model
i.e., resource agents and project agents. Each agent out of one of the two classes represents
a physical entity or an organisation in the real world.
In Section 4.2, we introduce a lease-based market mechanism for coordinating agent
decisions. In the mechanism, the scheduling decisions over a single activity are coordinated in a lease-based slot negotiation scenario. The scenario involves decisions of a
project agent and several resource agents.
Section 4.3 concludes the chapter by answering RQ1.
4.1
Agents, Schedules, and Utilities
The first main issue in agent-based modelling is to define accurately and properly the individual agents roles in a system. This issue depends on the decision what an agent should
encapsulate, namely, the decision on what precisely represents an agent (Lee et al., 2003).
Many encapsulation approaches exist for problems in a variety of situations. Among these
approaches, most of them fall into three major categories (cf. Shen and Norrie, 1999): (1)
the category of function-oriented approaches, (2) the category of physical-entity-oriented
approaches, and (3) the category of hybrid approaches,
In function-oriented approaches, agents are used to encapsulate some functions such
as task decomposition, activity coordination, conflict detection, and conflict resolution.
Agents defined in this category are referred to as task agents.
In physical-entity-oriented approaches, agents represent physical entities or organisations such as managers, workers, machines, and components; agents defined in the second
category are referred to as representative agents.
In hybrid approaches, both task agents and representative agents are employed. All
the four existing MAS solutions to DRCMPSP use hybrid modelling approaches. Examples of task agents are the coordinator agents in Lee (2002) and Confessore et al. (2007),
the mediator agents in Homberger (2007) and Wauters et al. (2010). Examples of representative agents are the activity agents and the resource agents in Lee (2002), the project
agents in Confessore et al. (2007), Homberger (2007), and Wauters et al. (2010).
The physical-entity-oriented approaches feature the self-interested nature of agents.
Plus, the approaches naturally define distinct sets of state variables that can be managed
efficiently by individual agents. Therefore, the approaches of the second category are appropriate for modelling the project-scheduling environment, where more physical entities
are involved compared to transaction-oriented information-system domains (cf. Lee et al.,
2003).
In DRCMPSPs, different resource types are managed by different resource-type managers. Similarly, different projects are managed by different project managers. These
(resource-type and project) managers are self-interested parties. They make scheduling
decisions autonomously with respect to their own objectives. Taking into account the
AGH-specific project-scheduling environment, we adopt the category of physical-entityoriented approaches. We will model resource-type managers and project managers as two
classes of agents, namely resource agents and project agents (see Figure 4.1).
In the following two subsections (i.e., 4.1.1 and 4.1.2) we specify the roles, schedules,
and utilities of the two agent classes.
49
4.1. Agents, Schedules, and Utilities

Encapsulation
approaches
3 categories
Function-oriented
approaches
[Task agents]
Physical-entity-oriented
approaches
[Representative agents]
Hybrid
approaches
[Task & representative agents]
2 classes
Resource agents
(4.1.1)
Project agents
(4.1.2)
Figure 4.1: Agent encapsulation approaches
4.1.1
Resource Agent, Schedule, and Utility
We model a first class of agents, namely resource agents, as the representatives of the
resource-type managers in a DRCMPSP. In the following, we define the role, the schedule,
and the utility of a resource agent.
Resource Agent
Let RAk denote the resource agent that is responsible for making schedules of resource
type Rk . The system includes as many resource agents as resource types, so |RAk | =
|Rk | = K (see 2.2.4).
In an AGH-specific DRCMPSP, a ground-service provider (e.g., a fuelling company)
can be seen as a resource-type manager. Hence, in our model, a resource agent represents
a ground-service provider. The role of a resource agent is managing the set of resources
of the same type (e.g., fuelling trucks) and makes the corresponding scheduling decisions
in order to maximise its utility.
Knowing the role of a resource agent, below we discuss what constitutes a resourceagent schedule.
Resource-agent Schedule
A schedule of a resource agent specifies for each of the activities, which request the use
of the resources managed by the resource agent, when and how many resources are
allocated to the activity.
An allocation can be represented by a tuple of three elements: (1) an activity, (2) a
time interval, and (3) a resource capacity of the resource type managed by the resource
agent. Below, we define the tuple as a resource-agent slot (see Definition 4.1).
50
R
= hA, I, Ri,
Definition 4.1 Resource-agent Slot. A resource-agent slot is a tuple i,j,k
in which
A = ai,j is an activity;
I = [ts , te ) is a time interval specified by a start time ts (inclusive) and an end time
te (exclusive);
R = (k : c) is the allocated resource capacities, defined by the resource type Rk and
a resource capacity c.
R
Figure 4.2 depicts a resource-agent slot i,j,k
on the timeline of the resource agent
RAk .
r
c
ai,j
ts
te
R
Figure 4.2: A resource-agent slot i,j,k
Resources of one type may be used by different activities from different projects. We
define a resource-agent schedule as a set of resource-agent slots, each of which involves
one activity (see Definition 4.2).
Definition 4.2 Resource-agent Schedule. A resource-agent
schedule k of resource

k
R
k
agent RAk is a set of resource-agent slots: = {i,j,k 1 i m 1 j ni ri,j
+
N }.
Figure 4.3 shows an example of a resource-agent schedule k consisting of six slots
( = {1 , 2 , . . . , 6 }). The dotted line in this figure indicates that the resource type
Rk is constrained by a maximum capacity ck (see resource-capacity constraint in 2.1.3).
Given a resource-agent schedule k , we can derive for each point in time the amount of
resources of Rk that are used by the scheduled activities, the so-called resource load. We
define resource load as follows.
k
Definition 4.3 Resource Load. Given a schedule k of a resource agent RAk , the
resource load of Rk at time point t is a function : T N, where
XX
R
R
R
(k , t) =
c(i,j,k
),
i,j,k
k t i,j,k
i
R
in which c() is the allocated resource capacity of slot (see Definition 4.1), and t i,j,k
R
stands for t I I i,j,k .
51
rk
ck
1
5
3
2
4
10:00
10:15
10:30
10:45
11:00
11:15
10:30
Figure 4.3: An example of a resource-agent schedule with six slots
The resource load should not exceed the maximum capacity of a resource type at any
time t, as the resource-capacity constraint should always be satisfied. We define a feasible
resource-agent schedule with resource-capacity constraint as follows.
Definition 4.4 A Feasible Resource-type Schedule. A schedule k of a resourceagent RAk is called feasible when k satisfies the following resource-capacity constraint:
(k , t) ck ,
t 0.
The primary task of a resource agent during scheduling is to construct a feasible

resource-agent schedule. Furthermore, if a resource agent has a choice among many
feasible resource-agent schedules, it would prefer a certain schedule to other schedules.
The preference can be measured by a utility function. In the following, we model the
utility of a resource agent.
Resource-agent Utility
Modelling resource-agent utilities addresses the self-interested nature of the resource
agents. In a DRCMPSP, a self-interested resource agent representing a resource-type manager is interested in allocating its own resources in the best way. Accordingly, resourcebased objectives are often considered by the resource agents while making scheduling
decisions.
A resource agent may consider a specific resource-based objective or a combination
of various resource-based objectives. Examples of resource-based objectives for a single
resource agent are minimising the resource procurement cost (i.e., a resource-investment
objective) and minimising the resource utilisation variation (i.e., a resource-levelling objective). Here, we choose a resource-levelling objective as an example objective to study
the utility of a resource agent. We note that choosing the resource-levelling objective is
arbitrary. The resource agents in the eventual MAS scheduling system are not restricted
to using such a particular objective only.
52
A resource-levelling objective strives for minimising the resource utilisation variation

over time. This objective is often achieved by minimising the sum of squared resource
utilisation costs, formulated as follows.
Find
k = arg min f (k ),
k
where f ( ) =
k
cuk
2 (k , t).
(4.1)
t0
We recall that cuk stands for the utilisation cost per unit of resource type Rk per unit
of time (see 2.1.4). It is important to notice that the objective function in Equation 4.1
is different from the one in Equation 2.15, where the latter minimises the overall costs of
all resource types. Instead, the objective here is only concerned with minimising the cost
of a single resource type (i.e., Rk ).
Since the objective of resource agent RAk is to minimise f (k ), we can model a
utility (performance measure of a given schedule) of RAk being the negative value of
f (k ). So, we have for resource agent RAk , a resource-levelling utility function:
URAk (k ) = cuk
4.1.2
2 (k , t).
(4.2)
t0
Project Agent, Schedule, and Utility
In our proposed agent-based model for AGH scheduling problems, the second class of
agents contains the project agents (see Figure 4.1). This subsection contains the model
of project agent, project-agent schedule and project-agent utility.
Project Agent
A project agent represents a project manager that is responsible for making scheduling
decisions for the corresponding project. Let PAi denote the project agent representing
the project manager of Pi . There are as many project agents as projects in the system,
so |PAi | = |Pi | = m (see 2.2.4).
In an AGH-specific DRCMPSP, a project refers to an aircraft turnaround process,
a project agent can be seen as a turnaround manager. It manages a set of groundhandling operations and makes the corresponding scheduling decisions to achieve certain
turnaround objectives.
Using a project agent to make scheduling decisions for all activities of the project
is a coarse-grained agent-based modelling approach (see 3.2.2). The coarse-grained
approach is in conformity with Confessore et al. (2007), Homberger (2007) and Wauters
et al. (2010). We have chosen to use the coarse-grained approach for the following
two reasons: (1) modelling each project manager by a software agent matches the selfinterested nature of agents; (2) a fine-grained modelling approach in which each activity
is represented by a software agent (see Lee, 2002) may create a vast amount of agents,
which as a consequence may cause an overload of inter-agent communications when a
project comprises a large number of activities.
53

Project-agent Schedule
In the scheduling phase, a project agent is responsible for finding for each of its activities
a schedule containing the required resource types. In case an activity requires resources
from more than one resource type, a schedule of an activity should comprise more than
one reservation. Each of the reservations is concerned with one resource type. Similar
to resource-agent slot, a reservation can be represented by a tuple of three elements: (1)
a time interval, (2) a resource requirement from a resource type, and (3) an activity, .
Below, we define the reservation tuple as a project-agent slot (see Definition 4.5).
P
Definition 4.5 Project-agent Slot. A project-agent slot is a tuple i,j,k
= hA, I, Ri,
in which
A = ai,j is an activity;
I = [si,j , si,j + pi,j ) is a time interval specified by start time si,j (inclusive) and
duration pi,j ;
k
R = (k : ri,j
) is a resource requirement defined by resource type Rk and required
k
amount ri,j .
Subsequently, we define an activity schedule (see Definition 4.6).

Definition 4.6 Activity
of an activity ai,j is a set of project Schedule. A schedule
P
k
agent slots i,j = {i,j,k
k {1, . . . , K} ri,j
N+ }.
Figure 4.4 shows an activity schedule i,j on the timeline of a project agent PAi .
In the figure, we notice that all slots in i,j have an identical time interval. This is
because all slots in i,j are related to the same activity (i.e., ai,j ), the time intervals of
I
the slots should be identical1 . Let = 0 denote the fact that two slots have the same
time interval I = I 0 , where I and I 0 0 . For any slots in an activity schedule, the
following equation holds.
I
P
P
i,j,k
= i,j,k
0,
P
P
i,j,k
, i,j,k
0 i,j .
(4.3)
Having defined an activity schedule in our agent-based model for DRCMPSP, we define
a project-agent schedule as follows.
Definition 4.7 Project-agent Schedule. A schedule of a project agent PAi is a set
of activity schedules i = {i,1 , i,2 , . . . , i,ni }, where i,j is the schedule of activity ai,j
(ai,j Ai ).
We recall that activities of a project are bound by precedence constraints and the
project may also have additional temporal constraints, such as a project-release-time
constraint and a project-deadline constraint (see 2.1.2). Below, we define a feasible
project-agent schedule (see Definition 4.8).
1 Slot-to-slot
relations are the same as interval-to-interval relations (see Figure 2.2). Likewise, the possible
temporal relations between a time point t and a slot are the same as the point-to-interval relations
(see Figure 2.3).
54
i,j
P
i,j,k
...
P
i,j,k
pi,j
si,j
Figure 4.4: An activity schedule i,j
Definition 4.8 A Feasible Project-agent Schedule. A schedule i of a project agent

PAi is called feasible when i satisfies all precedence constraints as well as all additional
temporal constraints:
I
P
P
ai,j ai,l , i,j,k
, i,l,k
0 i ,
P
P
i,j,k
i,l,k
0,
I
(4.4)
P
i,j,k
i ,
P
rli i,j,k
dli ,
I
where 0 indicates te () ts ( 0 ).
Similar to resource agents, a project agent having a choice among many feasible
project-agent schedules would prefer one feasible schedule to other feasible schedules.
In the following, we model the utility of a project agent.
Project-agent Utility
As discussed in 2.2.4, in the AGH-scheduling environment, a predefined time window at
a terminal gate (or at a remote stand) is assigned to an aircraft. The ending time of the
gate assignment is also the scheduled departure time of the aircraft for the next flight.
Thus, the departure time of an aircraft can be seen as the due time of its turnaround
process. A delayed departure is often punished by a delay penalty. As a consequence,
aircraft managers are trying to schedule all their ground-handling operations within the
gate-assignment time windows.
As mentioned in the resource-agent utility modelling, the resource utilisation costs
may vary from time to time. As a direct consequence, the price of receiving a ground
service varies as well. In this case, aircraft managers are trying to find the services with
relatively cheap prices for carrying out their ground-handling operations, while keeping
an eye on avoiding any departure delay. Hence, we have chosen for each project agent a
combination of two objectives: (1) minimising the project delay cost (i.e., cdl
i dli (i ))
and
(2)
minimising
the
total
service
costs
of
its
all
ground-handling
operations
(i.e.,
P
P
rc(
)).
i,j,k
P i
i,j,k
Find
i = arg min f (i ),
i
where f (i ) =
cdl
i
dli (i ) +
P
i,j,k
i
P
rc(i,j,k
).
(4.5)
55
Like in the resource-agent utility modelling, the utility function of a project agent PAi
is the negative value of f (i ):
X
P
rc(i,j,k
)
(4.6)
UPAi (i ) = cdl
i dli (i )
P
i
i,j,k
In the equations above, dli (i ) denotes the project delay given a schedule i (see
P
Equation 2.12). cdl
i denotes the delay cost per time unit for Pi . The function rc(i,j,k )
P
stands for the resource cost of the project-agent slot i,j,k .
The resource cost of a project-agent slot is set by a resource agent. In order to create
an incentive for project agents to reserve the slots that do not create resource utilisation
peaks, the resource agents will use a utility-decomposition technique to determine the
price of a slot. The detailed cost analyses will be discussed in Section 4.2.
4.1.3
A Conflict-free and Feasible Agent-based AGH Schedule
Earlier in this section, we defined a resource-agent schedule as well as a project-agent

schedule (see Definition 4.2 and 4.7). Below, we define an agent-based AGH Schedule.
Definition 4.9 An Agent-based AGH Schedule. An agent-based AGH schedule S
is a complete set of all agent schedules.
S = {S R , S P }
(4.7)
In Equation 4.7, S consists of two sets: (1) a complete set S R of all resource-agent
schedules (S R = {k k {1, . . . , K}}) and (2) a complete set S P of all project-agent
schedules (S P = {i i {1, . . . , m}}).
In order to retain an efficient solution to AGH scheduling problems an agent-based
AGH schedule need to be at least conflict free. Below we define a conflict-free agent-based
AGH schedule.
Definition 4.10 An Conflict-free Agent-based AGH Schedule. An agent-based
AGH schedule S is conflict free, when the following holds.
SR = SP ,
(4.8)

k
When an activity ai,j , of which the processing mode i,j = h{(k : ri,j
) k {1, . . . , K}
k
+
ri,j N }, pi,j i, on a resource type Rk is scheduled, two slots are created: (1) a resourceR
P
agent slot i,j,k
and (2) a project-agent slot i,j,k
. Subsequently, the resource-agent slot
R
R
R
R
R
i,j,k is included in S (i,j,k S ), and the project-agent slot i,j,k
is included in S P
P
P
(i,j,k S ). Since the two slots concern a same task (i.e., processing activity ai,j with
k
ri,j
amount of resource type Rk in a time interval I), a conflict-free schedule proclaims
R
P
the equivalence of the two slots: i,j,k
= i,j,k
. The equivalence implies that for any of
R
the slots in S there is an equivalent slot in S P , and vice versa.
Furthermore, an efficient solution to AGH scheduling problems requires an agent-based
AGH schedule to be at least feasible. Combining the definition of a feasible resource-agent
SR, SP S
56
schedule and the one of a feasible project-agent schedule, we can define a feasible agentbased AGH schedule as follows.
Definition 4.11 A Feasible Agent-based AGH Schedule. An agent-based AGH
schedule S is called feasible when none of the resource-capacity constraints, precedence
constraints, and additional temporal constraints are violated.
(k , t) ck ,
t 0, k S R
P
P
i,j,k
i,l,k
0,
P
P
P
ai,j ai,l , i,j,k
, i,l,k
0 i , i S
P
rli i,j,k
dli ,
(4.9)
P
i,j,k
i , i S P
In Section 4.2, we discuss how scheduling decisions of resource agents and project
agents can be coordinated in order to achieve such a conflict-free and feasible agent-based
AGH schedule.
4.2
Lease-based Market Mechanism
R
P
Scheduling the equivalence of a pair of slots (i,j,k
and i,j,k
) involves decisions of two
agents of different classes a resource agent RAk and a project agent PAi . Inevitably,
the decisions about the slots, such as the start times and finish times of the slots time
intervals, cannot be decided unilaterally by any one of the agents. The resource agent will
make sure that the slot is not violating the resource-capacity constraint and the project
agent will keep an eye on avoiding violation of precedence constraints and additional
temporal constraints. Moreover, when an activity requires more than one resource type,
the project agent also has to make sure that all project-agent slots of the activity schedule
have the same time interval (see Equation 4.3). Since the agents are autonomous decision
makers, the scheduling decisions of the agents have to be coordinated.
In this section, we describe a lease-based market mechanism. In the mechanism, resources of a certain type are regarded as merchandise or products owned by the resource
agent. A project agent leases a certain amount of resources for a period of time from a
resource agent to process one of its activities. A lease is a mutual commitment between
a project agent and resource agent. Since a lease (1) involves processing an activity, (2)
requires an amount of resources, and (3) lasts a period of time, it can be represented in
the form of a slot.
Since both the resource agent and the project agent are self-interested and autonomous
decision makers, they must have their own value systems on pricing any single slot. However, in the utility modelling of both classes of agents, the utilities are only concerned with
the entire agent schedule (i.e., a complete set of slots), instead of being concerned with
a single slot. Thus, we need techniques to decompose the agent utilities over individual
slots.
In this section, we first describe (1) how agent utilities are decomposed by resource
agents and project agents respectively for making scheduling decisions about a single
activity. Then, we present (2) the lease-based slot negotiation scenario that illustrates
4.2. Lease-based Market Mechanism
57
how a project agent interacts with one (or more than one) resource agent for scheduling
an activity.
4.2.1
Utility Decomposition
In 4.1.1 and 4.1.2, we saw that an agent schedule, both for a resource agent and for a
project agent, is composed of a set of slots. Agent utilities are performance measures based
on agent schedules. In this subsection, we investigate how resource agents and project
agents decompose their utilities over individual slots. We refer to the decomposed utilities
as (a) marginal resource-agent utility and (b) marginal project-agent utility, respectively.
Below, we derive the two marginal-utility formulas.
A: Marginal Resource-agent Utility
We recall that when a resource agent RAk considers the resource-levelling objective,
the utility URAk (k ) is the negative value of total squared resource utilisation cost (see
Equation 4.2).
R
Let i,j,k
be the resource-agent slot involving ai,j in the resource-agent schedule k ,
let k<i,j be the partial schedule of RAk when ai,j is going to be scheduled, and let ki,j
R
be the partial schedule of RAk when ai,j is scheduled. Thus, ki,j = k<i,j {i,j,k
}.
k
k
The difference between two utilities URAk (i,j ) and URAk (<i,j ) is the resource cost
R
of the slot i,j,k
. We refer to the difference as a marginal resource-agent utility. We
formulate it as follows.
X
mg
k
u
URA
(
)
=
c
[2 (k<i,j , t) 2 (ki,j , t)]
(4.10)
i,j
k
k
t0
We recall that (, t) is the resource load at the time point t given a schedule (see
Definition 4.3).
B: Marginal Project-agent Utility
Besides deciding on the decomposition of the resource-agent utility over individual slots,
we must also decide how to decompose the project-agent utility over individual activities.
Let i,j be the schedule of an activity ai,j (see Definition 4.6). i,j is a set of slots
P
k
{i,j,k
k {1, . . . , K} ri,j
N+ } and belongs to the project-agent schedule of PAi
<i,j
(i,j i ). Let i
be the partial schedule of PAi when activity ai,j is going to be
i,j
scheduled, and let i
be the partial schedule of PAi when ai,j is scheduled. Thus,
<i,j
i,j
=
.
i,j
i
i
We refer to the delay caused by scheduling an activity ai,j as a marginal delay
dlmg (i,j
). Equation 4.11 formulates the marginal delay.
i
i,j
<i,j
dlimg (i,j
) = tes
) tes
)
i,ni +1 (i
i,ni +1 (i
i
(4.11)
i,j
In this marginal delay formulation, the function tes
) denotes the earliest
i,ni +1 (i
possible start time of the fictitious activity ai,ni +1 given the current schedule i,j
.
i
58
That is, it denotes the earliest possible completion time of project Pi given the current
i,j
schedule i,j
. Thus the marginal delay cost using weight cdi becomes dcmg
) =
i
i (i
mg
i,j
dl
ci dli (i ).
Now the marginal project-agent utility for scheduling activity ai,j at si,j is defined as
the sum of the marginal delay cost and the marginal resource-agent utility.
mg
mg
i,j
mg
UPA
(i,j
) = cdl
) + URA
(i,j
)
i dli (i
i
k
i
k
4.2.2
(4.12)
Lease-based Slot Negotiation
Based on the marginal agent utility functions (see Equation 4.10 and Equation 4.12),
we now propose a scenario for inter-agent interactions referred to as a lease-based slot
negotiation. The scenario illustrates the interactions between a project agent PAi and
k
a collection of resource agents {RAk ri,j
N+ } for making the schedule of activity ai,j .
The scenario comprises the following five steps.
Step 1: Sending RfQs (see Figure 4.5) Project agent PAi initiates the
interaction by sending requests for quotations (RfQs) to the corresponding
k
resource agents {RAk ri,j
N+ }. The RfQ sent to RAk is a tuple that
consists of relevant information2 for scheduling ai,j :
<i,j
<i,j
k
RfQ ki,j = htes
), tls
), pi,j , ri,j
i.
i,j (i
i,j (i
ready to
schedule ai,j
Project Agent (P Ai )
k
N+ } )
Resource Agents ({RAk ri,j
<i,j
<i,j
k
tes
), tls
), pi,j , ri,j
i,j (i
i,j (i
Figure 4.5: Lease-based slot negotiation, step 1 Sending RfQs
Step 2: Receiving slot offers (see Figure 4.6) After the receipt of the
RfQ sent by PAi , each RAk uses its own pricing model (e.g., marginal resourceagent utility function given in Equation 4.10) to calculate a list of slot offers
k
Oi,j
, and sends the offers back to PAi .
2 For
<i,j
a problem without a project-deadline constraint, the latest possible start time tls
) of an
i,j (i
<i,j
activity ai,j may be positive infinity: tls
) = . In that case, the project agent will choose an
i,j (i
<i,j
upper bound of the start time for the slot request, denoted by tub
).
i,j (i
59
ready to
schedule ai,j
k
N+ } )
<i,j
<i,j
k
tes
), tls
), pi,j , ri,j
i,j (i
i,j (i
Calculates slot offers

k
Oi,j
k
Oi,j
Figure 4.6: Lease-based slot negotiation, step 2 Receiving slot offers
k
R
R
A slot offer oki,j,l Oi,j
is a resource-agent slot i,j,k,l
associated with a price Pr (i,j,k,l
):
R
R
oki,j,l = hi,j,k,l
, Pr (i,j,k,l
)i.
(4.13)
k
In Equation 4.13, l is the index of the offer oki,j,l in the offer list Oi,j
.
A
ai,j
ai,j
ai,j
ai,j
ai,j
<i,j
[tes
),
i,j (i
<i,j
[tes
(
)
+
i,j
i
<i,j
[tes
(
)
+
i,j
i
<i,j
[tls
),
i,j (i
Slot
I
<i,j
tes
) + pi,j
i,j (i
Price
R
k )
(k : ri,j
R
)
Pr (i,j,k,1
<i,j
1, tes
) + pi,j + 1)
i,j (i
k )
(k : ri,j
R
Pr (i,j,k,2
)
<i,j
2, tes
) + pi,j + 2)
i,j (i
...
k )
(k : ri,j
k )
(k : ri,j
R
Pr (i,j,k,3
)
...
k )
(k : ri,j
R
Pr (i,j,k,x
)
<i,j
tls
) + pi,j
i,j (i
k
Table 4.1: A list of slot offers Oi,j
for scheduling ai,j from RAk
Table 4.1 shows a list of offers sent by RAk to PAi . The half-open time interval of the
earliest slot offer oki,j,1 is
<i,j
<i,j
k
Ii,j,1
= [tes
), tes
) + pi,j ),
i,j (i
i,j (i
and the half-open time interval of the latest slot offer oki,j,x is
<i,j
<i,j
k
Ii,j,x
= [tls
), tls
) + pi,j ).
i,j (i
i,j (i
R
R
The resource capacity c(i,j,k,l
) of the slot i,j,k,l
in each offer should be equivalent to
k
the resource requirement ri,j in the RfQ:
R
k
c(i,j,k,l
) = ri,j
.
Step 3: Aggregating slot offers (see Figure 4.7) PAi receives from each
RAk a list of slot offers and aggregates the lists into a list of aggregated offers
i,j = {
O
oi,j,l }.
60
ready to
schedule ai,j
k
N+ } )
<i,j
<i,j
k
tes
), tls
), pi,j , ri,j
i,j (i
i,j (i
k
Oi,j

k
Oi,j
Aggregates offers
i,j
O
Figure 4.7: Lease-based slot negotiation, step 3 Aggregating and evaluating slot offers
Each aggregated offer oi,j,l contains the slot offers that have the same time interval.
I
R
R
i,j,k,l
0 = i,j,k 0 ,l00 ,
R
R
i,j,k,l
i,j,l
0 , i,j,k 0 ,l00 o
The resource price for each aggregated offer oi,j,l is the sum of the resource prices of
all the slots in oi,j,l :
X
R
Pr R (
oi,j,l ) =
Pr (i,j,k,l
0 ).
R
i,j,k,l
oi,j,l
0
i,j
PAi adds the potential marginal delay cost (i.e., dcmg
i (i,l ), see Equation 4.11) to
the summed resource price, and attains a total cost for each aggregated offer:
X
i,j
i,j
R
TC (
oi,j,l ) = Pr R (
oi,j,l ) + dcmg
Pr (i,j,k,l
) + dcmg
i (i,l ) =
i (i,l ).
R
i,j,k,l
oi,j,l
0
Activity
ai,j
ai,j
ai,j
ai,j
ai,j
Aggregated offer
Interval
<i,j
<i,j
[tes
),
tes
) + pi,j
(
i,j
i,j (i
i
<i,j
[tes
)
i,j (i
<i,j
[tes
(
)
i,j
i
+
+
<i,j
1, tes
)
i,j (i
<i,j
2, tes
(
)
i,j
i
i,j
R
Pr (i,j,k,1
) + dcmg
i (i,1 )
+ pi,j + 1)
k )}
{(k : ri,j
i,j
R
Pr (i,j,k,2
) + dcmg
i (i,2 )
+ pi,j + 2)
k )}
{(k : ri,j
k )}
{(k : ri,j
i,j
R
Pr (i,j,k,3
) + dcmg
i (i,3 )
...
k )}
{(k : ri,j
i,j
R
Pr (i,j,k,x
) + dcmg
i (i,x )
...
<i,j
[tls
),
i,j (i
Total cost
Resources
k )}
{(k : ri,j
<i,j
tls
) + pi,j
i,j (i
k
k
k
Table 4.2: Evaluating the aggregated offers for scheduling ai,j

Table 4.2 shows a list of aggregated offers and the total cost of each aggregated offer.
Step 4: Sending leases requests (see Figure 4.8) PAi sorts the aggregated offers in Table 4.2 based on the total cost, and chooses the aggregated
offer with the lowest total cost
61
arg min TC (
oi,j,l )
o
i,j,l
for scheduling ai,j . In case multiple aggregated offers have the same lowest
total cost, the one that starts first will be selected. PAi considers the slots in
the chosen aggregated offer as a set of leases, and sends the lease requests to
the corresponding resource agents.
ready to
schedule ai,j
k
N+ } )
<i,j
<i,j
k
tes
), tls
), pi,j , ri,j
i,j (i
i,j (i
k
Oi,j
Aggregates offers
i,j
O

k
Oi,j
arg min C T (
oi,j,l )
o
i,j,l
Figure 4.8: Lease-based slot negotiation, step 4 Sending leases requests
k
Step 5: Making leases (see Figure 4.9) Resource agent RAk in {RAk ri,j
+
R
R
N } receiving a lease request (i,j,k,l ) adds the lease to its schedule (i,j,k,l
k ), and sends an acknowledgement message to RAi . After receiving the
P
R
to its agent schedule
message, PAi adds an equivalent slot i,j,k,l
= i,j,k,l
P
(i,j,k,l i ).
Once making the schedule of ai,j has been completed, PAi can move on to schedule
the next unscheduled activity.
We note that in step 1 of the negotiation scenario, the RfQs sent by the project agent
PAi specify the earliest and latest possible start times of an activity. This guarantees
that the offers received in Step 2, as well as the leases made in Step 5 will neither violate
the precedence constraints nor the additional temporal constraint.
R
Likewise, in step 2 of the negotiation scenario, in case a slot i,j,k,l
violates the
R
resource-capacity constraint of RAk , the price of the slot Pr (i,j,k,l ) will be set to be
(positive) infinity by RAk . The underlying idea is that the project agent PAi will not
lease a slot with an infinite cost. In this way, resource-capacity constraints are not violated.
As long as the leases chosen makes both the resource-agent schedules and the projectagent schedule feasible, a global feasible schedule can be obtained.
62
ready to
schedule ai,j
k
N+ })
<i,j
<i,j
k
tes
), tls
), pi,j , ri,j
i,j (i
i,j (i
k
Oi,j
Aggregates offers
i,j
O

k
Oi,j
arg min C T (
oi,j,l )
o
i,j,l
Makes lease
R
i,j,k,l
k
ack
Makes lease
P
i,j,k,l
i
Figure 4.9: Lease-based slot negotiation, step 5 Making leases
An Example
Below, we illustrate the lease-based slot negotiation scenario by an example. In the
example, a project P1 in a DRCMPSP is released at rl1 = 0. The project has a due-time
constraint dt1 = 8, and a deadline constraint dl1 = 15. P1 comprises only one real activity
a1,1 , of which the mode 1,1 = h{(1 : 1), (2 : 2)}, 5i. The AoN network of P1 is depicted
in Figure 4.10.
P1 :
a1,0
a1,1
a1,2
0:0
(1:1), (2:2)
0:0
Figure 4.10: AoN network of an example project P1

The mode 1,1 specifies that (1) processing activity a1,1 requires one unit of resource
type R1 and two units of resource type R2 , (2) the estimated processing time is five time
units.
Scheduling a1,1 using the proposed lease-based slot negotiation scenario requires interactions among three agents one project agent (PA1 ) and two resource agents (RA1
and RA2 ). Below, we describe the scenario.
In step 1, PA1 sends out two RfQs: (i) RfQ 11,1 = h0, 10, 5, 1i to RA1 , and (ii) RfQ 21,1 =
h0, 10, 5, 2i to RA2 . In step 2, PA1 receives from each of the two resource agents a list of
slot offers (see Table 4.3 and Table 4.4). The calculations of the offer prices are carried out
by the two resource agents autonomously based on their own (resource-agent) utilities.
In Step 3, PA1 aggregates the two lists of offers and calculates the total cost of each
63
aggregated offer3 . We can see from Table 4.5 that the aggregated offer No. 4 has the
lowest total cost. Accordingly, in step 4, PA1 requests two leases for scheduling a1,1 :
R
R
R
1,1,1
= ha1,1 , [3, 8), (1 : 1)i and 1,1,2
= ha1,1 , [3, 8), (2 : 2)i. In step 5, RA1 adds 1,1,1
to
1
R
1
R
2
R
2
schedule : 1,1,1 ; similarly, RA2 adds 1,1,2 to schedule : 1,1,2 . After
receiving the acknowledgements from both of the two resource agents RA1 and RA2 , PA1
P
P
P
P
adds the two slots 1,1,1
and 1,1,2
to schedule 1 resulting in {1,1,1
, 1,1,2
} 1 . The
P
P
two slots together constitute by definition the schedule 1,1 of a1,1 : 1,1 = {1,1,1
, 1,1,2
}
(See Figure 4.11).
Offer
1
2
3
4
5
6
7
8
9
10
11
Slot
A
I
a1,1 [ 0, 5)
a1,1 [ 1, 6)
a1,1 [ 2, 7)
a1,1 [ 3, 8)
a1,1 [ 4, 9)
a1,1 [ 5, 10)
a1,1 [ 6, 11)
a1,1 [ 7, 12)
a1,1 [ 8, 13)
a1,1 [ 9, 14)
a1,1 [10, 15)
R
(1 : 1)
(1 : 1)
(1 : 1)
(1 : 1)
(1 : 1)
(1 : 1)
(1 : 1)
(1 : 1)
(1 : 1)
(1 : 1)
(1 : 1)
Price
Offer
300
200
150
150
140
120
120
100
100
100
100
1
2
3
4
5
6
7
8
9
10
11
Table 4.3: List of slot offers sent by RA1
Aggregated
Activity Interval
Offer
1
2
3
4
5
6
7
8
9
10
11
a1,1
a1,1
a1,1
a1,1
a1,1
a1,1
a1,1
a1,1
a1,1
a1,1
a1,1
[ 0,
[ 1,
[ 2,
[ 3,
[ 4,
[ 5,
[ 6,
[ 7,
[ 8,
[ 9,
[10,
Slot
A
I
a1,1 [ 0, 5)
a1,1 [ 1, 6)
a1,1 [ 2, 7)
a1,1 [ 3, 8)
a1,1 [ 4, 9)
a1,1 [ 5, 10)
a1,1 [ 6, 11)
a1,1 [ 7, 12)
a1,1 [ 8, 13)
a1,1 [ 9, 14)
a1,1 [10, 15)
R
(2 : 2)
(2 : 2)
(2 : 2)
(2 : 2)
(2 : 2)
(2 : 2)
(2 : 2)
(2 : 2)
(2 : 2)
(2 : 2)
(2 : 2)
Price
400
350
350
320
320
300
270
250
200
200
200
Table 4.4: List of slot offers sent by RA2
Resources
5) {(1 : 1), (2 : 2)}

6) {(1 : 1), (2 : 2)}
7) {(1 : 1), (2 : 2)}
8) {(1 : 1), (2 : 2)}
9) {(1 : 1), (2 : 2)}
10) {(1 : 1), (2 : 2)}
11) {(1 : 1), (2 : 2)}
12) {(1 : 1), (2 : 2)}
13) {(1 : 1), (2 : 2)}
14) {(1 : 1), (2 : 2)}
15) {(1 : 1), (2 : 2)}
Marginal
Delay
Cost
0
0
0
0
100
200
300
400
500
600
700
Resource
Costs
Total Cost
700
550
500
470
460
420
390
350
300
300
300
700
550
500
470
560
620
690
750
800
900
1000
Table 4.5: Aggregated offers for scheduling a1,1

With the scenario of the interaction between a project agent and two resource agents
as illustrated above, we successfully distribute the decision-making responsibilities and
3 We
assume that the unit-time delay cost of P1 is cd1 = 100.
64
1,1
P
1,1,1
P
1,1,2
10
15
Figure 4.11: Schedule of ai,j on the timeline of PA1

concerns among the individual and different types of agents. As a result of the lease-based
slot negotiation scenario, the overall schedule emerges.
4.3
Answer to Research Question 1
In this chapter, we addressed the first research question (see Section 1.2). [RQ1: How
can an AGH scheduling problem be represented in an agent-based model? ] We showed
that the AGH scheduling problem can be effectively modelled by an agent-based model.
The proposed model consists of (1) two classes of role-based agents resource agents
and project agents and (2) a lease-based market mechanism for coordinating the autonomous scheduling decisions of the individual agents.
Based on the illustrations of our proposed model in this chapter, we may answer
the first research question as follows. The essence of agent-based modelling lies in two
different aspects: (1) agent representation and (2) agent interaction. Both are briefly
discussed below.
Agent representation
For the first modelling aspect, we recall that in Section 2.2 an AGH scheduling problem
is formulated as an instance of a DRCMPSP/u. A DRCMPSP/u concerns two classes of
entities/organisations resource-type managers and project managers. The managers
may have their own self-interested objectives. Thus, in Section 4.1, we adopted a physicalentity-oriented agent-modelling approach, and modelled these two classes of entities as two
classes of agents: resource agents and project agents, respectively. The chosen physicalentity-oriented modelling approach provides a natural description of the AGH domain by
incorporating the two behavioural entities in a DRCMPSP/u. For modelling project
agents, we chose to use a coarse-grained approach. The chosen coarse-grained approach
allows the modelling of self-interested agents and avoids inter-agent communication overloads. The self-interested nature of the agents is represented by the utility modelling of
each of the two classes of agents. The chosen agent representation offers properties such
as self-interestedness and scalability to the agent-based scheduling system.
Agent interaction
For the second modelling aspect the following holds: in order to realise agent interaction, a
common language has to be defined. In the proposed model, we introduced a concept of
resource-time slot, that is used in both the resource-agent schedule and the project-agent
4.3. Answer to Research Question 1
65
schedule. In Section 4.2, we proposed a lease-based market mechanism. The mechanism

coordinates the scheduling decisions among two classes of heterogeneous agents. For
processing an activity, a lease (i.e., a time-resource slot) is negotiated by a resource agent
and a project agent. The agents evaluate the value of the slot based on their own value
systems (marginal agent utilities). As a result, the proposed coordination mechanism
successfully distributes the scheduling decisions over autonomous decision makers, and
as long as the slot chosen makes both the resource-agent schedule and the project-agent
schedule feasible, a global feasible schedule will be obtained. The proposed coordination
mechanism offers properties such as openness and efficiency to the agent-based scheduling
system.
Chapter 5
Online Iterative Scheduling

In a partially observable project-scheduling environment, pre-determined project schedules, i.e., schedules made before all projects have been released, frequently have to be
revised. This happens rather often in an AGH-scheduling environment where aircraft
often cannot arrive exactly at their expected arrival times. As discussed in 2.2.3, partial observability in a project-scheduling context is presented as variable project release
times. In this chapter, we address problems characterised by the first class of uncertainty.
Accordingly, we will answer research question 2, which reads as follows.
environment?
Scheduling solutions to problems that are under the nondeterministic aspect of uncertainty will be further investigated in Chapter 6 when we answer RQ3.
A straightforward solution to problems with variable project release times would be
to schedule the projects online when the projects are actually released. Online scheduling may guarantee the robustness of the schedules against variable project release times.
However, it can simultaneously be highly inefficient because the projects are scheduled sequentially according to the order of their actual release times. In this chapter, we propose
an online iterative (OI) approach (denoted by OI-MAS) in the proposed MAS scheduling
framework. OI-MAS aims at constructing an efficient and robust AGH schedule under
variable project release times.
OI-MAS consists of two components: (1) a clairvoyant online schedule generation
scheme (COSGS) and (2) an iterative schedule-improvement method (ISIM). The details
of the two components will be presented in Section 5.1 and in Section 5.2, respectively.
In Section 5.3, we conduct experiments to evaluate the performance of the proposed
approach, and provide empirical analyses of the system performance compared to three
state-of-art centralised and decentralised approaches (SASP, Bwd/Fwd, and GT-MAS).
Section 5.4 concludes this chapter by answering RQ2.
68
5.1
Clairvoyant Online Schedule Generation Scheme
In this section, we design a scheduling scheme that guides the scheduling procedure in
the proposed MAS scheduling system for solving DRCMPSP/u, in which variable project
release times occur. The designed scheme is in two levels. First, on the project level, we
adopt a clairvoyant online scheme (COS) in which the scheduling procedure of a project
can only start when the project is actually released. Second, on the activity level, we
adopt a serial schedule generation scheme (s-SGS) in which the schedule of a project is
built stepwise in accordance with the activity precedence relations. Below, we discuss
these two schemes in detail.
5.1.1
Clairvoyant Online Scheme
Traditional (offline) scheduling consists of employing a scheduling scheme where the

scheduling procedure can be carried out with full knowledge of the problem instance.
The knowledge is available in advance. However, in most planning and scheduling problems it is unlikely that all information necessary to define a problem instance is available
in advance. In an AGH scheduling environment, the relevant project information is gradually revealed along with the releases of the projects over time. As stated above, here
we focus on problems with variable project release times. For projects having expected
release times, the variable project release times mean that the actual project release
times are different from the expected ones. The variable project release times can also
mean that unanticipated new projects need to be incorporated on the fly.
In the context of variable project release times, two online scheduling schemes have
been proposed in the literature (cf. Vestjens, 1997): (1) a clairvoyant scheme and (2)
a non-clairvoyant scheme. If the online scheduling is clairvoyant, then the processing
requirement of all activities of a project is known as soon as the project is released or
even earlier. If the online scheduling is non-clairvoyant, then the processing requirements
of all activities of a project are not completely known at the projects release time. Instead,
the information is gradually revealed along with the progress of the project. In the latter
case, the project managers may, in the worst case, have to wait with scheduling an activity
until all the preceding activities have finished.
In the AGH-scheduling environment, the time scale on which services are required by
the aircraft makes the non-clairvoyant scheme impractical. The ground-service providers
need some preparation time before the actual services are to be provided. For this reason,
we adopt the clairvoyant online scheme (COS) in our MAS scheduling framework, i.e.,
assuming that the information of all activities of a project becomes known at the latest
at the moment the project is released. In practice, the starting activities (i.e., activities
having no (real) predecessors) of a project also require a certain amount of preparation
time before they can actually be performed. Therefore, a clairvoyant scheme assumes
that the information about starting activities of a project are known some time earlier
than the actual release time of a project, giving sufficient time for the preparation.
The COS employed is an incremental scheme in which the order of the projects to be
scheduled in a DRCMPSP/u is determined according to the order of the (actual) project
release times rli . In the next subsection, we discuss the scheme on the activity level,
69
5.1. Clairvoyant Online Schedule Generation Scheme
that is a scheme employed by each of the individual project agents to scheduling all its
activities.
5.1.2
Schedule Generation Schemes
Schedule generation schemes (SGSs) are the core of most centralised heuristic solution
procedures for RCPSP (cf. Kolisch and Hartmann, 1999). SGSs start from scratch and
build a feasible project schedule by stepwise extension of a partial project schedule. Two
different SGSs are distinguished: a serial SGS (s-SGS) and a parallel SGS (p-SGS). In
both s-SGS and p-SGS, a schedule of a project is constructed incrementally, where sSGS performs an activity-incremental procedure and p-SGS performs a time-incremental
procedure. A project agent at each step in both schemes chooses only one activity at a
time from a set of (precedent) eligible activities (i.e., non-scheduled activities of which
the predecessors are scheduled) to schedule. In case multiple activities are eligible, the
decision of choosing which activity is generally made through a priority-rule heuristic (see
3.1.2).
Readers who are interested in the details of these two schemes are referred to the work
by Kolisch and Hartmann (1999) for further reading. In the thesis, we adopt the s-SGS
for intra-project scheduling.
Combining COS and SGS, we have a complete scheme for scheduling a DRCMPSP/u
the clairvoyant online schedule generation scheme (COSGS).
5.1.3
An Example
Below, we use an example project P1 in a DRCMPSP/u to illustrate the COSGS. The

project P1 has an expected release time rl1 = 0, and a due-time constraint dt1 = 16. P1
consists of three precedence-related real activities: a1,1 a1,2 a1,3 . The AoN network
of P1 is depicted in Figure 5.1.
P1 :
a1,0
a1,1
a1,2
a1,3
a1,4
00
12
22
32
00
Figure 5.1: AoN network of an example project P1

0
10
15
Start time
Slot price
Marginal
Delay Cost
Total Cost
1200
100
1300
900
300
1200
600
400
1000
600
500
1100
10
500
600
1100
11
500
700
1200
12
5001 time
700
In the context
we assume that P1 is released
Step III of variable project release times,
... clairvoyant
...
...
unit laterImprove
than athe
1,2 expected release time (rl1 = 1). In the COSGS, the
a1,1
a1,2
a1,3
online scheme prevents this late-releasing incident from invalidating the current schedule.
1200
Step I
According
to Figure 5.1, the processing modes of the three real activities are
as1050
follows.
Schedule a
6
200
1,2
Step II
Schedule a1,3
a1,1
a1,1
a1,2
1,1 = h{(1 : 2)}, 5i
1,2 = h{(2 : 2)}, 3i
1,3 =ah{(3
1,2 : 2)}, 4i
a1,3
1250
...
70
1
2
3
4
5
6
7
8
..
.
A
a1,1
a1,1
a1,1
a1,1
a1,1
a1,1
a1,1
a1,1
..
.
Slot
I
[1, 6)
[2, 7)
[3, 8)
[4, 9)
[5, 10)
[6, 11)
[7, 12)
[8, 13)
..
.
R
(1 : 2)
(1 : 2)
(1 : 2)
(1 : 2)
(1 : 2)
(1 : 2)
(1 : 2)
(1 : 2)
..
.
Price
600
600
600
600
600
600
600
600
..
.
1
2
3
4
5
6
7
8
..
.
Table 5.1: Offers sent by RA1
1
2
3
4
5
6
7
8
..
.
A
a1,2
a1,2
a1,2
a1,2
a1,2
a1,2
a1,2
a1,2
..
.
Slot
I
[6, 9)
[7, 10)
[8, 11)
[9, 12)
[10, 13)
[11, 14)
[12, 15)
[13, 16)
..
.
R
(2 : 2)
(2 : 2)
(2 : 2)
(2 : 2)
(2 : 2)
(2 : 2)
(2 : 2)
(2 : 2)
..
.
Marginal
Delay Cost
0
0
0
0
100
200
300
400
Resource
Costs
600
600
600
600
600
600
600
600
Total
Cost
600
600
600
600
700
800
900
1000
..
.
..
.
..
.
Table 5.2: Aggregated offer for scheduling a1,1
Price
600
550
500
500
400
400
300
300
..
.
Aggregated offer
A
I
Rs
a1,1 [1, 6) {(1 : 2)}
a1,1 [2, 7) {(1 : 2)}
a1,1 [3, 8) {(1 : 2)}
a1,1 [4, 9) {(1 : 2)}
a1,1 [5, 10) {(1 : 2)}
a1,1 [6, 11) {(1 : 2)}
a1,1 [7, 12) {(1 : 2)}
a1,1 [8, 13) {(1 : 2)}
..
..
..
.
.
.
1
2
3
4
5
6
7
8
..
.
Aggregated
A
I
a1,2
[6, 9)
a1,2 [7, 10)
a1,2 [8, 11)
a1,2 [9, 12)
a1,2 [10, 13)
a1,2 [11, 14)
a1,2 [12, 15)
a1,2 [13, 16)
..
..
.
.
offer
Rs
{(2 : 2)}
{(2 : 2)}
{(2 : 2)}
{(2 : 2)}
{(2 : 2)}
{(2 : 2)}
{(2 : 2)}
{(2 : 2)}
..
.
Marginal
Delay Cost
0
0
0
0
100
200
300
400
Resource
Costs
600
550
500
500
400
400
300
300
Total
Cost
600
550
500
500
500
600
600
700
..
.
..
.
..
.
Instead, PA1 starts to make its project-agent schedule as soon as P1 is actually released.
The scheduling process of PA1 is carried out in an s-SGS, in which the three activities
are scheduled sequentially.
The proposed lease-base market mechanism (see Section 4.2) is employed to schedule
each of the three activities. For instance, P1 starts by negotiating with the resource
agent1 RA1 for making a schedule of a1,1 . The slot offers sent by RA1 are listed in
Table 5.1. The aggregated offers and the total cost2 of each aggregated offer can be found
in Table 5.2. In the table, we can see that four aggregated offers (No. 1 to No. 4)
have the same lowest total cost (600). The first offer that has a slot h[1, 6), (1 : 2), a1,1 i is
chosen by PA1 to schedule a1,1 since among four offers it is the first that starts (see step
4 in the slot negotiation scenario in 4.2.2). The schedule of the activity a1,1 is decided:
P
1,1 = {1,1,1
} = {h[1, 6), (1 : 2), a1,1 i}).
Similarly, a1,2 and a1,3 are scheduled using the same negotiation scenario. Table 5.3 to
5.6 show the slot offers and the aggregated offers for scheduling a1,2 and a1,3 . Eventually,
1 In
the example, each of the three activities requires only one resource type (R1 for a1,1 , R2 for a1,2 ,
and R3 for a1,3 , respectively). Thus, P1 negotiates with only one resource agent for scheduling an
activity. In practice, a project agent might need to negotiate with more than one resource agent in case
an activity requires multiple resource types.
2 We assume the delay cost per unit time of P is cdl = 100.
1
1
71
5.1. Clairvoyant Online Schedule Generation Scheme
1
2
3
4
5
6
7
8
..
.
A
a1,3
a1,3
a1,3
a1,3
a1,3
a1,3
a1,3
a1,3
..
.
Slot
I
[11, 15)
[12, 16)
[13, 17)
[14, 18)
[15, 19)
[16, 20)
[17, 21)
[18, 22)
..
.
R
(3 : 2)
(3 : 2)
(3 : 2)
(3 : 2)
(3 : 2)
(3 : 2)
(3 : 2)
(3 : 2)
..
.
Price
900
900
700
700
400
400
400
400
..
.
1
2
3
4
5
6
7
8
..
.
Aggregated
A
I
a1,3 [11, 15)
a1,3 [12, 16)
a1,3 [13, 17)
a1,3 [14, 18)
a1,3 [15, 19)
a1,3 [16, 20)
a1,3 [17, 21)
a1,3 [18, 22)
..
..
.
.
offer
Rs
{(3 : 2)}
{(3 : 2)}
{(3 : 2)}
{(3 : 2)}
{(3 : 2)}
{(3 : 2)}
{(3 : 2)}
{(3 : 2)}
..
.
Marginal
Delay Cost
0
0
100
200
300
400
500
600
Resource
Costs
900
900
700
700
400
400
400
400
Total
Cost
900
900
800
900
700
800
900
1000
..
.
..
.
..
.
a project-agent schedule 1 is obtained. Figure 5.2 depicts the project-agent schedule on

the projects timeline.
P
P
P
1 = {1,1 , 1,2 , 1,3 } = {{1,1,1
}, {1,2,2
}, {1,3,3
}}
= {h[1, 6), (1 : 2), a1,1 i, h[8, 11), (2 : 2), a1,2 i, h[15, 19), (3 : 2), a1,3 i}
1,1
1,2
1,3
P
1,1,1
P
1,2,2
P
1,3,3
10
15
(5.1)
Figure 5.2: Project-agent schedule 1 made by the COSGS

The total cost of the project-agent schedule 1 consists of two parts: (1) a project
delay cost (i.e., 300), and (2) a total resource cost (i.e., 600 + 500 + 400 = 1500). In all,
the total cost of 1 is 1800. Accordingly, the utility of PA1 is 1800.
5.1.4
A Discussion of Employing COSGS
We note that the choice of employing the COSGS completely overcomes the schedule
disruption caused by variable project-release-time uncertainty. However, there are potential drawbacks. We mention (1) scheduling online reduces the amount of available
information, (2) scheduling online can result in losing opportunities for a better allocation of the resources to the activities, and (3) both COS and SGS are one-pass scheduling
schemes without backtracking. The latter drawback implies that earlier determined activity schedules have no further changes in the COSGS. In order to reduce these drawbacks,
we propose in the following section a method to improve iteratively the earlier obtained
schedule in the course of scheduling.
72
5.2
Iterative Schedule-improvement Method
In this section, we describe an iterative schedule-improvement method (ISIM). For the sake
of providing utmost clarity, we emphasise that iterative and incremental are in no way
synonyms. In very special cases they are, but certainly not in our OI-MAS approach to
DRCMPSP/u.
In OI-MAS, we use two incremental schemes (COS and sSGS) and one iterative scheme
(ISIM). The COS is an incremental scheme on the project level and the sSGS is an
incremental scheme on the activity level. A complete schedule of a DRCMPSP/u is first
constructed project by project, and activity by activity in the COSGS. Afterwards, in the
ISIM a project-agent schedule is iteratively reconsidered for improvement.
It is important to notice that agent-based modelling enables autonomous decision
making. This allows us to propose a schedule-improvement method in which agents can
continuously search for opportunities from which they can improve the current schedules.
Schedule improvement is meant in terms of increasing an agents utility. We note that
there are two cases in which an activity schedule can be improved: (1) when there is
a schedule change of one of the activitys neighbouring activities (i.e., the activitys immediate predecessors and immediate successors), and (2) when there is a change of the
resource-type profile that is used by the activity. In the sequel, we describe in detail how
the ISIM improves the earlier obtained schedules in these two cases (5.2.1 and 5.2.2),
respectively.
5.2.1
ISIM by Secure-time-window Update
We recall that an activity ai,j has a dynamic earliest possible start time tes
i,j and a dynamic
ls
latest possible start time ti,j in the scope of the scheduling process. The earliest possible
start time tes
i,j of ai,j can be computed using Equation 5.2.
es
tes
i,j = max (rli , si,l + pi,l , ti,o + pi,o )
(5.2)
Equation 5.2 can be interpreted as follows. If ai,j has no immediate predecessors
( A i,j = ), the earliest possible start time tes

i,j of ai,j equals to the actual release time rli
of the project Pi . Otherwise, if A i,j 6= and ai,l is a scheduled immediate predecessor

of ai,j (ai,l ai,j i,l 6= ), tes
i,j should not be smaller than the scheduled finish time
(si,l + pi,l ) of ai,l . Furthermore, if A i,j 6= and ai,o is an unscheduled immediate

predecessor of ai,j (ai,o ai,j i,o = ), tes
i,j should be no smaller than the earliest
ef
es
possible finish time (ti,o = ti,o + pi,o ) of ai,o .
Similarly, the latest possible start time tls
i,j of ai,j can be computed using Equation 5.3.
ls
tls
i,j = min (dli pi,j , si,l pi,j , ti,o pi,j )
(5.3)
While scheduling the activity ai,j , project agent PAi communicates these two time
ls
points (tes
i,j and ti,j ) to the corresponding resource agents for the enquiry of slot offers
(see step 1 in the slot negotiation in 4.2.2). Since ai,j can only start in between the two
time points mentioned (both inclusive), we arrive at Equation 5.4.
73
5.2. Iterative Schedule-improvement Method
(5.4)
ls
tes
i,j si,j ti,j
Once all the neighbouring activities (immediate predecessors and immediate successors) of an activity ai,j are scheduled, rescheduling ai,j within the updated earliest/latest
possible start time will not cause any further delay of Pi . We therefore define a secure time
window for an activity when all the neighbouring activities of the activity are scheduled.
Definition 5.1 Secure Time Window. The secure time window of an activity ai,j is
a time interval that exists only when all the neighbouring activities of ai,j are scheduled.
The time interval starts from the activitys earliest possible start time tes
i,j (inclusive), and
ends by the activitys latest possible finish time tlf
(exclusive).
Formally,
we have
i,j
lf
s
Ii,j
= [tes
i,j , ti,j ).
In the following, we describe how to use the secure time window of an activity to
improve the activitys current schedule.
We illustrate the ISIM by using the same example project P1 as in 5.1.3. We consider
the project schedule 1 (Equation 5.1) obtained by the COSGS as the initial schedule.
In general, ISIM strives for improving i in terms of the project-agent utility UPAi (i ).
Below, we describe the first iteration of the ISIM. Without loss of generality, we assume
that the resource prices of the slot offers sent by the resource agents in the first iteration
are the same as they were in the COSGS.
s
We first look at the activity a1,1 . The secure time window I1,1
= [1, 8) of a1,1 was
activated by the scheduling of the activity a1,2 in the COSGS (see Figure 5.3). The
s
secure time window I1,1
allows PA1 to send new RfQs in the ISIM. In consequence,
three slot offers are received from RA1 (see Table 5.7). From the aggregated offer list
P
in Table 5.8, we can see that the schedule 1,1,1
= h[1, 6), (1 : 2), a1,1 i remains the best
option among all three slots. Therefore, no improvement can be made with respect to
1,1 in the first iteration of ISIM.
Slot
Price
A
I
R
1 a1,1 [1, 6) (1 : 2) 600
2 a1,1 [2, 7) (1 : 2) 600
3 a1,1 [3, 8) (1 : 2) 600
Table 5.7: Slot offers sent by RA1 in the first iteration of the ISIM
Aggregated offer
A
I
Rs
1 a1,1 [1, 6) {(1 : 2)}
2 a1,1 [2, 7) {(1 : 2)}
3 a1,1 [3, 8) {(1 : 2)}
Marginal
Delay Cost
0
0
0
Resource
Costs
600
600
600
Total
Cost
600
600
600
Table 5.8: Aggregated offers for scheduling a1,1 in the first iteration of the ISIM
74
1,1
1,2
1,3
P
1,1,1
P
1,2,2
P
1,3,3
10
15
s
I1,1
s
Figure 5.3: The secure time window I1,1
of a1,1 in iteration 1
1,1
1,2
1,3
P
1,1,1
P
1,2,2
P
1,3,3
10
15
s
I1,2
s
1,1
1,2
1,3
P
1,1,1
P
1,2,2
P
1,3,3
10
15
s
I1,3
19
s
s
For the activity a1,2 , a secure time window I1,2
= [6, 15) was activated by the
scheduling of a1,3 in the COSGS (see Figure 5.4). In consequence, seven slot offers
are received from RA2 (see Table 5.9). According to Table 5.10, a better schedule for
P
P
a1,2 can be made: 1,2,2
= h[12, 15), (2 : 2), a1,2 i. The change of the schedule 1,2,2
from
h[8, 11), (2 : 2), a1,2 i to h[12, 15), (2 : 2), a1,2 i will not cause any further delay of P1 . Instead,
P
it gives a lower resource cost (300) compared to the resource cost (500) of 1,2,2
in the
COSGS.
Once the new schedule of a1,2 is determined, the secure time window of a1,3 has been
s
= [15, 19) (see Figure 5.5). The secure time window coincides with the
changed to I1,3
schedule of a1,3 . Evidently, no schedule improvement can be made for a1,3 in iteration 1.
In all, PA1 through the first iteration of the ISIM revises the schedule 1,2 of a1,2
from h[8, 11), (2 : 2), a1,2 i to h[12, 15), (2 : 2), a1,2 i. The schedule revision results an improvement of total cost reduction of 200. The total cost of the project-agent schedule of
PA1 in iteration 2 is 1600, and the utility of PA1 is 1600.
P
1,1 = {1,1,1
} = {h[0, 5), {(1 : 2)}, a1,1 i}
P
1,2 = {1,2,2
} = {h[12, 15), {(2 : 2)}, a1,2 i}
P
1,3 = {1,3,3
} = {h[15, 19), {(3 : 2)}, a1,3 i}
Likewise, the schedule update of 1,2 causes a new update of the secure time window
s
I1,1
of the activity a1,1 . This creates a new opportunity for PA1 to reiterate its schedule
(i.e., iteration 2) for improvement. As a result, it turns out that the efficiency of 1 cannot
75
1
2
3
4
5
6
7
Slot
Price
A
I
R
a1,2 [6, 9) (2 : 2) 600
a1,2 [7, 10) (2 : 2) 550
a1,2 [8, 11) (2 : 2) 500
a1,2 [9, 12) (2 : 2) 500
a1,2 [10, 13) (2 : 2) 400
a1,2 [11, 14) (2 : 2) 400
a1,2 [12, 15) (2 : 2) 300
Table 5.9: Slot offers by RA2 in the first iteration of the ISIM
1
2
3
4
5
6
7
Aggregated
A
I
a1,2 [6, 9)
a1,2 [7, 10)
a1,2 [8, 11)
a1,2 [9, 12)
a1,2 [10, 13)
a1,2 [11, 14)
a1,2 [12, 15)
offer
Rs
{(2 : 2)}
{(2 : 2)}
{(2 : 2)}
{(2 : 2)}
{(2 : 2)}
{(2 : 2)}
{(2 : 2)}
Marginal
Delay Cost
0
0
0
0
0
0
0
Resource
Costs
600
550
500
500
400
400
300
Total
Cost
600
550
500
500
400
400
300
Table 5.10: Aggregated offers for scheduling a1,2 in the first iteration of the ISIM
be further improved in iteration 2. Thus, the project schedule obtained in iteration 1 is
currently the best schedule of PA1 .
We note that updates of activity secure time windows can only be caused by the
schedule changes of activities in the same project. Schedule changes of other projects
will not influence the secure time windows of this projects activities. The reason is
that precedence constraints only exist among activities of the same project. In the next
subsection, we discuss how the ISIM can improve a project-agent utility when schedule
changes of other projects occur.
5.2.2
ISIM by Resource-type-profile Update
Let us illustrate the ISIM in case there is an update of the resource-type profile. We
describe the method with the help of the same example project depicted in Figure 5.1.
This time we look at the timeline of the resource type R2 (see Figure 5.7). We remind
readers that R2 is the resource type required by the activity a1,2 . In Figure 5.7, the areas
under the dotted line are the resources leased by earlier scheduled activities.
Remember that in iteration 1 of the ISIM, activity a1,2 (of which 1,2 = h{(2 : 2)}, 3i)
P
was (re)scheduled on R2 at the slot 1,2,2
= h[12, 15), (2 : 2), a1,2 i. The resource price of
P
1,2,2 is 300 (see Table 5.9). We assume that after a1,2 has been (re-)scheduled in iteration
1, an activity a2,1 (2,1 = h{(2 : 2)}, 5i) of a newly released project P2 is then scheduled
P
at the slot 2,1,2
= h[13, 18), (2 : 2), a2,1 i (see Figure 5.7). The newly scheduled activity
a2,1 causes a profile update of the resource type R2 . The resource-type-profile update
76
Iteration 1
1,1
1,2
1,3
1
1,1
2
1,2
3
1,3
Iteration 2
0
10
15
1,1
1,2
1,3
1
1,1
2
1,2
3
1,3
10
15
Figure 5.6: Improves project-agent schedule 1 using the ISIM

2
2,1
2
1,2
Original
10
15
2
2,1
Resource-type
profile update
2
1,2
Schedule
improvement of
10
2
1,2
a1,2
10
15
2
2,1
15
Figure 5.7: Schedule improvement of a1,2 when R2 profile changes
changes the market in a way that the prices for the slot offers that overlap with the time
interval [13,18) will be raised.
When this resource-type-profile update occurs, RA2 would prefer the already scheduled activities to reschedule to a lower resource-cost slot in order to minimise its resource
levelling cost. To do so, RA2 will multicast a list of new slot offers to the project agents of
which the activities are scheduled at the slots overlapping with [13,18). As a consequence,
PA1 is informed by a new list of slot offers for scheduling a1,2 (see Table 5.13). Two issues
are worth noticing in the new list of offers: (1) the prices of two offers (i.e., offer number
6 and offer number 7) have been raised, and (2) the current cheapest offer is the offer
having a time interval [8,11).
P
The changes in the offer prices imply that the slot 1,2,2
= h[12, 15), (2 : 2), a1,2 i that
was leased by PA1 is now worth 300 more (600 300 = 300). This gives the project
P
agent PA1 an incentive to decommit from the lease 1,2,2
= h[12, 15), (2 : 2), a1,2 i, and
0P
recommit to a new lease 1,2,2 = h[8, 11), (2 : 2), a1,2 i. From the decommitment, PA1
will receive a compensation of 600 from RA2 . Adversely, from the recommitment, PA1
0P
pays 400 to RA2 for the new lease 1,2,2
. In all, PA1 saves 200 by rescheduling a1,2
77
1
2
3
4
5
6
7
Slot
I
[6, 9)
[7, 10)
[8, 11)
[9, 12)
[10, 13)
[11, 14)
[12, 15)
A
a1,2
a1,2
a1,2
a1,2
a1,2
a1,2
a1,2
R
(2 : 2)
(2 : 2)
(2 : 2)
(2 : 2)
(2 : 2)
(2 : 2)
(2 : 2)
Price
600
550
400
400
400
400
300
Table 5.11: Old offers sent by RA2
1
2
3
4
5
6
7
A
a1,2
a1,2
a1,2
a1,2
a1,2
a1,2
a1,2
Slot
I
[6, 9)
[7, 10)
[8, 11)
[9, 12)
[10, 13)
[11, 14)
[12, 15)
R
(2 : 2)
(2 : 2)
(2 : 2)
(2 : 2)
(2 : 2)
(2 : 2)
(2 : 2)
Price
600
550
400
400
400
600
600
Table 5.12: New offers sent by RA2
Table 5.13: ISIM - Resource offers update
from h[12, 15), (2 : 2), a1,2 i to h[8, 11), (2 : 2), a1,2 i, and the total cost of the schedule 1
in iteration 2 is 1400. The project-agent schedule obtained in iteration 2 is depicted in
Figure 5.8.
1,1
COSGS
1,2
ISIM-Iteration 1
P
1,3,3
10
15
1,1
1,2
1,3
P
1,1,1
P
1,2,2
P
1,3,3
ISIM-Iteration 2
1,3
P
1,2,2
P
1,1,1
10
15
1,1
1,2
1,3
P
1,1,1
P
1,2,2
P
1,3,3
10
15
Figure 5.8: Project-agent schedule 1 in iteration 2
Likewise, the rescheduling of activity a1,2 causes again the resource-type-profile update of the resource type R2 , this update creates new opportunities for earlier scheduled
activities of other projects on resource type R2 . We remind readers that the rescheduling
of a1,2 causes also the secure-time-window updates of a1,1 and a1,3 . These updates create
new opportunities to revise the project-agent schedule in the next iteration in order to
increase PA1 s utility. Therefore, the ISIM by resource-type-profile update leads to an
indirect inter-project-agent interaction. Each project agent improves its schedule by the
schedule changes of other project agents, and an improved global multi-project schedule
emerges.
In the following section, we conduct experiments to evaluate the performance of the
proposed OI-MAS scheduling approach.
78
5.3
Experiments
We remind the reader that the proposed OI-MAS scheduling approach consists of two
components. (1) a clairvoyant online schedule generation scheme (COSGS) and (2) an
iterative schedule-improvement method (ISIM). As we discussed in Section 5.1, when
projects in a DRCMPSP/u are scheduled in a COSGS, the presence of the first class of
uncertainty partial observability presented by variable project release times cannot
influence the obtained schedules. Therefore, the schedules made in the COSGS are robust
under the variable-project-release uncertainty. This section focuses on investigating by
experiments the efficiency of the schedules made by the proposed OI-MAS approach.
Since the COSGS is a single-pass scheduling scheme, the efficiencies of the schedules
built by OI-MAS highly depend on the effectiveness of the schedule-improvement method
(ISIM). In this section, we conduct experiments and empirically investigate two questions:
(1) how effective is ISIM?, and (2) how efficient are the schedules constructed by OI-MAS?
We first introduce the experimental setup (5.3.1). Subsequently, we present and discuss
the obtained results (5.3.2).
5.3.1
Experimental Setup
The introduction to the experimental setup includes (a) a description of the problem
instances, (b) performance criteria, and (c) the computational environment in terms of
hardware and software.
A: Problem Instances
We employ two sets of problem instances: (1) a set of 80 benchmark problems extracted
from the Library for Multi-project Scheduling Problem (MPSPLib3 ), and (2) a set of
10 simulated AGH scheduling problems. Below, we describe the properties of the two
problem sets.
(1) problem instances from MPSPLib
MPSPLib is developed and maintained by Homberger (2007). The library comprises
140 multi-project problem instances. The number of projects (m) in each instance is
2, 5, 10, or 20. Each multi-project problem instance is made up of RCPSP instances
from the Library for Project Scheduling Problems PSPLib4 , which is developed and
maintained by Kolisch and Sprecher (1997). The multi-project problem instances differ
in the composition of the chosen RCPSP instances as well as in the number of global
resource types5 (K = 1, 2, 3, 4) and the release times of the projects.
We have chosen 80 problem instances from the MPSPLib for experimenting our MAS
scheduling solution. The other 60 problem instances in MPSPLib are beyond our scope
3 MPSPLib
is accessible at http://www.mpsplib.com/. Last accessed on August 5, 2010.

is accessible at http://129.187.106.231/psplib/. Last accessed on July 15, 2009.
5 Some problem instances in MPSPLib have so-called local resource types. Local resource types refer
to the resource types of which the resource amount is dedicated to a single project. We decided to
use problem instances with only global resource types to highlight the importance of the self-interested
nature of resource agents.
4 PSPLib
5.3. Experiments
79
of study because they consider problems with local resource types. The properties of the
80 chosen problem instances can be found in Appendix B: Properties of the chosen 80
MPSPLib Instances.
For brevity reasons, in the rest of this thesis, we will use the alias in Table B.1 to
refer to the corresponding problem instance.
(2) simulated AGH scheduling problem instances
Besides experimenting with benchmark problems, we are also interested in investigating
the performance of OI-MAS in simulated AGH scheduling problems. We simulate a set
of AGH scheduling problems taking into account both the variety of aircraft turnaround
processes and the difference in airport sizes.
First, we can distinguish several types of aircraft turnaround processes based on the
differences in aircraft models (Boeing 747, Airbus 320, etc), aircraft usages (cargo or
passenger aircraft) and docking locations (terminal gate or remote stand). Different
turnaround processes may require different sets of ground handling operations. For instance, (i) the precedence relations among activities may be different, (2) same type of
activities may require different types and amounts of resources, and (iii) activity processing durations may also be different in different turnaround processes. Nevertheless,
ground handling activities performed in the same type of turnaround process share a
large scale of similarities. Based on these observations, we simulate 10 types of aircraft
turnaround processes by using 10 project instances (J301 1 J301 10) from PSPLib.
One project instance consists of 30 activities, which resembles the number of ground
handling operations required for an aircraft turnaround. The shared 4 resource types in
an instance can be considered as 4 self-interested ground service providers. The optimal
makespans for these 10 projects range from 30 to 60. We take the minute as the unit of
time, these makespans resemble aircraft turnaround durations in actual situation.
Second, we consider a full range of airport sizes in terms of the number of aircraft
movements. The busiest airport in the world, Atlanta International Airport in 2009,
handled on average 1,300 aircraft a day (ACI, 2009). This means that, in every minute
at peak hours, almost 2 aircraft land and another 2 take off. On the other hand, a small
regional airport only handles a couple of aircraft a day.
According to the two types of varieties, we simulate a set of 10 instances of AGH
scheduling problems (see Table 5.14).
B: Performance Criteria
The effectiveness of ISIM is evaluated by the improvement ratio of each project-agent
schedule. The improvement ratio of a project-agent schedule measures how much the
utility of a project agent is improved by applying ISIM.
The efficiency of schedules made by OI-MAS is evaluated by comparing the OI-MAS
schedules to the schedules obtained by three other well known solution methods in the
literature. Each of the three solution methods is chosen from a different solution category.
They are (1) a centralised single-pass priority-rule-based heuristic approach SASP
by Lova and Tormos (2001), (2) a centralised forward-backward metaheuristic approach
(Fwd/Bwd) by Lova et al. (2000), and (3) a game theoretical MAS approach (GT-MAS)
80
Instance
IA2
IA3
IA6
IA10
IA20
IA30
IA40
IA60
IA80
IA120
No. of
operations
per aircraft
30
30
30
30
30
30
30
30
30
30
No. of
aircraft
2
3
6
10
20
30
40
60
80
120
No. of
resource
types
4
4
4
4
4
4
4
4
4
4
Project instances
Arrival period
J301 1 J301 2
J301 3 J301 5
J301 5 J301 10
J301 1 J301 10
(J301 1 J301 10) 2
(J301 1 J301 10) 3
(J301 1 J301 10) 4
(J301 1 J301 10) 6
(J301 1 J301 10) 8
(J301 1 J301 10) 12
30 mins
20 mins
10 mins
6 mins
3 mins
2 mins
2 per 3 mins
1 min
4 per 3 mins
2 per 1 min
Table 5.14: Simulated AGH Scheduling Problems

by Wauters et al. (2010). In general, each of the three solution methods produces the
best schedules in their solution category.
The efficiency evaluation takes the form of two performance measures: (1) average
project delay (APD in Equation 2.22) and (2) total squared resource utilisation (TSRU
in Equation 2.14).
C: Computational Environment
To perform experiments, we implemented OI-MAS in a java-based agent programming
platform Emerge (a component of CHAP Common Hybrid Agent Platform6 ). The
experiments took place on a desktop computer with a 32bit 2.2GHz Intel Core 2 Duo
processor and a 2G DDR2 RAM.
5.3.2
Results and Analysis
Below, we study the experimental results concerning both ISIM and OI-MAS as a whole.
We subsequently investigate (a) the effectiveness of the schedule-improvement method
ISIM, (b) the efficiency of the multi-project schedules constructed by the proposed OIMAS approach, with comparison to the three other well-known solution methods, and (c)
the flexibility of OI-MAS.
A: Effectiveness of ISIM
To evaluate the effectiveness of ISIM, we keep track of the schedules built by project
agents in every iteration. The improvement ratio of a project-agent schedule is in terms
of utility improvement of each project agent. We recall that the utility of a project agent
is the negative value of its total cost a combination of the project delay cost and the
projects resource cost (see Equation 5.5).
6 CHAP
can be found at http://chap.sourceforge.net/, last accessed on August 1, 2010.
81
5.3. Experiments
f (Si ) = cdl
i max(si,ni +1 dti , 0) +
Rk R
cuk
u2k (Si , t)
(5.5)
0t
We assume that the project unit delay cost cdl

i = 100 for all projects, and the resource
unit utilisation cost cuk = 1 for all resource types. In reality, OI-MAS allows different
(resource and project) agents to choose their own cost models.
I90/2/1
I90/2/2
I90/2/3
I90/2/4
I90/2/5
I90/2/6
I90/2/7
I90/2/8
I90/2/9
I90/2/10
Avg.
Imprv.
Ratio
9.2%
3.5%
14.1%
12.0%
7.3%
7.4%
6.6%
8.2%
3.7%
10.9%
I120/2/1
I120/2/2
I120/2/3
I120/2/4
I120/2/5
I120/2/6
I120/2/7
I120/2/8
I120/2/9
I120/2/10
18.1%
12.1%
20.1%
22.0%
18.3%
3.5%
10.6%
10.0%
14.5%
21.8%
Problem
I90/5/1
I90/5/2
I90/5/3
I90/5/4
I90/5/5
I90/5/6
I90/5/7
I90/5/8
I90/5/9
I90/5/10
Avg.
Imprv.
Ratio
8.1%
5.1%
9.0%
3.4%
13.1%
3.3%
1.5%
3.8%
1.3%
7.8%
I120/5/1
I120/5/2
I120/5/3
I120/5/4
I120/5/5
I120/5/6
I120/5/7
I120/5/8
I120/5/9
I120/5/10
21.1%
10.2%
25.2%
22.9%
21.0%
4.2%
10.5%
13.4%
17.2%
22.8%
Problem
I90/10/1
I90/10/2
I90/10/3
I90/10/4
I90/10/5
I90/10/6
I90/10/7
I90/10/8
I90/10/9
I90/10/10
Avg.
Imprv.
Ratio
18.1%
12.1%
20.1%
22.0%
18.3%
3.5%
10.6%
10.0%
14.5%
21.8%
I120/10/1
I120/10/2
I120/10/3
I120/10/4
I120/10/5
I120/10/6
I120/10/7
I120/10/8
I120/10/9
I120/10/10
30.3%
23.1%
26.3%
24.6%
23.0%
5.1%
12.4%
15.7%
21.5%
29.0%
Problem
I90/20/1
I90/20/2
I90/20/3
I90/20/4
I90/20/5
I90/20/6
I90/20/7
I90/20/8
I90/20/9
I90/2/10
Avg.
Imprv.
Ratio
28.4%
21.3%
19.2%
23.2%
19.0%
5.3%
11.2%
9.2%
12.9%
15.2%
I120/20/1
I120/20/2
I120/20/3
I120/20/4
I120/20/5
I120/20/6
I120/20/7
I120/20/8
I120/20/9
I120/2/10
32.2%
21.1%
31.9%
24.6%
36.1%
4.9%
18.4%
15.1%
20.7%
32.1%
Problem
Table 5.15: Average improvement ratios by ISIM on the 80 MPSPLib problem instances
Table 5.15 and Table 5.16 show the average improvement ratios by the ISIM of (i)
the 80 MPSPLib problem instances and (ii) the 10 simulated AGH scheduling problems,
respectively. From the average improvement ratios shown in the tables, we derive two
observations as follows.
Observation 1 All initial project schedules made in the COSGS are improved
by the ISIM. On average, the improvement ratio is 15.1%.
Observation 2 The improvement ratios are dependent on the problem size.
In general, more improvement can be obtained in large problems with more
projects.
82

Problem Avg. Imprv. Ratio
IA2
2.2%
IA3
8.1%
IA6
8.7%
IA10
12.2%
IA20
14.6%
IA30
17.3%
IA40
18.2%
IA60
18.9%
IA80
21.0%
IA120
23.3%
Table 5.16: Average improvement ratios by ISIM on the simulated AGH instances
Problem
I90/10/1
I90/10/2
I90/10/3
I90/10/4
I90/10/5
I90/10/6
I90/10/7
I90/10/8
I90/10/9
I90/10/10
P1
37.6%
18.3%
56.8%
20.3%
30.3%
3.0%
3.3%
16.1%
2.4%
37.4%
P2
26.6%
4.3%
49.3%
18.4%
22.1%
2.6%
3.9%
35.5%
39.1%
1.4%
P3
19.8%
7.1%
12.7%
24.7%
25.0%
12.4%
5.6%
3.7%
27.8%
44.1%
P4
3.6%
34.1%
13.1%
4.4%
13.3%
1.7%
15.0%
2.3%
3.0%
13.2%
P5
28.1%
9.3%
9.84%
27.5%
13.9%
0.2%
6.2%
6.2%
11.7%
22.7%
P6
3.4%
8.9%
5.14%
12.9%
20.3%
6.5%
10.4%
5.4%
21.9%
43.9%
P7
9.1%
16.1%
26.7%
38.2%
20.6%
1.9%
38.5%
8.6%
13.5%
3.1%
P8
8.0%
11.8%
7.05%
37.3%
15.3%
1.6%
4.2%
10.7%
6.0%
14.4%
P9
26.0%
7.8%
19.7%
8.5%
7.2%
4.5%
13.9%
8.0%
3.7%
17.9%
P10
18.6%
3.8%
0.96%
27.1%
14.6%
1.1%
5.5%
2.9%
16.3%
21.0%
Table 5.17: Project-by-project improvement ratios by ISIM on 10 I90/10 instances

Furthermore, we have chosen 10 problem instances and looked into the improvement
ratios project by project. Table 5.17 shows the project-by-project improvement ratios on
the 10 I90/10 instances.
Observation 3 The ISIM improvement ratio varies from project to project.
In Table 5.17, we see that some project schedules can be improved significantly (e.g.,
56.8% for project P1 in problem instance I90/10/3). However, some others only make
little improvement (e.g., 0.2% of project P5 in problem instance I90/10/6). This is due to
the difference in project release times, as well as the project structure itself. In general,
the earlier the projects are released, the more iterations of improvement there are. This
gives the earlier-released projects more chances for schedule improvement. However, it
does not necessarily mean that more improvements are made within the earlier-released
projects. We notice that the activity network and the resource requirements of a project
play important roles of improvement ratios. In general, the more resource types/amounts
an activity requires, the more chance there is that the activity schedule can be improved.
Based on the three observations listed above, we validate the effectiveness of the ISIM
83
5.3. Experiments
in improving schedules made in the COSGS.
B: Efficiency of OI-MAS
In order to investigate the efficiency of OI-MAS, we first look at the number of iterations
needed for ISIM in order to achieve a stable7 schedule.
Problem instances Min Max Avg Problem instances Min Max Avg
I90/2
2
5
3 I120/2
4
9
5
I90/5
5
26
12 I120/5
7
28
14
I90/10
10
69
34 I120/10
13
99
46
I90/20
18 203 63 I120/20
20 289 69
Table 5.18: Minimal, maximal, and average numbers of iterations to achieve a stable
schedule
2.6E+5
P1
P2
P3
P4
P5
2.4E+5
P6
P7
P8
P9
P10
2.2E+5
Total costs per project
2E+5
1.8E+5
1.6E+5
1.4E+5
1.2E+5
1E+5
0.8E+5
0.6E+5
10
15
20
25
30
35
40
45
50
Number of iterations
Figure 5.9: Schedule improvement by ISIM for the 10 projects in I90/10/1
Table 5.18 shows the minimal, maximal, and average numbers of iterations needed for
ISIM to achieve a stable schedule. In additional, Figure 5.9 plots the evolution of the
7 In
this context, stable means that no more improvement can be made by ISIM. Later in Chapter 6, we
will introduce the notion of stability in a different context.
84
schedules improvement for all the 10 projects in problem instance I90/10/1. Based on
Table 5.18 and Figure 5.9, we arrive at the following observation.
Observation 4 After a small amount of iterations, agents can find stable
schedules.
When the scheduling time scale is critical, such as in the AGH scheduling environment,
the number of iterations in order to reach a much improved schedule is crucial. From
Table 5.18, we see that the maximum number of iterations to achieve a stale schedule is
289. In average, project agents require fewer than 70 iterations to reach a stable schedule.
The small number of iterations demonstrates the efficiency of ISIM in making schedule
improvement.
Below, we compare the efficiency of the obtained OI-MAS schedules to the state-of-theart solution methods. We look at the schedules made for both the MPSPLib instances
(see Table 5.19 and Table 5.20) and the simulated AGH instances8 (see Table 5.21).
For the time-based objective (APD) , we observe that two approaches (GT-MAS and
Fwd/Bwd) outperform OI-MAS. Within these two approaches, GT-MAS performs the
best in general. In all, GT-MAS, Fwd/Bwd, and OI-MAS outperforms the single-pass
heuristic approach SASP. Nevertheless, with respective to the resource-based objective
(resource levelling measure TSRU in our case), OI-MAS outperforms significantly all three
other approaches and results in a lowest total squared resource utilisation (see Table 5.20).
Based on observation No. 4 and the two tables above, we can conclude the efficiency of
OI-MAS.
Problem
instances
I90/2
I90/5
I90/10
I90/20
I120/2
I120/5
I120/10
I120/20
OI-MAS
135.5 (-9.64%)
379.78 (-4.97%)
227.92 (-16.4%)
142.5 (-5.35%)
51 (-7.27%)
232 (-2.27%)
139.1 (-3.90%)
215.5 (-5.23%)
APD (percentage)
GT-MAS
Fwd/Bwd
103.15 (-31.2%) 110.3 (-26.4%)
245.56 (-38.6%) 314.7 (-21.3%)
169.37 (-37.9%) 201.89 (-25.9%)
85.44 (-43.3%) 90.45 (-39.9%)
35.2 (-36.1%)
37.9 (-31.1%)
178.8 (-24.7%) 192.1 (-19.1%)
114.33 (-21.0%) 125.1 (-13.6%)
158.6 (-30.3%) 164.3 (-27.7%)
SASP
149.95 (0)
399.62 (0)
272.6 (0)
150.6 (0)
55 (0)
237.38 (0)
144.74 (0)
227.4 (0)
Table 5.19: Comparison of four methods on average project delay (APD)
C: Flexibility of OI-MAS
In OI-MAS, the decision on a lease commitment is dependent on the utility measurement
of two agents. The case of two agents choosing a different utility measurement may
result in two different global schedules. We conduct a series of 30 experiments using the
8 Because
the simulated AGH instances are not benchmark instances, there are no schedules made by other
three approaches available for comparison. A special gratitude goes to Tony Wauters for generating the
results by his GT-MAS approach.
5.3. Experiments
Problem
instances
I90/2
I90/5
I90/10
I90/20
I120/2
I120/5
I120/10
I120/20
85
TSRU (percentage)
OI-MAS
GT-MAS
Fwd/Bwd
SASP
155492 (-19.5%)
198201 (+2.59%)
199343 (+3.18%)
193196 (0)
440645 (-18.8%)
540851 (-0.38%)
542149 (-0.14%)
542908 (0)
2884382 (-3.88%) 3044724 (+1.47%) 3015612 (+0.50%) 3000659 (0)
13510595 (-32.5%) 21014051 (+4.99%) 20183423 (+0.84%) 20015696 (0)
154613 (-26.4%)
216778 (+3.25%)
213464 (+1.67%)
209953 (0)
698139 (-18.3%)
859159 (+0.50%)
858641 (+4.35%)
854925 (0)
5692162 (-13.1%) 6744306 (+3.00%) 6698644 (+2.30%) 6548068 (0)
18134135 (-14.3%) 21249026 (+0.39%) 21205962 (+0.19%) 21166573 (0)
Table 5.20: Comparison of four methods on total squared resource utilisation (TSRU)
Problem
APD
TSRU
No. of average iterations
GT-MAS
instances OI-MAS GT-MAS OI-MAS GT-MAS OI-MAS
IA2
26
6
13586
16908
3
4160
IA3
15
1.67
26234
38322
8
3532
IA6
18.2
4.57
64190
81887
16
6220
IA10
27.9
15.41
151087
180471
29
4688
IA20
56.4
44.1
382580
453284
55
3402
IA30
72.5
59.5
721869
844369
104
4780
IA40
91.3
77.0
1093058 1277400
137
5479
IA60
80.9
74.7
2472212 2953207
166
5338
IA80
86.6
76.2
4169612 5097988
229
3750
IA120
108.4
104.7
7851954 9318896
336
4778
Table 5.21: Comparison of APD and TSRU on simulated AGH instances
problem instance I90/10/1. In the experiments, we assume (1) project agents choose a
same project unit delay cost (cdl
i = 100, Pi P) in all the experiments, and (2) resource
agents choose a different resource-unit-utilisation cost (cuk = {0, 1, . . . , 30}, Rk R) in
each experiment. Figure 5.10 shows the evaluations of the 30 schedules in terms of APD
and TSRU. We observe a clear trade-off between project delay and resource levelling.
The higher the average project delay goes (cf. x-axis), the less total squared resource
utilisation (cf. y-axis) will be. From these results, we see that agents employing the same
scheduling approach (OI-MAS as a whole) can result in different schedules when they
emphasise different values. This gives the self-interested parties, not only project agents
but also resource agents, a natural way of making decisions themselves based on their own
value systems. In all, the autonomous decision making brings flexibility in the scheduling
processing of OI-MAS.
86
1579505
1237691
1139545
1141247
1090245
1038455
1062607
1012299
980727
990223
944235
922731
889073
845737
853239
813037
795045
775505
777185
751675
738259
760621
736201
691277
719967
691959
656391
691047
657983
646685
626327
1200
1600000
1050
1400000
900
1200000
750
1000000
600
800000
450
600000
300
400000
150
200000
10 12 14 16 18 20 22 24 26 28 30
TSRU
335
418
474.6
492.5
522
544.4
563
585.3
603.5
605.2
651.7
693.2
724.8
794.4
765.1
813.1
839.5
890.1
934.5
901.7
958.2
936.4
1009.5
1106.8
1053.7
1103
1137.4
1069.4
1118.3
1110.5
1177.3
APD
TSRU
Resource-unit utilisation cost ck
APD
TSRU
Figure 5.10: Trade-offs between project-agent objective and resource-agent objective
5.4
In this chapter, we addressed our second research question. [RQ2: How can agents make
and coordinate their local decisions in order to achieve a globally efficient and robust schedule in a partially observable environment? ] Partial observability in project-scheduling
context is presented by variable project release times.
We proposed OI-MAS, an online iterative multiagent scheduling approach. OI-MAS
aims at constructing an efficient and robust multi-project schedule under variable-projectrelease-time uncertainty. Subsequently, validating both the efficiency and the robustness
of the schedules constructed by OI-MAS can answer our research question 2.
OI-MAS deals with the efficiency and the robustness by its two components: (1) a
clairvoyant online schedule generation scheme (COSGS), and (2) an iterative scheduleimprovement method (ISIM).
Within the two components, the COSGS focuses on the robustness aspect of OI-MAS.
In the COSGS, project agents adopt a clairvoyant online scheme in which the scheduling
process of a project agent starts as soon as the project is actually released. Employing
the COSGS effectively eliminates the possibility of schedule disruptions caused by the
variable project release times. Evidently, the schedules obtained are robust with respect
to the variable project release times.
Furthermore, the ISIM focuses on the efficiency aspect of OI-MAS. In the ISIM, project
agents and resource agents revise iteratively their earlier determined schedules in order
to increase their utilities. Based on the experiments and the analyses, we may conclude
that the ISIM is effective, and the schedules constructed by OI-MAS are efficient.
In all, we can conclude that OI-MAS provides efficient and robust multi-project schedules in a partially observable project-scheduling environment.
Chapter 6
Stable Proactive Scheduling

In Chapter 5 we have seen that the clairvoyant online scheduling scheme employed by
project agents is able to overcome the problem of having schedules disrupted by the
first class of environmental uncertainty variable project release times. However, the
scheme given does not offer a solution for uncertainties raised on the processing times of
activities (a.k.a., nondeterminism). In this chapter, we address problems characterised
by the second class of uncertainty variable activity processing times. Accordingly, we
will answer research question 3, which reads as follows.
environment?
Given the uncertainty of variable activity processing times, the agents have to construct collaboratively schedules that, to a certain extent, are tolerant to minor incidents.
We recall that in Section 3.3, five classes of scheduling approaches for dealing with
uncertainty are discussed. In this chapter, we extend our study on one of the five classes,
i.e., the class of proactive-reactive scheduling approaches. We focus on developing an
agent-based robust-proactive-scheduling approach.
The chapter is organised as follows. In Section 6.1, we introduce the concept of
stability as a solution-robustness measure for project schedules. In Section 6.2, we present
an agent-based solution model for constructing a stable (and yet efficient) multi-project
schedule. In Section 6.3, we simulate DRCMPSPs/u with variable activity processing
times and evaluate the performance of the proposed stable scheduling procedure. Based
on the findings, Section 6.4 answers the research question 3.
6.1
Stability: Solution Robustness
In general terms, a robust decision is referred to as a decision that is immune to uncertainty and looks good to all constituents long after it is made. Robustness in the context
of project scheduling under uncertainty has two major forms (cf. Sevaux and Sorensen,
88
2002): (1) robustness in the objective-function space (a.k.a. quality robust), and (2) robustness in the solution space (a.k.a. solution robustness). Below, we discuss briefly the
two forms of robustness.
Definition 6.1 Quality Robustness. A schedule is called quality robust when it remains high quality in terms of the objective value when disruptions occur during project
executions.
Typical quality-robust schedules under uncertainty are achieved by building so-called
flexible schedules that can be easily repaired, i.e., changed into new high-quality schedules
in terms of objective functions whenever a disruption occurs.
Definition 6.2 Solution Robustness. A schedule is called solution robust when the
activity start times in the schedule are insensitive to disruptions during project executions.
Solution robustness is often known as stability (cf. Herroelen and Leus, 2004). It
means that given the uncertainty during execution, one would like the realised schedule
to resemble the expected schedule as much as possible. In this chapter we focus on solution
robustness.
In the remainder of this section, we will first investigate how to measure the stability
of a given project schedule1 (see 6.1.1). In 6.1.2, we discuss the concept of stability
in proactive-reactive project-scheduling procedures. Subsequently, 6.1.3 presents two
classes of existing solution methods for stable proactive scheduling based on (1) organising resource flows between project activities, and (2) reserving extra slack time and/or
resource capacity. Lastly, in 6.1.4, we discuss the (in)applicability of the approaches in
an agent-based model for DRCMPSP/u.
6.1.1
Stability Measures
A commonly used stability measurement of a project schedule is proposed by Leus (2003)

and Herroelen and Leus (2004) in a single-project environment. When a project is executed differently from it was scheduled, instability cost has to be paid. In practice, instability costs may include financial costs, inventory costs or various organisational costs.
Leus (2003) and Herroelen and Leus (2004) measured the instability costs as the weighted
sum of the deviations between the scheduled activity start times in the project schedule
and the actually realised activity start times during project execution. They optimise
the stability of a project schedule by minimising the instability cost. The expression to
minimise is as follows.
n
X
j=1
wj (E(sj ) sj ),
(6.1)
in which E is the expectation operator, sj is the start time of activity aj in the baseline
schedule S = {s1 , s2 , . . . , sn }, and sj is a stochastic variable representing the actually
achieved start time of activity aj (after project execution). Consequently, the real project
1 Actually,
it is the instability that is measured.
6.1. Stability: Solution Robustness
89
execution is a stochastic vector S = {s1 , s2 , . . . , sn }. In Equation 6.1, wj stands for the

non-negative marginal cost per unit time overrun the scheduled start time of activity aj .
This measure for instability cost in a single-project problem can be easily adapted to
a measure in a multi-project problem. In Equation 6.7, we show the new measure.
ni
m X
X
i=1 j=1
wi,j (E(si,j ) si,j ),
(6.2)
where i is the index of a project, and j is the index of an activity in a project.
6.1.2
Stability in Proactive-reactive Scheduling Procedures
We recall that proactive-reactive scheduling is a two-stage scheduling procedure (see

3.3.1). In the first stage, proactive scheduling constructs a baseline schedule prior
to the project start. Then in the second stage while executing the baseline schedule, reactive scheduling revises the schedule when it is invalidated by unexpected events. In this
subsection, we discuss stability in the proactive scheduling procedure and in the reactive
scheduling procedure, respectively. We refer to the two procedures as (a) stable proactive
scheduling and (b) stable reactive scheduling.
A: Stable Proactive Scheduling
Stable proactive scheduling is also known as fault-tolerant scheduling. In a projectscheduling context, stable proactive scheduling aims at constructing a baseline project
schedule (i.e., a project schedule proactively constructed prior to the project start) that
incorporates anticipated project-execution variability. Having the property of stability
for a baseline schedule in project-scheduling domain is more crucial than in any other
scheduling domain. This is because a baseline project schedule is used to organise resources, negotiate contracts with sub-contractors (or service providers), etc. A stable
baseline schedule is able to absorb some level of (un)expected disruptions during the
project execution without any reactive scheduling (Davenport et al., 2001).
We should emphasise that no matter how much we try to protect the baseline schedule
against possible disruptions during the building process of proactive scheduling, we can
never totally eliminate the possibility of having a disruption that renders a stable baseline
schedule infeasible. In order to restore the schedule feasibility, some un-executed activities
have to be re-scheduled. Therefore, a proactive scheduling will always require a reactive
component to deal with schedule disruptions that cannot be absorbed by the baseline
schedule.
B: Stable Reactive Scheduling
The reactive scheduling action may be based on various underlying strategies. At one
extreme, reactive scheduling may involve a full scheduling of the unexecuted activities
when the baseline schedule is invalidated. Such an approach is referred to as a (full)
rescheduling approach. A reactive scheduling procedure may, in principle, be capable of
maintaining optimal solutions if an exact (re)scheduling algorithm is employed. However,
90
alongside the high computational effort required, the main disadvantage of this procedure
is that the resulting schedule can differ completely from the original baseline schedule. In
order to generate a reactive schedule that deviates from the original baseline schedule as
little as possible, stable reactive scheduling is introduced.
The goal of stable reactive scheduling is to deliver quickly a new schedule that is
optimal (or near-optimal) in terms of minimum deviation from the baseline schedule. In
practice, many constraints prevent a reactive scheduling from conducting the optimisation
procedures. Below, we mention two constraints that exist in the AGH scheduling problem.
First, it is often undesirable to advance the baseline-scheduled starting time of an
activity. In AGH domain, an aircraft, for instance, will not take off before its scheduled
takeoff time. Even if it can be guaranteed that all passengers taking the flight are on
board, the aircraft will normally not leave early in order to avoid upsetting the global airtraffic schedule. Other areas of real-life scheduling environments exist where activities are
frequently not allowed to commence before their scheduled start (even though sometimes
technically possible), e.g., course scheduling, sports timetabling, and railway scheduling.
Second, it is often required that resource allocation to activities remain constant, i.e.,
the same resource flow is maintained. Such a reactive scheduling policy is often preferred
when transferring resources between activities are not achievable at short notice. In AGH
domain, ground handling operations that require the same type of resources are carried
out at different terminal gates. Transferring key staff or scarce equipment with high setup
costs is often unwanted and sometimes unachievable.
The aforementioned two constraints in AGH domain render most reactive scheduling
procedures inapplicable2 . In this thesis, we focus our research on constructing a stable
proactive baseline schedule, and employ a right-shift-rule policy for reactive scheduling
procedure (cf. Sadeh et al., 1993). When during execution, an activity encounters an
incident that causes its processing time being longer than estimated, the right shift rule
moves forward in time all the activities that are affected by this incident. The affected
activities can be those (i) making use of the same resources or (ii) having precedence
constraints with the activity.
6.1.3
Solution Models for Stable Proactive Scheduling
In this subsection, we present two solutions models for stable proactive scheduling. They
are (a) the solution model based on organising resource flows and (b) the solution model
based on allocating redundancies.
A: Organising Resource Flows
The first solution model for stable proactive scheduling is to organise resource flows between project activities. The way in which renewable resources are passed on between
project activities can be represented by a resource flow network. Below, we define the
network.
Definition 6.3 Resource Flow Network. A resource flow network Gk of a resource
type Rk is a directed graph Gk = (Vk , Ek ), which comprises a set of vertices Vk and a set
2A
survey of reactive scheduling procedures can be found in van de Vonder et al. (2007).
91

of directed edges Ek .
k
k
Vk = {vsk } {vi,j
|ri,j
N+ } {vtk },
|fvi,j
Ek = {fvi,j
k v k
k v k
0
0 0
i ,j 0
i ,j
N }.
(6.3)
(6.4)
In Equation 6.3, vsk and vtk are two vertices that represent the source and the sink
k
of the resource flows, respectively. In addition, vi,j
is a vertex representing the activity
k
ai,j that requests resources of Rk for execution (ri,j
N+ ). In Equation 6.4, the flow
+
quantity fvi,j
N represents the amount of resource units of Rk passing on from
k v k
0 0
i ,j
activity ai,j (when it finishes) to activity ai0 ,j 0 (when it starts).

A resource flow network must satisfy certain constraints in order to be called feasible.
Below, we define a feasible resource flow network.
Definition 6.4 A Feasible Resource Flow Network. A resource flow network Gk
is called feasible when it satisfies the following two constraints:
X
X
fvsk v =
fvvtk = ck ,
(6.5)
X
vVk
vik0 ,j 0 Vk
fvk0
i
k
vi,j
,j 0
vVk
vik00 ,j 00 Vk
fvi,j
k v k
00
i ,j 00
k
= ri,j
.
(6.6)
We remind the reader that in the thesis we consider only renewable resources (see
Definition 2.4). It means that the amount of resources consumed by an activity at a time
point t will be fully renewed at the next time point t+1. Subsequently, the two constraints
in Definition 6.4 can be explained as follows. The first constraint in Equation 6.5 proclaims
that the sum of all flows going out of the source vertex should be equal to the sum of
all flows going into the sink vertex, and both the sums should be equal to the maximum
resource capacity ck . The second constraint (see Equation 6.6) proclaims that for each
k
intermediate vertex vi,j
, the sum of flows going into this vertex must be equal to the sum
of flows going out of the vertex, which must be equal to the resource requirement of the
k
activity ai,j : ri,j
.
Artigues et al. (2003) introduce a simple method to generate a feasible resource flow
network. The method extends p-SGS by iteratively rerouting flow quantities until a
feasible overall flow is obtained. The method doesnt attempt to maximise schedule
stability, thus will be used as a benchmark in the experiments in Section 6.3.
For a resource type Rk , it is often possible to make different resource allocation decisions for the same baseline schedule. Different allocation decisions will be result in
different resource flow networks. Below, we employ an example to illustrate the idea of
resource-flow-based stable proactive scheduling.
On the left side of Figure 6.1, the AoN networks of two projects (P1 and P2 ) in
a multi-project scheduling problem are shown. Each of two projects consists of four
real activities (A1 = {a1,1 , a1,2 , a1,3 , a1,4 } and A2 = {a2,1 , a2,2 , a2,3 , a2,4 }). The activity
92
a1,0
P1 :
0:0
a1,1
a1,3
1:1
2:2
0:0
0
2:3
1:1
P2 :
a2,32
2:2
2 1:1
a2,2
3
P
2,2,2
a2,5
2,1
P
1,4,1
2 3
2,4
P
2,4,1
1,4
2,3,2
P
2,1,1
1:2
5
1,3
P
1,3,2
1,1
P2,3
1,1,1
P
2,2
a2,3
2:3
P
1,4,1
P
1,2,2
0:0
1,4
2 1,2
0:0
a2,4 2
a2,1
a1,5
a1,4
22:3
0:0
1,3
P
1,3,2
1,1
P
1,1,1
0
2:2
a2,1
2
1,2
P
1,2,2
0:0
a1,3
1:31,2
a2,0
a1,4
1:1
a1,0
P1 :
a1,5
a1,2
a1,1
2,2
2,3
0
0
r The AoN networks
1:3
P
Figure 6.1:
of 2:2
two projects (left) and theproject
schedules
(right)
P
a2,5
a2,0
P2 :
2,2,2
2,3,2
2
2,4
4
0:0
0:0
1 P
1
2,4,1
modes are3 shownRin the
AoN networks.
for
a2,2
a2,4 Two resource types R and R are required
2,1,1
R
1analysis
processing2 the project
activities.
In this example, we
vs1 focus on the resource-flow
2,4,1
v
0
1
21
3
4t
5
6
3 c = 4.
of the resource
type
R1 ,2:3which
has 1:2
a maximum capacity:
1
2
1
R
R
2
1
v1,1
1,1,1
vs1
1,4,1
1
v1,1
4
1
v1,4
2
1
1 R 2
2,1,1
v2,1
R
1,1,1
vt1
R
2
1,4,1
1
v2,4
R
2,4,1
1
v2,1
1
2,1 v1,4
P
1 2,1,1 2
1
v2,4
34
3
R
2,1,1
1
0
vs1
R
1
1
2,4,1
v1,1
v1,4
1
R
1,1,1
13
2
1
v2,1
R
1,4,1
31
1
vt1
1
v2,4
Figure 6.2:
A
resource
flow
network
of Rt 1 and the corresponding resource profile
0
1
2
3
4
5
6
r
According to the schedules of the two projects shown on the right side of Figure 6.1, one
1
1
v1,1
possible resource
flow
organised. The
resource flow network is shown on the
1 of Rv11,4can be
1
4
1
R
left side of Figure 6.2. Correspondingly, the right side of Figure 6.21,4,1
shows the scheduled
3
R
1 profile of R1 . The flows in the
1
resource
figures
indicate
that,
at
time
point 0, one of the
2,1,1
vs
vt
1
2
1
available resource
units
is
transferred
from
the
source
vertex
to
a
(f
= 1), and
3
1,1
vs1 v1,1
1
R
2
2,4,1
1
R
1 transferred
1 to a2,1 (fv 1 v 1 = 3). Later
1
the rest three are
at time point 3, when both a1,1
1,1,1
v2,1
v2,4
s
2,1
1 v
1
and a2,1 are finished, the resource unit used by a1,1
is
transferred
= t1);
0
1
2
3 to a
41,4 (f
5 v1,1
6 1,4
1 v 1
two of the three resource units used by a2,1 are transferred to a2,4 (fv1,1
= 2); and
2,4
1 v 1 = 1). Finally, at time point
the rest resource unit used by a2,1 goes to the sink (fv2,1
t
1 v 1 = 1
5, resource units used by a1,4 and a2,4 are all transferred to the sink vertex (fv1,4
t
1 v 1 = 2).
and fv2,4
t
2:3
1:2
93

1
1
v1,1
1
v1,4
Alternatively, for the same project schedules depicted on the right side of Figure 6.1,
3
R
2,1,1
another
6.3).
The difference
between the two
R
vs1 resource flow can be organised
vt1 (see Figure
2,4,1
2
1at time point 3, where in the latter case the
resource flow
networks
lies
resource
unit used
3
2
1
R
R
1
1
by a1,1 is transferred
to
a
(f
=
1)
instead
of
to
a
.
In
addition,
the
three
1
1
2
v1,1 v2,4
1,1,1 1,4 1,4,1
v2,1
v2,4
2,4
1 v 1
resource units used by a2,1 go different ways: one
t
0 goes
1 to 2a2,4 (f
3 v2,1
4 2,45 = 1),
6 one goes
1 v 1
1
1
to a1,4 (fv2,1
=
1),
and
the
last
goes
to
the
sink
(f
=
1).
v2,1 vt
1,4
r
vs1
1
v1,1
1
1
v1,4
vt1
1
3
1
1
v2,1
2
1
v2,4
R
1,4,1
R
2,1,1
2
1
R
2,4,1
R
1,1,1
Figure 6.3: An alternative resource flow network of R1 and the resource profile
The possibility of generating different resource flow networks for the same baseline
schedule may have a serious impact on the stability of the baseline schedule. Let us
assume that activity a2,1 encounters a minor disruption during execution. The disruption
causes a longer processing time of a2,1 than it was estimated (p2,1 > p2,1 , where p2,1
denotes the actual processing time of a2,1 ). In case the resource flows of R1 are organised
according to Figure 6.2, only one activitys schedule (i.e., the one of a2,4 ) has to be revised.
The schedule of a1,4 remains intact. However, if the resource flows of R1 are organised
according to Figure 6.3, both of the two activity schedules (1,4 and 2,4 ) have to be
revised, incurring higher instability costs.
Organising an optimal resource flow network for a single-project scheduling problem
with a single disruption is proven to be NP-hard by Leus (2003). Undoubtedly, in practice, exact methods for large multiple-project problems with multiple disruptions are
inapplicable. In order to deal with problem complexity, Deblaere et al. (2007) presented
three heuristics for organising resource flows. They are (1) minimise the number of extra
arcs (MinEA), (2) maximise the sum of pairwise floats (MaxPF), and (3) minimise the
estimated disruption (MinED). These heuristics are based on surrogate mixed-integerprogramming (MIP) formulation of the original strongly NP-hard problem.
B: Allocating Redundancies
Apart from organising resource flows, the second solution model for stable proactive
scheduling is to allocating redundancies (protections). Redundancy often takes form of
slack in time or (extra-)capacity in resource. By reserving extra time and/or resources,
the baseline schedule is able to absorb locally some level of expected (or unexpected)
disruptions during project execution without cascading the disruption to a larger scale
(cf. Davenport et al., 2001).
However, for AGH scheduling problems in which we are interested, pure resource
94
redundancy is unrealistic (cf. Davenport and Beck, 2000). We give two main reasons.
First, the resource redundancy is achieved by allocating multiple identical sets of resources
for an activity (cf. Ghosh, 1996). The cost of providing redundant resources is so high
that almost none of the service providers would double its resource inventory. Second,
allocating resource redundancies is often not practical in problems with decentralised
decision-making processes and large geometric span. In such problem settings, in case
no disruption occurs, the extra reserved resources cannot be easily re-allocated to other
activities at a short notice.
In contrast, time redundancy is relevant. Allocating time redundancies is achieved
by adding slack time windows before (or after) the schedules of individual activities.
Below, we employ an example to illustrate the idea of slack-time-based stable proactive
scheduling.
2
a1,2
3
P1 :
3
0:0
1:1 2:3
2:3
P1 :P1 : a1,0a1,0 a1,1a1,1
1:1 1:1
0:0 0:0
a1,1
a1,2a1,2
a1,0
2:3
a1,4
2 0
a1,3
a1,5a
0:0
1,5
a1,3a1,3
2:20:0
0:0
Figure 6.4: The AoN network of a project P1 with a disrupted activity a1,1
2:2 2:2
1,3
1,3
P
1,3,2
P
1,3,2
1,11,31,3 1,2
P
P P
P
1,1,1
1,3,21,3,2 1,2,2
1,10 1,11
P
P
1,1,1
1,1,1
0
01
12
23
2 1,231,2
1,1
P
1,1,1
5
P
P
1,2,2
1,2,2
34
45
56
6t
Figure 6.5: Schedule 1 without slack time
1,1
0 1,11
P
P
1,1,11,1,1
01
12
23
1,31,3 1,2
P
P
P
1,3,2
1,2,2
1,3,2
31,241,2
6 t
P
P
1,2,2
1,2,2
34
4 5
5 6
Figure 6.6: Schedule 01 with a slack time
Figure 6.4 depicts the AoN network of a project P1 consisting of three real activities
(A1 = {a1,1 , a1,2 , a1,3 }). Figure 6.5 shows an optimal in terms of minimum project
makespan schedule 1 of P1 . An alternative schedule 01 with a one-time-unit slack
P
time window inserted after 1,1,1
is shown in Figure 6.6. Let us assume that a minor
disruption occurs while processing activity a1,1 . The disruption causes ai,j to be processed
one time unit longer than estimated (p1,1 = p1,1 + 1). When the disruption occurs, the
earlier considered optimal schedule 1 has to be revised. The revision requires that both
of the two successors of a1,1 be rescheduled, causing high instability costs.
In contrast, although the schedule 01 is suboptimal compared to 1 in terms of
minimum project makespan, the added one-time-unit slack time window [3, 4) helps to
absorb the disruption, and keeps the schedules of a1,2 , and a1,3 intact. Thus, 01 is more
95
stable than 1 in the sense that it is less sensitive to small fluctuations in the activity
duration of a1,1 . With a slack time protected schedule, disruptions will likely have local
impact.
In slack-time-based approaches, the length of the slack time can either be analytically
determined by a linear programming solver in case the disruption model is known or more
practically determined by heuristic procedures.
For analytical approaches, Lambrechts et al. (2010) provided an overview of approaches for determining the expected duration increase an activity experiences due to
resource breakdowns. We argue that in an agent-based model for DRCMPSP/u, project
agents analytically determining the optimal slack time windows for its activities is an
impossible task. In order to fulfil this task agents must not only know the pattern and
frequency with which incidents occur, but also the resource requirement of other project
agents. To make things worse, other project agents may also try to insert an optimal
slack time after each project.
For heuristic procedures, Leus (2003) proposed a two-stage procedure, where at the
first stage, a (sub)optimal deterministic schedule is built; and at second stage, slack
times are determined by a heuristic called activity-dependent float factor and inserted
in front of activities. The problem of applying this two-stage solution procedure is
the need of an almost complete re-scheduling at the second stage. When the problem is
modelled in an agent-based model, re-scheduling an activity means de-committing a set
of earlier reserved slots, and recommitting a new set of slots. In case this re-scheduling
is not favourable to the resource managers, they may forbid this move in extreme cases
or impose some penalty cost (often known as decommitment penalty) for this change.
Therefore, a practical agent-based solution model for project managers is to pre-estimate
the slack time and construct a schedule with the estimated slacks.
We notice that in a project scheduling problem where no deadline constraint is introduced, slack time windows can be large enough if one is only interested in keeping the
baseline schedule stable instead of being interested in efficiency.
6.1.4
Towards an Agent-based Stable Scheduling
Various approaches of the two solution models have been proposed. In this subsection,
we discuss how to adapt the solution models in an agent-based scheduling model.
In an agent-based model for DRCMPSP/u, the information about intra-project interactivity precedence relations are not known to resource agents. The information asymmetry prevents resource agents from employing a slack-time-based solution to achieve a
stable proactive baseline schedule. Likewise, the resource flow networks are kept private to the resource agents themselves. The project agents, on the other hand, will
not be able to pursue a stable baseline schedule by organising resource flows. In this
subsection, we discuss the (in)applicability of existing slack-time-based approaches and
resource-flow-based approaches in an agent-based model for DRCMPSP/u .
Despite the attempts of reducing problem complexity by the three heuristics, solving
the surrogate MIP problems is still computationally expensive (see Deblaere et al., 2007).
For large multiple-project problems with multiple disruptions, constructive procedures
are needed. Deblaere et al. (2007) proposed a single-pass constructive procedure, namely
96
myopic activity-based optimisation (MABO). Unlike most resource-allocation procedures,

MABO works activity-based rather than resource-based, which means that inter-activity
precedence relations are used to construct the resource flow. The activity-based procedure
of MABO makes it inapplicable in an agent-based model, where inter-activity precedence
relations are not known to resource agents.
In this thesis, we investigate approaches for different types of agents. Agent using
different approaches to improve the schedule stability should be possessing the information
that are available to them. In the following section, we present our agent-based stable
proactive scheduling approaches.
6.2
Agent-based Stable Proactive Scheduling
In this section, we propose an agent-based stable proactive scheduling procedure, in which

two classes of agents employ different methods to construct stable proactive schedules.
First, resource agents organise their resource flows to make the schedules stable (see
6.2.1). Second, project agents insert time redundancies (in the form of slack time windows) after its activity schedules to protect the schedule stability(see 6.2.2).
6.2.1
Constructive Heuristic Procedures by Resource Agents
We present three constructive heuristic approaches for resource agents allocating resources
to activities. They are (a) earliest finished predecessor first (EFPF), (b) richest predecessor first (RPF), and (c) cohabited predecessor first (CPF). Below, we describe the three
heuristics individually.
A: Earliest Finished Predecessor First
Let us assume that in a resource flow network of resource type Rk , the amount of resources
k
ri,j
used by an activity ai,j can be obtained in two different ways: (i) it can be obtained
k
totally from activity ai0 ,j 0 (fvk0 0 vi,j
= ri,j
) or (ii) it can be obtained totally from activity
k
ai00 ,j 00 (fvk00
i
i ,j
k
vi,j
,j 00
k
= ri,j
). The two different ways of organising resource flows result in
two different resource flow networks (see Figure 6.7). The resource profiles of the two
options are shown in Figure 6.8.
Let the expected finishing times of the two scheduled activities (ai0 ,j 0 and ai00 ,j 00 )
be fi0 ,j 0 and fi00 ,j 00 (fi0 ,j 0 < fi00 ,j 00 ), respectively. In case the activity ai0 ,j 0 undergoes
a minor incident during its execution, the actual processing time pi0 ,j 0 will be larger
than it was expected (pi0 ,j 0 < pi0 ,j 0 ). Let us assume that the actual finishing time fi0 ,j 0
(fi0 ,j 0 = si0 ,j 0 + pi0 ,j 0 ) of ai0 ,j 0 does not exceed the starting time si,j of ai,j (fi0 ,j 0 < si,j ). If
the resource flows are organised according to the first option, the disruption of ai0 ,j 0 will
not influence the schedule of ai,j . Instead, if the resource flows are organised according
to the second option, both the schedules of ai00 ,j 00 and ai,j will be invalidated, incurring
higher instability cost. Therefore, the resource flows in the first option is more stable
than the one in the second.
Although resource agent RAk cannot deliberately insert slack time window in between
two activities, the difference between the scheduled finish time of ai0 ,j 0 and the scheduled
97
6.2. Agent-based Stable Proactive Scheduling
vsk rk
vsk
rik ,j
i ,j
rik ,j
vik ,jrk
i ,j
vik ,j
vik ,jk
vik ,j
rik ,j
ri ,j
vtk
ri ,j
vsk
option 1
option 1
rik ,j
vskk
vikr,j
k
vik ,j
i ,j
rik ,j
k
rvki ,j
k
vi,j
option 2
option 2
rik ,j rik ,j
rik ,j rik ,j
vsrkik ,j
vsk
rik ,j
ri ,j
k
ri,j
k k
ri,j
vi,j
rik ,j
rk
vikr,jk i,j
vikr,j
k
i ,j
i,j
k
k
k
vi ,j
vi ,j
vi,j
rik ,j
vtk
vtk
i,j
k
ri,j
vtk
vikk,j
k
k
vri,j
i,j
k
ri,j
vtk
vtk
rik ,j rik ,j
rik ,j rik ,j
Figure 6.7: Two options of obtaining resources for ai,j in a resource flow network
ck
ck
ck
iR ,j ,k
ck
iR ,j ,k
option 1
option 1
R
,j ,k
iR,ji,k
0 0
R
iR ,ji,k,j ,k
fi ,jf i ,j
f
fi ,j i ,j
option 2
option 2
fi ,j
R
R i,j,k
i,j,k
R
iR ,j ,ki ,j ,k
fi ,j
si,j
si,j
k
ck c
t t
R
i ,j ,k
iR ,j ,k
iR ,j ,ki ,j ,k
R R
i,j,k
i,j,k
fi ,j fis,ji,j
si,j
Figure 6.8: Two options of obtaining resources for ai,j in a resource-profile diagram
start time of ai,j (i.e., fi0 ,j 0 si,j ) in the first resource-flow option acts like a slack time
window that protects the stability of the schedule. Thus, the larger the difference is, the
more stable the resource-agent schedule will be. Based on this reasoning, we can propose
a first constructed heuristic. We refer it to as earliest finished predecessor first (EFPF).
In EFPF, a resource agent while organising the flow-in resources for an activity, will first
choose the resources from the activity that has the earliest finishing time.
B: Richest Predecessor First
In a resource flow network, the edges show the interdependencies between activities in
terms of resource flows. When an activity undergoes an incident, the number of edges
going out of the activitys vertex indicates the possible number of activities of which the
schedules might be invalidated. Likewise, the number of edges going into an activitys
vertex indicates the likelihood of the activity being affected by earlier disruptions. Thus,
98
it is clear that in general the less the number of edges is in a resource flow network, the
more stable the schedule will be.
Based on this reasoning, we can propose a second constructive heuristic. We refer it to
as richest predecessor first (RPF). In RPF, a resource agent while organising the flow-in
resources for an activity, will first choose the activity that has the most non-transferred
resources. Below, we illustrate the RPF heuristic by an example.
ck
3
vik ,j
vsk
vtk
1
vik ,j
iR ,j ,k
iR ,j ,k
1
0
Figure 6.9: The resource flow network and the resource3
2
k
vi,j
vik ,j diagram
profile
of
RA2k
vsk
vtk
1 on resource
Let us assume that two activities (ai0 ,j 0 and ai00 ,j 00 ) have been scheduled
agent RAk . Thev kresource
flow network
the resource1 profile
diagram of RAk are
option and
1
vik ,j
i ,j
3
3
1
shown in Figure 6.9. An activity ai,j is scheduled on RAk and there
are two possibilities
k
of allocating
resources to ai,j v(see
Figure 6.10 and Figure 6.11).
vsk
t
1
vik ,j
k2
k
v3ik ,j vi ,j vi,j
1
option 2
3
k
vsk vs
vik ,j
vsk
option 1
vtk
1
vik ,j
option 2
4 vik ,j
3
12
ck
k
2
vi,j
vtk
vtk
vik ,j vik ,j
ck
vsk
1iR ,j ,k
k
vi,j
R1
vik ,j i ,j ,k
vtk
R
i,j,k
option 1
,j ,k Two options of allocating resources
Figurei6.10:
for a0i,j in resource flow networks
R
k
2 It is clear
flows is more stable than the
iR ,j ,kthat the first option of organising cresource
ck
4
second.
Since
the
schedule
of
a
in
the
second
option
is
vulnerable
to disruptions to both
option
2
1,2
R
1
4i ,j ,k
activities ai0 ,j 0 and ai00 ,j 00 , while in the first option,

it is only vulnerable
to the schedule
iR ,j ,k
3
R
disruption
of ai0 ,j 0 .
i,j,k
0
t
3
2
R
i ,jflow
,k
network.
In consequence,
ckRPF tries to reduce the number of edges in a resource
R
2
i,j,k
1
iR ,j ,kdecisions
interdependencies
between
activities
imposed
by
resource-allocation
are reduced.
4
3
2
option 1
iR ,j ,k
iR ,j ,k
option 2
1
0
ck
4
3
iR ,j ,k
R
i,j,k
vik ,j
99

ck
4
iR ,j ,k
3
2
ck
option 1
iR ,j ,k
3
2
iR ,j ,k
iR ,j ,k
option 2
1
0
R
i,j,k
ck
4
iR ,j ,k
3
2
R
i,j,k
iR ,j ,k
1
0
Figure 6.11: Two options of allocating resources for ai,j in resource-profile diagrams
C: Cohabited Predecessor First
As we discussed in RPF, the edges in a resource flow network create resource-related
interdependencies among activities. Apart from resource-related interdependencies, we
reminder the reader that there is another type of activity interdependencies the precedence relations (see 2.1.2). Precedence relations are inherent interdependencies once a
problem is known. They are represented by arcs in AoN networks. Since precedence
relations are inherent, they are unavoidable interdependencies.
Based on this reasoning, we can propose a second constructive heuristic. We refer it
to as cohabited predecessor first (CPF). Two activities are called cohabited when they
belong to the same project. In CPF, a resource agent while allocating resources for an
activity, will first choose the resources that are released from activities belonging to the
same project. Below, we illustrate the RPF heuristic by an example.
Let us assume that two activities (ai,j 0 and ai0 ,j 0 ) have been scheduled on resource
agent RAk , both activities require two units of resources. An newly scheduled activity
ai,j , of which the resource requirement is also two units, belongs to the same project as
the activity ai,j 0 . Similar to earlier examples, there are also two possibilities of allocating
resources to ai,j (see Figure 6.12 and Figure 6.13).
The two options seem equally stable judging from the number of edges in the resource
flow networks. However, in case ai,j and ai,j 0 are precedence related (ai,j 0 ai,j ), a
disruption occurring at the execution of ai,j 0 will also invalidate the schedule of ai,j .
Therefore, the first option is more stable than the second. Since the resource flow in the
second option is vulnerable to both disruptions occurring in ai,j 0 and ai0 ,j 0 .
We note that although the resource agent RAk cannot guarantee the precedence relation between the two activities3 (ai,j and ai,j 0 ), choosing a cohabited activity as a resource
3 Intra-project
precedence relations are only known to the corresponding project agent.
100

k
vi,j
k
vi,j
vsk
2
k
vi,j
option 1
vsk
vtk
2
vik ,j
vtk
2
vik ,j
2
option 2
k
vi,j
vsk
vtk
2
vik ,j
k
vi,j
c
Figure 6.12: Two options of allocating resources
for ai,j in resource flow networks
4
R
i,j
,k
R
i,j,k
source increases the chance of reducing the number of resource-related interdependencies.

2
CPF
ck tries to attach resource-related interdependencies onRthe existing precedence-related
,k
1
interdependencies,
therefore making the consequence
of ai ,jdisruption
as local as possible.
4
3
6.2.2
2
option 1
R
i,j
,k
Coevolving Slack Time Windows by Project Agents

ck
i ,j ,k
option 2
For1a project
agent, stable proactive scheduling
means
to minimising the instability costs
4
of its project schedule. According to the stability measure
shown in Equation 6.1, the
R
0
t
3
objective
function for stable scheduling
for a project
agenti,j
PA,ki can be represented by the
2
following function.
arg min f (tslk

i )=
tslk
i
n
X
j=1
iR ,j ,k
wi,j (E(s
i,j ) si,j ),
0
R
i,j,k
(6.7)
slk
where tslk
= htslk
i
i,1 , . . . , ti,ni i is a vector of ni (the number of real activities of Pi )
lengths of slack time windows. A slack time window with a length tslk
i,j is inserted after
the schedule i,j of ai,j during the scheduling process.
As discussed in 6.1.4, analytically determining the optimal slack time windows by a
project agent for all its activities is impossible. First, activities are not all equally likely
to be disturbed and will not have the same expected disturbance length. Second, some
activity start times may need to be better protected than others, for instance because
of critical position of the activity in an AoN network. Third, when slack is spread out
evenly, propagation of a disturbance throughout the network is not taken into account:
an activity can not only be disturbed by delays in its immediate predecessors, but also
because of disruptions of its transitive predecessors that could not be completely absorbed
before reaching the activity.
Hence, multiple project agents determining optimal slack times of their own activities
becomes a strategic decision game with no prior information about the payoff matrix. By
playing the game the project agents can gain some information about their own rewards
vik ,j
option 2
vi,j
vsk
6.2. Agent-based Stable Proactive Scheduling 2
vtk
vik ,j
k
vi,j
101
ck
4
R
i,j
,k
3
2
ck
option 1
R
i,j
,k
2
1
0
iR ,j ,k
4
3
R
i,j,k
iR ,j ,k
option 2
ck
4
R
i,j
,k
3
2
iR ,j ,k
R
i,j,k
Figure 6.13: Two options of allocating resources for ai,j in resource-profile diagrams
although these rewards still depend on how other project agents play the game. Many
multiagent learning techniques require that the payoff matrix is known by the agents.
Techniques that can still be used when the payoff matrix is not known in advance are
for instance evolutionary game theory (EGT, see Weibull (1997), Nash Q-learning (see
Hu and Wellman, 2003), and coevolutionary algorithms (Co-EAs, see Paredis (2000)).
In all cases convergence to a stable state is an important issue. We have chosen the
use Co-EAs for the following reasons. First, we are interested in a proof of concept viz.
can appropriate slack times be learnt. Second, we expect Co-EAs to be less sensitive
for requirements that must be met to guarantee convergence. In the remainder of the
subsection, we describe the Co-EAs for agents learning appropriate slack times.
In the Co-EAs, each project agent is equipped with an evolution strategy (ES) for
learning a proper vector of slack-time-window lengths. All project agents together in an
AGH scheduling ecosystem are coevolving their individual strategies.
ES is a subclass of EAs that use selection, recombination, and mutation to iteratively
reproduce better-fit offsprings. Instead of encoding linear binary genotypes as in GAs,
ES encodes problem-specific linear real-valued genotypes and typically uses self-adaptive
mutation rates. Below, we propose a self-adaptive (1,1)-ES used by a project agent to
learn a proper vector of slack time windows4 .
Algorithm 6.1 describes the self-adaptive (1,1)-ES used by project agent PAi . In the
remainder of the section, we discuss the elements of the ES. The elements include (a)
genotype and phenotype, (b) mutation, (c) fitness evaluation, and (d) initialisation and
termination.
4 The
canonical notation of an ES is denoted by (/, )-ES or (/ + )-ES, where denotes the total
number of individuals in the population, denotes the number of selected parents for reproduction, and
denotes the number of offsprings. The comma sign means that the new generation is selected only
from the best fitting offsprings. The plus sign means that the new generation is selected from the best
fitting individuals from both the parents and the offsprings.
102
Algorithm 6.1 Self-adaptive (1,1)-Evolution Strategy used by PAi

1:
2:
3:
4:
5:
6:
7:
8:
9:
10:
11:
12:
13:
14:
15:
16:
17:
18:
19:
t := 0;
t
t
t
t
i;
, i,1
, . . . , i,n
Create an initial individual hi,1
, . . . , i,n
i
i
for all j {1, . . . , ni } do
t
:= di,j
pi,j e;
tslk,t
i,j
end for
repeat
for all j {1, . . . , ni } do
t+1
t
i,j
:= i,j
ei Ni,j (0,1) ;
t+1
t+1
t
i,j := i,j + i,j
Ni,j (0, 1);
slk,t+1
t+1
ti,j
= di,j pi,j e;
end
for
if f (tslk,t
) f (tslk,t+1
) then
i
i
for all j {1, . . . , ni } do
t+1
t
i,j
:= i,j
;
t+1
t
i,j := i,j ;
end for
end if
t := t + 1;
until termination condition
A: Genotype and Phenotype

Two vectors of variables are used to encode an individual (genotype) for the project
agent PAi : (1) a vector of ni object variables:

i = hi,1 , . . . , i,ni i and (2) a vector of ni
strategy variables: i = hi,1 , . . . , i,ni i. Altogether, an individual for the project agent
PAi is encoded as a vector of 2 ni real numbers.
hi,1 , . . . , i,ni , i,1 , . . . , i,ni i
{z
} |
{z
}
|
(6.8)
tslk
i,j = di,j pi,j e,
(6.9)
An object variable i,j R0 is a problem-related scaling factor that determines the

length of the slack time window tslk
i,j N (phenotype) to be inserted after the schedule of
activity ai,j . The length of the slack time window is computed as follows.
where pi,j is the estimated processing duration of ai,j , and dxe is a ceiling function
returning the smallest integer no less than x.
A strategy variable i,j R is a mutation parameter that represents the mutation
step size of the objective variable i,j . In ESs, the step sizes are also encoded in the
genotypes and they themselves undergo variation and selection. This encoding gives ESs
an important feature namely self-adaptation. Later in this section, we will describe how
mutation works in the chosen ES.
103

B: Mutation
Mutations in (1,1)-ES are realised by adding some i,j to each i,j . i,j values are
randomly drawn using a given normal distribution N (, ), where is the mean and
is the standard deviation (mutation step size). In practice, the mean is always set to
zero and the vector

i is mutated by replacing i,j by
0
i,j
= i,j + N (0, )
= i,j + N (0, 1)
In a self-adaptive ES, the mutation step size is not set by the user, rather, it is
also evolving. As specified in the individual encoding, we have chosen for each objective
variable i,j an evolving mutation parameter i,j . The mutation mechanism is thus
specified by the following formulas.
0
i,j
= i,j ei Ni,j (0,1)
0
i,j
= i,j +
0
i,j
(6.10)
Ni,j (0, 1)
(6.11)
In Equation 6.10, the proportionality constant i is an external parameter to be set

by the user. It can be interpreted as a kind of learning rate. It is usually inversely
proportional to the square root of the problem size:
i 1/ ni .
We refer the reader to the work by B
ack (1996) for more detailed discussion on the
choice of i .
C: Fitness Evaluation
In order to determine the fitness value of each individual, a project agent will calculate
the lengths of the slack time windows based on Equation 6.9. The slack time windows
are incorporated in the negotiation process with resource agents. By running simulations,
the stability of each project is obtained (see Equation 6.1).
We remind readers that project-deadline constraint is not considered in our AGH
scheduling problems (see Definition 2.11). In this case, a project agent who is purely
interested in the schedule stability will allocate maximum slack time window for each of
its activities. Allocating maximum slack time windows without deadline constraint will
create a 100% stable project-agent schedule, meaning the instability cost equals to 0.
However, the efficiency (measured in terms of project delay and resource utilisation cost)
of the schedule will be immensely decreased. Therefore, a project agent should consider a
trade-off between schedule efficiency and schedule stability. This leads us to the following
fitness function of a project agent PAi (see Equation 6.12).
dl
fPAi (i (tslk
i )) = ci dli (i )
P
i,j,k
i
P
rc(i,j,k
)
ni
X
j=1
wi,j (E(si,j ) si,j ),
(6.12)
104
P
P
, where cdl
P
i dli (i ) is the delay cost,
i rc(i,j,k ) is the resource cost, and
i,j,k
Pni
j=1 wi,j (E(si,j ) si,j ) is the instability cost.

In case the fitness value of a new individual is greater than an earlier obtained fitness
value (fPAi (i (tslk,t

)) fPAi (i (tslk,t+1
)), the old individual is replaced by the new one.
i
i
Otherwise, the old one remains.
D: Initialisation and Termination
The ES used by a project agent starts by computing an initial population, i.e., the first
generation. In the (1,1)-ES, the first generation is also the first individual since the popula
0
0
tion size is 1. We let the ES start with a positive real-valued vector
0 = hi,1
, . . . , i,n
i,
i
0
0
where i,j is randomly chosen 0 i,j 1.
As to the termination condition, we specify maximum number of generations for different experimental settings. Details of the experiments can be found in Section 6.3.
6.3
Experiments
In this section, we conduct experiments and empirically evaluate whether our proposed
algorithms for the two types of agents produce efficient and robust schedules in a nondeterministic environment. We first describe our experimental setup (6.3.1). The experimental results and analysis are presented in 6.3.2.
6.3.1
Experimental Setup
The problem instances that are used to evaluate our agent-based stable proactive scheduling algorithms are the same problem instances (i.e., 80 MPSPLib instances and 10 simulated AGH instances) as being used in Section 5.3.
The nondeterminism assumes that the uncertainty resides in the activity durations. In
order to simulate the nondeterministic aspect of scheduling-environment uncertainty, we
employ a random generator that generates stochastic actual activity processing durations.
Project management literature suggests that activity durations generally follow a beta
distribution (see Kerzner, 2006). The probability density function of a beta distribution
is shown in Equation 6.13.
x1 (1 x)1
,
(6.13)
B(, )
R0
where B(, ) is a beta function: B(, ) = 1 t1 (1 t)1 dt.
In the experiments, we have chosen the following parameters = 2 and = 5 for
generating the random numbers x: f = (x, 2, 5). The chosen and values make the
probability of x with a right-skewed beta distribution. It resembles the fact that the actual
activity processing times are close to the estimated ones. Figure 6.14 plots the probability
density function of the chosen beta distribution f . The minimum and maximum values
of this distribution are chosen to be 0.5 times and 2.25 times of the estimated activity
f (x, , ) =
105
0.6
0.4
1.5
0.2
1.0
0.0
0.0
0.5
dbeta(x, 2, 5, 0, FALSE)
2.0
0.8
2.5
1.0
6.3. Experiments
0.0
0.2
0.4
0.6
0.8
1.0
Figure 6.14: Probability density function

of a beta ( = 2, = 5) distribution
10
12
14
16
18
rbeta(1000, 2, 5, 0) * 17.5 + 5
Figure 6.15: 1000 samples of actual activity

processing duration pi,j (pi,j = 10)
duration pi,j . Thus, to simulate the actual activity durations pi,j we have the following
equation (Equation 6.14).
1
7
pi,j = ( x + ) pi,j
4
2
(6.14)
When x equals to the expected value ( +

= 72 ) of the beta distribution, the simulated
activity processing duration equals to the estimated duration (pi,j = pi,j ). Figure 6.15
shows 1000 samples of simulated actual activity processing durations pi,j when pi,j = 10.
In the experiments, we assume (1) in case that the actual processing duration pi,j of
an activity ai,j is smaller than the estimated one pi,j (pi,j < pi,j ), unused resources will
not be reallocated, (2) the weight factor wi,j in the stability measurement (Equation 6.7)
is identical for all activities: wi,j = 20, (3) project agents choose the same project unit
delay cost (cdi = 100, Pi P), and (4) resource agents choose the same resource-unitutilisation cost (cuk = 1, Rk R).
6.3.2
Results and Analysis
In this subsection, we present our experimental results for two distinct cases: (a) the
performance of the three constructive heuristics (i.e., EFPF, RPF, and CPF) used by
resource agents in improving schedule stability, and (b) the performance of the (1,1)-ES
learning approach used by project agents for increasing their utilities. We recall that
project-agent utility is a tradeoff between schedule efficiency and schedule stability (see
6.2.2).
A: Performance Evaluation of EFPF, RPF, and CPF
To evaluate the performance of the three constructive heuristics, 100 simulation runs for
each problem instance have been generated. Table 6.1 shows the average stability of the
106
schedules in which the resource flows are organised by four different approaches. First,
column 2 shows the average schedule stability where the resource flows are organised by
Artigues et al. (2003). Since the Artigues et al. (2003) approach does not attempt to
maximise schedule stability, we use the obtained stability as a benchmark. Column 3
to 5 shows the average schedule stability by using three proposed constructive heuristic
approaches (EFPF, RPF, and CPF).
Of the three heuristics developed in the thesis, RPF performs generally the best.
EFPF performs rather close to RPF, and the obtained stability is only slightly worse.
CPF follows EFPF and it is able to improve the schedule stability from 2.2% to 14.9%.
Problem Total project stability (wi,j = 20, i {1, . . . , m} j {1, . . . , ni })

instances Artigues et al.
EFPF
RPF
CPF
I90/2
13064
10646 (-16.2%) 10504 (-17.3%)
12380 (-2.6%)
I90/5
18688
15862 (-15.1%) 15402 (-17.6%)
17252 (-7.7%)
I90/10
25724
21276 (-16.8%) 20702 (-19.5%) 22716 (-11.7%)
I90/20
36850
31658 (-14.1%) 30432 (-17.4%) 32244 (-12.5%)
I120/2
20682
17470 (-15.5%) 17326 (-16.2%)
19962 (-3.5%)
I120/5
31646
27282 (-13.8%) 26256 (-17.0%)
30040 (-5.1%)
I120/10
47880
39052 (-18.4%) 39060 (-18.4%) 42789 (-10.6%)
I120/20
83050
67384 (-18.9%) 65962 (-20.6%) 72408 (-12.8%)
IA2
IA3
IA6
IA10
IA20
IA30
IA40
IA60
IA80
IA120
1840
2814
5648
9357
18524
29157
39641
65414
78454
125710
1586 (-13.8%)
1514 (-17.7%)
1800 (-2.2%)
2401 (-14.7%)
2415 (-14.2%)
2698 (-4.1%)
4815 (-14.7%)
4698 (-16.8%)
5159 (-8.7%)
8227 (-12.1%)
8225 (-12.1%)
8307 (-11.2%)
15749 (-15.0%) 15729 (-15.1%) 16161 (-12.8%)
24282 (-16.7%) 23689 (-18.8%) 25389 (-12.9%)
31547 (-20.4%) 31547 (-20.4%) 34087 (-14.0%)
56048 (-14.3%) 55041 (-15.9%) 56154 (-14.2%)
65848 (-16.1%) 64124 (-18.3%) 66887 (-14.7%)
103415 (-17.7%) 102485 (-18.5%) 106940 (-14.9%)
Table 6.1: Comparison of three heuristics on total project stability over 100 simulations
From the results shown in Table 6.1, we observe that the improvements made by
RPF and EFPF are insensitive to the project numbers in a problem instance and to the
activity numbers in a project. In contrast, the performance of CPF is highly dependent
on the number of projects in a problem instance. The more projects there are in a
problem instance, the better CPF performs. However, for large problem instances it
cannot outperform the other two heuristics.
In summary, we may conclude that the stability of a baseline schedule can be increased
through proper resource allocation. From the three proposed heuristics, RPF and EFPF
are preferred in general cases, and CPF is applicable when the problem size is large.
107
6.3. Experiments
P2
160000
Total costs
150000
140000
95000
85000
Total costs
105000
P1
200
400
600
800
1000
200
400
1000
P4
210000
200
400
600
800
1000
200
400
600
800
1000
Iteration
P6
140000
136000
Total costs
142000
P5
138000
240000 250000 260000 270000 280000
Iteration
200
400
600
800
1000
200
400
265000
Iteration
600
800
1000
Iteration
P8
230000
235000
245000
Total costs
255000
250000
P7
240000
Total costs
800
230000
Total costs
210000
200000
190000
Total costs
220000
P3
Total costs
600
Iteration
250000
Iteration
200
400
600
800
1000
200
400
600
800
1000
Iteration
200000
Iteration
P10
Total costs
265000
275000
190000
180000
Total costs
285000
P9
200
400
600
Iteration
800
1000
200
400
600
800
1000
Iteration
Figure 6.16: (1,1)-ES learning curves of the 10 projects in I90/10/1 with a particular
instance of incidents
108
160000
Total costs
140000
95000
P2
150000
105000
115000
P1
85000
Total costs
170000
0e+00
2e+04
4e+04
6e+04
8e+04
1e+05
0e+00
2e+04
250000
230000
Total costs
4e+04
6e+04
8e+04
1e+05
0e+00
2e+04
6e+04
8e+04
1e+05
142000
Iteration
P6
240000
136000
260000
Total costs
140000
280000
4e+04
138000
Total costs
1e+05
210000
2e+04
P5
Total costs
8e+04
P4
Iteration
0e+00
2e+04
4e+04
6e+04
8e+04
1e+05
0e+00
2e+04
4e+04
6e+04
8e+04
1e+05
260000
Iteration
250000
P8
230000
240000
250000
Total costs
260000
P7
240000
270000
Iteration
2e+04
4e+04
6e+04
8e+04
1e+05
0e+00
190000
Total costs
200000
P9
4e+04
6e+04
8e+04
1e+05
Iteration
P10
265000
180000
2e+04
295000
Iteration
285000
0e+00
275000
Total costs
6e+04
P3
0e+00
Total costs
4e+04
Iteration
190000 200000 210000 220000 230000
Iteration
0e+00
2e+04
4e+04
6e+04
Iteration
8e+04
1e+05
0e+00
2e+04
4e+04
6e+04
8e+04
1e+05
Iteration
Figure 6.17: (1,1)-ES learning curves of the 10 projects in I90/10/1 with random instances
of incidents
6.4. Answer to Research Question 3
109
B: Performance Evaluation of (1,1)-ES

To evaluate the performance of the (1,1)-ES learning approach used by project agents, we
consider two scenarios. First, we use the beta random generator to generate a particular
instance of incidents. We let project agents learn a vector of slack time windows that
maximise their utilities given that particular instance of incidents. Second, for every
simulation, we generate new beta random incidents. Project agents are expected to learn
a vector of slack time windows that perform well, in general, in maximising their utilities.
The learnt vector is expected to improve schedule stability while keeping the schedule
efficient (in terms of APD and TSRU).
To illustrate the results, we plot the learning curves of the 10 projects in instances
I90/10/1 for the two scenarios in Figure 6.16 and Figure 6.17, respectively. For the
particular-instance-incident scenario (see Figure 6.16), we see that (1,1)-ES can quickly
(in average within 1000 iterations) learn a proper vector of slack time windows. However,
for the random-instance-incident scenario (see Figure 6.17), the learning is rather slow.
Project agents are able to learn a vector of slack time windows that improves their utilities
to a certain extent. However, the learnt vector is not always the best.
In real-world project-scheduling environment, e.g., the one of AGH, one can never
expect that a particular instance of incidents reoccurs in the same way as it did before.
Yet, the good news is that incidents are never completely random. Based on certain
environmental conditions (weather forecast, time schedule, historical data), a disruptive
pattern can be predicted. Once a disruptive pattern is known, the proposed (1,1)-ES is
able to learn quickly a proper vector of slack time windows that increases the stability of
schedules, and safeguards the efficiency of schedules.
6.4
In this chapter we addressed the third research question. [RQ3: How can agents make
and coordinate their local decisions in order to achieve a globally efficient and robust
schedule in a nondeterministic environment? ] The notion of nondeterminism in a projectscheduling environment is represented as variable activity processing times.
Our research was as follows. First, we studied stability, i.e., a solution robustness
often considered in project-scheduling problems. Subsequently, we proposed an agentbased stable proactive scheduling procedure. The procedure aimed at constructing an
efficient and robust multi-project schedule under variable-activity-processing-time uncertainty. The procedure has two components: (1) three constructive scheduling heuristics
employed by resource agents, and (2) a coevolving slack-time-window inserting strategy
employed by project agents.
Based on the experiments and the analyses given above, we may conclude that the
proposed stable proactive scheduling procedure is effective in constructing both efficient
and robust schedules, therefore answer our RQ3.
Chapter 7
Conclusions
In this chapter, we provide a conclusive answer to our research questions and to the
problem statement. In Section 7.1, we repeat the three research questions and summarise
the answers given in earlier chapters. Based on the answers to the research questions,
Section 7.2 formulates our answer to the problem statement. Finally, in Section 7.3,
we discuss our research in a broader perspective by giving recommendations for future
research.
7.1
Answers to the Research Questions
In Section 1.2, we formulated three research questions. Throughout the thesis, we addressed and answered these questions in three consecutive chapters (Chapter 4, 5, and 6).
In this section, the answers to the three research questions are revisited and placed in an
overall context.
7.1.1
Agent-based Model for AGH Scheduling Problem
As we have shown in Section 1.1, current AGH scheduling problems are decision problems
with large-scale informational and managerial decentralisation. The scheduling process is
a distributed decision process amongst multiple organisations. Multiagent systems have
proved to be suitable to address such distributed decision-making problems. Employing
a multiagent system as our solution framework calls for an adequate agent-based model
of the AGH scheduling problem. This led to our first research question.
model?
In Chapter 4, we showed that the AGH scheduling problem can be effectively modelled
by an agent-based model. The proposed model consists of (1) two classes of role-based
agents resource agents and project agents and (2) a lease-based market mechanism
for coordinating the autonomous scheduling decisions of the individual agents.
112
Conclusions
For modelling agents, we adopted a physical-entity-oriented modelling approach. The

chosen physical-entity-oriented approach provides a natural description of the AGH domain by incorporating the two behavioural entities: (i) ground-handling service providers
(resource agents), and (ii) aircraft ground-handling managers (project agents). For modelling project agents, we chose to use a coarse-grained approach. The chosen coarsegrained approach allows the modelling of self-interested agents and avoids inter-agent
communicational overload. The self-interested nature of the agents is represented by the
utility modelling of each of the two classes of agents. The chosen agent representation
offers properties such as self-interestedness and scalability to the agent-based scheduling
system.
For modelling agent interactions, we proposed a lease-based market mechanism that
coordinates the scheduling decisions among two classes of heterogeneous agents. In the
mechanism, we introduced a concept of resource-time slot, that is used as a common language for inter-agent interactions. For processing an activity, a lease (i.e., a time-resource
slot) is negotiated by a resource agent and a project agent. The agents evaluate the value
of the slot based on their own value systems (marginal agent utilities). As a result, the
proposed coordination mechanism successfully distributes the scheduling decisions over
autonomous decision makers. As long as the slot chosen makes both the resource-agent
schedule and the project-agent schedule feasible, a global feasible schedule will be obtained. The proposed coordination mechanism offers properties such as flexibility and
scalability to the agent-based scheduling system.
7.1.2
Efficiency and Robustness under Partial Observability
The AGH scheduling environment is well known for its large number of disturbances
stemming from various sources. The disturbances cause a high degree of uncertainty
in making AGH schedules. In the thesis, we first focused on investigating scheduling
solutions under partial observability. Partial observability in AGH scheduling can be
interpreted as variable aircraft arrival times, i.e., the actual arrival time of an aircraft at
the airport is often different from (most of the times, it is later than) the one foreseen in
the original flight plan. This led to our second research question.
environment?
In Chapter 5 we proposed OI-MAS, an online iterative multiagent scheduling approach. OI-MAS deals with the efficiency and the robustness of AGH schedules by two
components: (1) a clairvoyant online schedule generation scheme (COSGS), and (2) an
iterative schedule-improvement method (ISIM).
Within the two components, the COSGS focuses on the robustness aspect. In the
COSGS, project agents adopt a clairvoyant online scheduling scheme in which the scheduling process of a project agent starts as soon as the project is actually released. Employing the COSGS effectively eliminates the possibility of schedule disruptions caused by the
variable project release times. Evidently, the schedules obtained are robust with respect
to the the variable project release times.
7.2. Answer to the Problem Statement
113
Furthermore, the second component ISIM of OI-MAS focuses on efficiency. In the

ISIM, project agents and resource agents revise iteratively their earlier determined schedules in order to increase their utilities. Based on the experiments and the analyses, we
may conclude that the ISIM is effective, and the schedules constructed by OI-MAS are
efficient.
In summary, we may conclude that OI-MAS provides efficient and robust AGH schedules in a partially observable environment.
7.1.3
Efficiency and Robustness under Nondeterminism
Apart from partial observability, the second class of uncertainty we have investigated in
this thesis is nondeterminism. Nondeterminism in AGH scheduling context is represented
by variable ground-handling operational times. During the scheduling phase of AGH,
each of the ground-handling operations has an estimated processing duration. However,
during the execution phase, the actual processing durations may differ from the original
estimations. Nondeterminism led to our third research question.
environment?
In Chapter 6 we studied stability, i.e., a solution robustness often considered in projectscheduling problems. Subsequently, we proposed an agent-based stable proactive scheduling procedure. The procedure aims at constructing an efficient and robust multi-project
schedule in a nondeterministic environment.
The proposed agent-based stable scheduling procedure has two components: (1) three
constructive scheduling heuristics employed by resource agents, and (2) a coevolving slacktime-window inserting strategy employed by project agents. Based on the experiments
and the analyses given in Section 6.3, we may conclude that the proposed stable proactive scheduling procedure is effective in constructing both efficient and robust schedules.
Therefore, we answered our RQ3.
7.2
Answer to the Problem Statement
In this section, we provide an answer to the problem statement posed in Chapter 1. Our
answer is based on the answers to the three research questions discussed in the previous
section. First, let us reiterate our problem statement.
robust?
Our research provides an affirmative answer to the problem statement, of which the
essence may be summarised in three parts. First, we proposed an agent-based model
for the AGH scheduling problem. In the proposed model, two classes of role-based selfinterested agents (resource agents and project agents) coordinate their local decisions in
114
Conclusions
a lease-based market mechanism. The model provides three desired properties that are
self-interestedness, flexibility, and scalability. Second, we addressed schedule efficiency
and robustness in a partial observable environment. The proposed OI-MAS approach
dealt with efficiency by employing an iterative schedule improvement method and dealt
with robustness by a clairvoyant online schedule generation scheme. Third, we addressed
schedule efficiency and robustness in a nondeterministic environment. Three constructive
heuristic approaches were proposed for resource agents to increase the schedule robustness.
A (co)evolutionary-strategy-based slack-time-window inserting approach was proposed for
project agents to increase the schedule efficiency and robustness.
7.3
Recommendations for Future Research
The research presented in the thesis indicates several important and promising areas of
future research. In this section, we mention three of the most interesting areas.
Generalisation to various real-world scheduling problems
In our research, the AGH scheduling problem is formulated as a DRCMPSP/u. It is a
fairly generalised and realistic multi-project scheduling problem. Yet, many other interesting generalisations of real-world project scheduling problems are worth to be further
investigated. Below, we mention two of them.
1. Generalisation of project-deadline constraints. An assumption we made for AGH
scheduling problems is that aircraft turnaround process can be delayed forever
until a feasible schedule is found. In practice, a turnaround process has often a hard
deadline. Once a deadline constraint is imposed, the primary scheduling objective
is to find a feasible schedule. It is interesting to investigate how the agents in
our MAS scheduling system can construct feasible schedules under project-deadline
constraints (or even under variable project-deadline constraints).
2. Generalisation of resource transition. The assumption to be relaxed is that the
resource transition periods are irrelevant. In the thesis, we assumed that resources
released from an activity can be immediately used by another activity. In practice,
there is often a transition period needed to transfer resources from one activity to
another. Transition time may vary according to the resource type and the distance
between the two activities. A generalisation of our agent-based scheduling model
would consider the transition period during the scheduling process.
Cooperation in agent negotiations
In our research we assumed complete self-interestedness of all agents, and pure competition in the sense that the agents try to maximise their own utilities in every round of
inter-agent negotiation. Research in game theory and social science has shown that selfinterestedness and mutual aid are not at all incompatible (see, e.g., Axelrod, 1984; Mayoh,
2002). Cooperative behaviour in self-interested multiagent games shows promising results.
For instance, cooperation in non-zero games increase the overall social welfare as well as
7.3. Recommendations for Future Research
115
the individual utilities (see de Jong, 2009). Therefore, an interesting direction of future
research is to investigate cooperative behaviours of the project agents and the resource
agents in the proposed MAS scheduling system. For instance, the following two research
topics can be addressed: (1) how can agents behave cooperatively in the proposed marketbased coordination mechanism? and (2) what are the benefits of introducing cooperation
in scheduling?
Solid agent learning research
In the second class of scheduling problems under uncertainty, we have empirically investigated a learning approach (i.e., (1,1)-ES) for constructing a stable project schedule by
inserting appropriate inter-activity slack time windows. Abstracting from the application
domain of AGH, we may state that the issue is to learn an optimal policy mapping from
a continuous domain of states to a continuous domain of actions based on observations
about incidents. Here, solid agent learning research can be conducted to investigate the
applicability of various learning approaches, both theoretically and empirically. These
approaches, for instance, include reinforcement learning (see Roos (2010) for stochastic approximation on robust scheduling) and Nash-Q learning (to be transferred to this
domain).
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Appendix A
Airport Ground-Handling
Operations
The following list extracted from European Council Directive 96/67/EC (EU Council,
1996) provides an exhaustive range of operations that ground handlers deal with for
common commercial flights.
1. Ground administration and supervision comprise:
(a) representation and liaison services with local authorities or any other entity,
disbursements on behalf of the airport user and provision of office space for its
representatives;
(b) load control, messaging and telecommunications;
(c) handling, storage and administration of unit load devices;
(d) any other supervision services before, during or after the flight and any other
administrative service requested by the airport user.
2. Passenger handling comprises any kind of assistance to arriving, departing, transfer or transit passengers, including checking tickets and travel documents, registering
baggage and carrying it to the sorting area.
3. Baggage handling comprises handling baggage in the sorting area, sorting it,
preparing it for departure, loading it on to and unloading it from the devices designed to move it from the aircraft to the sorting area and vice versa, as well as
transporting baggage from the sorting area to the reclaim area.
4. Freight and mail handling comprises:
(a) for freight: physical handling of export, transfer and import freight, handling
of related documents, customs procedures and implementation of any security
procedure agreed between the parties or required by the circumstances;
128
Appendices
(b) for mail: physical handling of incoming and outgoing mail, handling of related
documents and implementation of any security procedure agreed between the
parties or required by the circumstances.
5. Ramp handling comprises:

(a) marshalling the aircraft on the ground at arrival and departure;
(b) assistance to aircraft packing and provision of suitable devices;
(c) communication between the aircraft and the air-side supplier of services;
(d) the loading and unloading of the aircraft, including the provision and operation
of suitable means, as well as the transport of crew and passengers between the
aircraft and the terminal, and baggage transport between the aircraft and the
terminal;
(e) the provision and operation of appropriate units for engine starting;
(f) the moving of the aircraft at arrival and departure, as well as the provision
and operation of suitable devices;
(g) the transport, loading on to and unloading from the aircraft of food and beverages.
6. Aircraft services comprise:
(a) the external and internal cleaning of the aircraft, and the toilet and water
services;
(b) the cooling and heating of the cabin, the removal of snow and ice, the de-icing
of the aircraft;
(c) the rearrangement of the cabin with suitable cabin equipment, the storage of
this equipment.
7. Fuel and oil handling comprises:
(a) the organisation and execution of fuelling and defuelling operations, including
the storage of fuel and the control of the quality and quantity of fuel deliveries;
(b) the replenishing of oil and other fluids.
8. Aircraft maintenance comprises:
(a) routine services performed before flight;
(b) non-routine services requested by the airport user;
(c) the provision and administration of spare parts and suitable equipment;
(d) the request for or reservation of a suitable parking and/or hangar space.
9. Flight operations and crew administration comprise:
(a) preparation of the flight at the departure airport or at any other point;
(b) in-flight assistance, including redispatching if needed;
Appendix A: Airport Ground-Handling Operations
129
(c) post-flight activities;

(d) crew administration.
10. Surface transport comprises:
(a) the organisation and execution of crew, passenger, baggage, freight and mail
transport between different terminals of the same airport, but excluding the
same transport between the aircraft and any other point within the perimeter
of the same airport;
(b) any special transport requested by the airport user.
11. Catering services comprise:
(a) liaison with suppliers and administrative management;
(b) storage of food and beverages and of the equipment needed for their preparation;
(c) cleaning of this equipment;
(d) preparation and delivery of equipment as well as of bar and food supplies.
Appendix B
Properties of the 80 Chosen

MPSPLib Instances
In this appendix, we provide an overview of the properties of all 80 chosen problems instances from MPSPLib. The problems are used in our empirical experiments in Chapter 5
and 6.
Table B.1: Properties of the chosen 80 problem instances from MPSPLib
No. of real
activities per
project
No. of
projects
AC1
AC2
AC3
AC4
AC5
AC6
AC7
AC8
AC9
AC10
90
90
90
90
90
90
90
90
90
90
2
2
2
2
2
2
2
2
2
2
2
2
2
1
1
2
2
2
1
1
2
2
2
2
2
1
1
1
1
1
4
4
4
4
4
4
4
4
4
4
AC1
AC2
AC3
AC4
AC5
AC6
AC7
AC8
AC9
AC10
90
90
90
90
90
90
90
90
90
90
5
5
5
5
5
5
5
5
5
5
5
5
5
1
1
5
5
5
1
1
5
5
5
5
5
1
1
1
1
1
4
4
4
4
4
4
4
4
4
4
Alias
Problem instance
I90/2/1
I90/2/2
I90/2/3
I90/2/4
I90/2/5
I90/2/6
I90/2/7
I90/2/8
I90/2/9
I90/2/10
mp
mp
mp
mp
mp
mp
mp
mp
mp
mp
j90
j90
j90
j90
j90
j90
j90
j90
j90
j90
a2
a2
a2
a2
a2
a2
a2
a2
a2
a2
nr5
nr5
nr5
nr5
nr5
nr5
nr5
nr5
nr5
nr5
I90/5/1
I90/5/2
I90/5/3
I90/5/4
I90/5/5
I90/5/6
I90/5/7
I90/5/8
I90/5/9
I90/5/10
mp
mp
mp
mp
mp
mp
mp
mp
mp
mp
j90
j90
j90
j90
j90
j90
j90
j90
j90
j90
a5
a5
a5
a5
a5
a5
a5
a5
a5
a5
nr5
nr5
nr5
nr5
nr5
nr5
nr5
nr5
nr5
nr5
No. of
No. of
different release
instances times
No. of
resource
types
132
Alias
Appendices
Table B.1 continued from previous page
No. of real
No. of
No. of
No. of
activities per
different release
Problem instance
projects
project
instances times
No. of
resource
types
I90/10/1
I90/10/2
I90/10/3
I90/10/4
I90/10/5
I90/10/6
I90/10/7
I90/10/8
I90/10/9
I90/10/10
mp
mp
mp
mp
mp
mp
mp
mp
mp
mp
j90
j90
j90
j90
j90
j90
j90
j90
j90
j90
a10
a10
a10
a10
a10
a10
a10
a10
a10
a10
nr5
nr5
nr5
nr5
nr5
nr5
nr5
nr5
nr5
nr5
AC1
AC2
AC3
AC4
AC5
AC6
AC7
AC8
AC9
AC10
90
90
90
90
90
90
90
90
90
90
10
10
10
10
10
10
10
10
10
10
10
10
10
1
1
10
10
10
1
1
10
10
10
10
10
1
1
1
1
1
4
4
4
4
4
4
4
4
4
4
I90/20/1
I90/20/2
I90/20/3
I90/20/4
I90/20/5
I90/20/6
I90/20/7
I90/20/8
I90/20/9
I90/20/10
mp
mp
mp
mp
mp
mp
mp
mp
mp
mp
j90
j90
j90
j90
j90
j90
j90
j90
j90
j90
a20
a20
a20
a20
a20
a20
a20
a20
a20
a20
nr5
nr5
nr5
nr5
nr5
nr5
nr5
nr5
nr5
nr5
AC1
AC2
AC3
AC4
AC5
AC6
AC7
AC8
AC9
AC10
90
90
90
90
90
90
90
90
90
90
20
20
20
20
20
20
20
20
20
20
10
10
10
1
1
10
10
10
1
1
10
10
10
10
10
1
1
1
1
1
4
4
4
4
4
4
4
4
4
4
I120/2/1
I120/2/2
I120/2/3
I120/2/4
I120/2/5
I120/2/6
I120/2/7
I120/2/8
I120/2/9
I120/2/10
mp
mp
mp
mp
mp
mp
mp
mp
mp
mp
j120
j120
j120
j120
j120
j120
j120
j120
j120
j120
a2
a2
a2
a2
a2
a2
a2
a2
a2
a2
nr5
nr5
nr5
nr5
nr5
nr5
nr5
nr5
nr5
nr5
AC1
AC2
AC3
AC4
AC5
AC6
AC7
AC8
AC9
AC10
120
120
120
120
120
120
120
120
120
120
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
1
1
1
1
1
4
4
4
4
4
4
4
4
4
4
I120/5/1
I120/5/2
I120/5/3
I120/5/4
I120/5/5
I120/5/6
I120/5/7
I120/5/8
I120/5/9
I120/5/10
mp
mp
mp
mp
mp
mp
mp
mp
mp
mp
j120
j120
j120
j120
j120
j120
j120
j120
j120
j120
a5
a5
a5
a5
a5
a5
a5
a5
a5
a5
nr5
nr5
nr5
nr5
nr5
nr5
nr5
nr5
nr5
nr5
AC1
AC2
AC3
AC4
AC5
AC6
AC7
AC8
AC9
AC10
120
120
120
120
120
120
120
120
120
120
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
1
1
1
1
1
4
4
4
4
4
4
4
4
4
4
I120/10/1
I120/10/2
mp j120 a10 nr5 AC1

mp j120 a10 nr5 AC2
120
120
10
10
10
10
10
5
4
4
133
Appendix B: Properties of the 80 Chosen MPSPLib Instances

Table B.1 continued from previous page
No. of real
No. of
No. of
No. of
activities per
different release
Alias
Problem instance
projects
project
instances times
I120/10/3 mp j120 a10 nr5 AC3
120
10
10
5
I120/10/4 mp j120 a10 nr5 AC4
120
10
10
5
I120/10/5 mp j120 a10 nr5 AC5
120
10
10
5
I120/10/6 mp j120 a10 nr5 AC6
120
10
10
1
I120/10/7 mp j120 a10 nr5 AC7
120
10
10
1
I120/10/8 mp j120 a10 nr5 AC8
120
10
10
1
I120/10/9 mp j120 a10 nr5 AC9
120
10
10
1
I120/10/10 mp j120 a10 nr5 AC10
120
10
10
2
I120/20/1
I120/20/2
I120/20/3
I120/20/4
I120/20/5
I120/20/6
I120/20/7
I120/20/8
I120/20/9
I120/20/10
mp
mp
mp
mp
mp
mp
mp
mp
mp
mp
j120
j120
j120
j120
j120
j120
j120
j120
j120
j120
a20
a20
a20
a20
a20
a20
a20
a20
a20
a20
nr5
nr5
nr5
nr5
nr5
nr5
nr5
nr5
nr5
nr5
AC1
AC2
AC3
AC4
AC5
AC6
AC7
AC8
AC9
AC10
120
120
120
120
120
120
120
120
120
120
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
20
6
10
10
10
10
1
1
1
1
1
No. of
resource
types
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
4
Summary
In the preface we stated that the classical decision theory in project management with a
single decision maker soon becomes inapplicable because of the large-scale informational
and managerial decentralisation. This prediction is thoroughly investigated in the thesis.
Obviously, the rapid change in both technology and the structure of the market place in
recent years has called for new paradigms for managing large and distributed projects.
Within the field of distributed artificial intelligence, the research area of multiagent systems provide a natural way to model and solve problems with inherent complexity that
is caused by large-scale decentralisation.
Our research starts from a practical problem of such a decentralised setting scheduling airport ground handling (AGH) operations. At an airport, many aircraft are turning
around at the same time. Each of the aircraft turnaround processes can be seen as a
project involving a multitude of organisations working simultaneously on diverse activities. The general goal of our research is to investigate the characteristics of the AGH
scheduling problem and provide an adequate solution model that can solve the problem
efficiently and robustly. Our proposed multiagent scheduling system, that is discussed in
this thesis, may be used to solve a wider range of real-world scheduling problems.
In this thesis, we aim to investigate approaches within a multiagent-system solution
framework for designing such a scheduling system. Since agents have only a limited view
and control of the overall scheduling problem, Chapter 1 presents the following problem
statement.
robust?
To answer the problem statement we formulate in Chapter 1 three research questions.
They deal with (1) agent-based modelling for AGH scheduling problems, (2) schedule
efficiency and robustness under partial observability, and (3) schedule efficiency and robustness under nondeterminism. Precise formulations of the three research questions are
given later in this summary. In the remainder of Chapter 1, a five-step research methodology is presented.
In Chapter 2, we identify the characteristics of an AGH scheduling problem and reformulate the problem into a more generic problem, viz. that of a project scheduling problem.
A formal description is presented and a range of extensions and variations is discussed. We
136
Summary
reformulate the AGH scheduling problem as a decentralised resource-constrained multiproject scheduling problem under uncertainty (DRCMPSP/u), in which uncertainty is
categorised into two classes: (1) partial observability, and (2) nondeterminism.
Chapter 3 reviews the existing solution methods in the literature of project scheduling
problems in both OR and AI research. We focus on presenting the state-of-the-art solution
methods for solving (1) multi-project scheduling problems, (2) decentralised scheduling
problems, and (3) project scheduling under uncertainty. We discuss the limitations of the
reviewed solution methods and their (in)applicabilities for solving the AGH scheduling
problem. The discussion leads us to a new agent-based model, which we call a lease-based
multiagent model.
In Chapter 4, we start to address the first research question, which reads as follows.
model?
To answer this research question, we propose a novel agent-based model that adopts a
coarse-grained physical-entity-oriented modelling approach to represent the agents. The
model consists of the roles, schedules, and utilities of two classes of agents resource
agents and project agents. We design a market-based coordination mechanism in which
the scheduling decisions of the individual agents are coordinated in a lease-based negotiation scenario. The proposed agent representation and inter-agent coordination mechanism
offer properties such as self-interestedness, flexibility, and scalability to the agent-based
scheduling system.
Chapter 5 addresses the second research question, which reads as follows.
environment?
To answer this research question, we propose an online iterative scheduling approach
in the multiagent setting, called OI-MAS. This approach is composed of (1) a clairvoyant
online schedule-generation scheme (COSGS), and (2) an iterative schedule-improvement
method (ISIM). By employing the approach and experimenting with it in 80 benchmark
problems and 10 simulated AGH scheduling problems, we demonstrate the efficiency and
robustness of the resulting schedules.
In Chapter 6, we address the third research question, which reads as follows.
environment?
To answer this research question, we investigate proactive scheduling procedures for
constructing stable baseline schedules. In the proactive procedure, different approaches
(heuristics and evolutionary learning approaches) are proposed for the two classes of
agents to construct stable baseline schedules. A scheduling environment is simulated
where the processing times of activities are nondeterministic. By conducting experiments
137
with the proposed approaches, we show that the constructed schedules are both efficient
and robust.
The last chapter of the thesis contains the research conclusions and recommendations
for future research. We show that (1) the proposed agent-based model for AGH scheduling
problems has the desired system properties such as self-interestedness, flexibility, and
scalability; (2) the proposed OI-MAS approach enables the agents to construct efficient
and robust schedules under partial observability; and (3) the proposed heuristics and
learning approaches enable the agents to construct efficient and robust schedules under
nondeterminism. Taking the conclusions as answers to the three corresponding research
questions, we are able to give an affirmative answer to our problem statement. Lastly,
we provide a short discussion on three potential future research lines.
Samenvatting
Klassieke beslissingstheorieen die uitgaan van een centrale beslisser zijn in de praktijk niet
direct toepasbaar op het operationele projectmanagement van productie- en dienstverleningprocessen. Dit komt door dat de huidige bedrijfs-informatiesystemen en organisaties
heterogeen en gedistribueerd zijn. Bovendien worden hun interoperabiliteit en samenwerking beperkt doordat bepaalde informatie of kennis niet gedeeld wordt (bijv. vanwege
competitie) en externe factoren die van invloed zijn op de processen vaak onvoorspelbaar
zijn, zoals het weer. Voorts eisen de snelle technologische en markt-ontwikkelingen op het
gebied van productie- en dienstverleningsprocessen nieuwe flexibele, efficiente en robuuste oplossingen voor grootschalig en gedistribueerd projectmanagement. Eerdere studies
aangaande multiagentsystemen hebben veelbelovende resultaten opgeleverd en doen vermoeden dat deze systemen een goed alternatief zijn voor centrale beslissers om complexe
projectmanagement problemen te modelleren en op te lossen.
Deze dissertatie onderzoekt het vermoeden diepgand. Het gaat daarbij uit van een
praktisch gedecentraliseerd planningsprobleem: het plannen van grondafhandeling op een
vliegveld (Airport Ground Handling - AGH). Er wordt onderzocht of het mogelijk is een
planningssysteem te ontwerpen op basis van de bestaande theorie over multiagentsystemen
dat leidt tot een efficient en robuust AGH-projectmanagement.
Hiertoe wordt in hoofdstuk 1 het toepassingsdomein gentroduceerd. Op een vliegveld
wordt een groot aantal vliegtuigen tegelijkertijd afgehandeld wat betreft schoonmaken,
bevoorrading, bijtanken, veiligheidscontroles, etc. Ieder vliegtuig kan worden gezien als
een individueel project, waarbinnen meerdere organisaties tegelijkertijd verschillende activiteiten uitvoeren.
Dit leidt tot de volgende probleemstelling.
PS: Kan een verzameling agenten, handelend vanuit eigenbelang, een efficiente en robuuste globale planning voor grondafhandeling maken, door
slechts hun eigen lokale planningsbeslissingen te co
ordineren?
Om antwoord te geven op de probleemstelling, worden drie onderzoeksvragen geformuleerd. Zij zijn gericht op (1) multiagent modellering van AGH-planningsproblemen, (2)
efficientie en robuustheid van de planning in geval van gedeeltelijk inzicht, en (3) efficientie
en robuustheid van de planning onder onvoorspelbare factoren. Om tot een verantwoord
onderzoek te komen wordt aan het eind de onderzoeksmethodologie gepresenteerd.
In hoofdstuk 2 worden de kenmerken van een AGH-planningsprobleem gedentificeerd.
Het probleem wordt geextrapoleerd naar een generieke problematiek: het projectplan-
140
Samenvatting
ningsprobleem. De formele beschrijving van het projectplanningsprobleem wordt gegeven

en enkele variaties en uitbreidingen besproken. Het AGH-planningsprobleem wordt opnieuw geformuleerd als een gedecentraliseerd multi-projectplanningsprobleem met beperkte
middelen en onzekerheid (decentralised resource-Constrained multi-project scheduling problem under uncertainty ). Hierbij wordt onzekerheid in twee klassen ingedeeld: (1) gedeeltelijk inzicht en (2) onvoorspeldbaarheid.
Hoofdstuk 3 bespreekt bestaande OR- en AI- oplossingsmethoden uit de literatuur
voor projectplanningsproblemen. We presenteren state-of-the-art methoden voor het
oplossen van (1) multi-project planningsproblemen, (2) gedecentraliseerde planningsproblemen, en (3) projectplanning met onzekerheid. We bespreken de beperkingen van de
beschouwde methoden en hun (on)toepasbaarheid voor het oplossen van het
AGH-planningsprobleem. Uit deze bespreking wordt een nieuw multiagent model gedistilleerd, het lease-based multiagent model.
In hoofdstuk 4 wordt de eerste onderzoeksvraag besproken.
OV1: Hoe kan een AGH-planningsprobleem worden gerepresenteerd in een
multiagentmodel?
Ter beantwoording van deze onderzoeksvraag wordt een multiagentmodel voorgesteld,
waarin de agenten worden gerepresenteerd via een physical-entity-oriented modellering
met lage granulariteit. Het model bevat de rollen, planningen en utilities van twee klassen
van agenten: resource agents en project agents. Een op de markt gebaseerd mechanisme
wordt ontworpen, waarin de planningsbeslissingen van de individuele agenten worden
geco
ordineerd in een op lease gebaseerd onderhandelingsscenario. Het voorgestelde mechanisme voor representatie en co
ordinatie van agenten levert een multiagentplanningssysteem op met als eigenschappen self-interestedness, flexibiliteit en schaalbaarheid.
Hoofdstuk 5 behandelt de tweede onderzoeksvraag.
OV2: Hoe kunnen agenten lokaal beslissingen maken en co
ordineren, om een
globaal efficiente en robuuste planning te maken, wanneer zij slechts
inzicht hebben in een deel van het probleem?
In antwoord op deze onderzoeksvraag wordt een online, iteratieve planningsaanpak in
een multiagent omgeving (d.i., OI-MAS) voorgesteld. Deze aanpak bestaat uit (1) een
alleswetend online planninggeneratie-schema (Clairvoyant Online Schedule-Generation
Scheme (COSGS)) en (2) een iteratief planningverbeteringsmethode (Iterative Schedule
Improvement Method (ISIM)). Deze aanpak wordt toegepast op 80 benchmark problemen
en 10 gesimuleerde AGH-planningsproblemen. Zo wordt de efficientie en robuustheid van
de gemaakte planningen aangetoond.
In hoofdstuk 6 wordt de derde onderzoeksvraag behandeld.
OV3: Hoe kunnen agenten lokaal beslissingen maken en co
ordineren, om een
globaal efficiente en robuuste planning te maken, onder onvoorspelbare
systeemcondities?
Pro-actieve planningsprocedures worden ingezet om stabiele baseline-planningen te
construeren. Hiertoe worden verschillende aanpakken voorgesteld (heuristieken en evolutionair leren). Een AGH-planningsprobleem wordt gesimuleerd onder onvoorspelbare
141
verwerkingstijden van activiteiten. Door middel van experimenten wordt aangetoond dat
de geconstrueerde planningen efficient en robuust zijn.
In het laatste hoofdstuk worden conclusies getrokken, en aanbevelingen voor verder onderzoek gedaan. Onze drie conclusies zijn: (1) de voorgestelde multiagent modellen voor
AGH-planningsproblemen hebben de gewenste eigenschappen, zoals self-interestedness,
flexibiliteit en schaalbaarheid; (2) de voorgestelde OI-MAS aanpak stelt de agenten in
staat om, zoals met een beperkt inzicht, efficiente en robuuste planningen te produceren;
en (3) de voorgestelde heuristische aanpak in combinatie met de gekozen leeraanpak stelt
de agenten in staat efficiente en robuuste planningen te maken in geval van onvoorspelbaarheid. De conclusies zijn tevens de antwoorden op de drie onderzoeksvragen. Ze leiden
naar een bevestigend antwoord op de centrale probleemstelling. Tot slot worden nog drie
potentiele verdere onderzoeksrichtingen voorgesteld.
Curriculum Vitae
Xiaoyu Mao was born in Xian, Shaanxi, P.R. China, on December 6, 1980. In the same
city, he attended primary school and high school (Xian Tie Yi High School, graduated
in 1999). He then started his Bachelor study on Computer Science and Technology at
the School of Computer Science in Northwestern Polytechnical University, China. After obtaining his Bachelor degree with honours in July 2003, he travelled to France and
started a six-month transition semester on French-language learning and Electronic Engineering study at Ecole Speciale de Mecanique et dElectricite (ESME-Sudria), Paris.
This study was followed by an Engineering Diploma pursuing on Real-time and Systems
at Institut National des Sciences Appliquees, Toulouse (INSA-Toulouse). In addition to
the engineering studies, he enrolled himself in a Research Master program on Critical Information System and Network. After his graduation with double diplomas (i.e., a French
Engineering Diploma and a Master of Science) in 2005, he accepted a position as a Ph.D.
researcher in Casimir program at Almende B.V., a private innovative research company
located in Rotterdam, the Netherlands. His research was co-supervised by Professor Jaap
van den Herik and Professor Eric Postma at Tilburg Center for Cognition and Communication (TiCC), Tilburg University, as well as by Doctor Nico Roos at the Department
of Knowledge Engineering (DKE), Maastricht University and Doctor Alfons Salden at
Almende B.V. Currently, Xiaoyu works as a technology consultant at ASK Community
Systems B.V., Rotterdam.
List of Publications
The investigations performed during this PhD research resulted in the following publications.
Mao, X., ter Mors, A., Roos, N., and Witteveen, C. (2006). Agent-based scheduling for
aircraft deicing. In P.-Y. Schobbens, W. Vanhoof, and G. Schwanen (Eds.) Proceedings
of the 18th BelgiumNetherlands Conference on Artificial Intelligence, (pp. 229-236).
BNVKI.
ter Mors, A., Mao, X., Roos, N., Witteveen, C., and Salden, A. (2007a). Multi- agent system support for scheduling aircraft de-icing. In Proceeding of ISCRAM 2007 - Intelligent
Human Computer Systems for Crisis Response and Management, (pp. 467-478).
Mao, X., ter Mors, A., Roos, N., and Witteveen, C. (2007b). Coordinating competitive
agents in dynamic airport resource scheduling. In P. Petta, J. P. M
uller, M. Klusch, and
M. P. Georgeff (Eds.) Multiagent System Technologies, 5th German Conference, MATES
2007, Leipzig, Germany, September 24-26, 2007, Proceedings , (pp. 133-144).
Mao, X., ter Mors, A., Roos, N., and Witteveen, C. (2007c). Using neuro-evolution in
aircraft deicing scheduling. In K. Tuyls, S. de Jong, M. Ponsen, and K. Verbeeck (Eds.)
ALAMAS 2007 Adaptive and Learning Agents and Multi-Agent Systems, (pp. 138-145).
ter Mors, A. W., Mao, X., Zutt, J., Witteveen, C., and Roos, N. (2008a). Robust
reservation-based multi-agent routing. In M. Ghallab, C. Spyropoulos, N. Fakotakis, and
N. Avouris (Eds.) Proceedings of the 18th European Conference on Artificial Intelligence,
(pp. 929-930). IOS Press, Amsterdam. Accepted as poster.
Mao, X., Roos, N., and Salden, A. (2008b). Distribute the Selfish Ambitions. In A.
Nijholt, M. Pantic, M. Poel, and H. Hondorp (Eds.) Proceedings of the 20th Belgian
Dutch Conference on Artificial Intelligence, (pp. 137-144). BNVKI.
Mao, X., Roos, N., and Salden, A. (2009). Stable Multi-project Scheduling of Airport
Ground Handling Services with Heterogeneous Agents, In Decher, Sichman, Sierra, and
Castelfranchi (Eds.) Proceedings of the 8th International Conference on Autonomous
Agents and Multiagent Systems (AAMAS09), May, 10-15, 2009, Budapest, Hungary,
(pp. 537-544).

1998
(CWI1 )
1 Johan van den Akker

DEGAS - An Active, Temporal Database of Autonomous Objects
2 Floris Wiesman (UM) Information Retrieval by
Graphically Browsing Meta-Information
3 Ans Steuten (TUD) A Contribution to the
Linguistic Analysis of Business Conversations
within the Language/Action Perspective
4 Dennis Breuker (UM) Memory versus Search in
Games
5 Eduard W. Oskamp (RUL) Computerondersteuning bij Straftoemeting
8 Jacques H.J. Lenting (UM) Informed Gambling: Conception and Analysis of a Multi-Agent
Mechanism for Discrete Reallocation
2000
1 Frank Niessink (VU) Perspectives on Improving
Software Maintenance
2 Koen Holtman (TU/e) Prototyping of CMS
Storage Management
3 Carolien M.T. Metselaar (UvA) Sociaalorganisatorische Gevolgen van Kennistechnologie; een Procesbenadering en Actorperspectief
1999
4 Geert de Haan (VU) ETAG, A Formal Model of

Competence Knowledge for User Interface Design
1 Mark Sloof (VU) Physiology of Quality Change

Modelling; Automated Modelling of Quality
Change of Agricultural Products
5 Ruud van der Pol (UM) Knowledge-Based Query

Formulation in Information Retrieval
2 Rob Potharst (EUR) Classification using Decision Trees and Neural Nets
6 Rogier van Eijk (UU) Programming Languages

for Agent Communication
3 Don Beal (UM) The Nature of Minimax Search
7 Niels Peek (UU) Decision-Theoretic Planning of

Clinical Patient Management
4 Jacques Penders (UM) The Practical Art of

Moving Physical Objects
8 Veerle Coup
e (EUR) Sensitivity Analyis of
Decision-Theoretic Networks
5 Aldo de Moor (KUB) Empowering Communities: A Method for the Legitimate User-Driven
Specification of Network Information Systems
9 Florian Waas (CWI) Principles of Probabilistic

Query Optimization
6 Niek J.E. Wijngaards (VU) Re-Design of Compositional Systems
10 Niels Nes (CWI) Image Database Management

System Design Considerations, Algorithms and
Architecture
7 David Spelt (UT) Verification Support for Ob- 11 Jonas Karlsson (CWI) Scalable Distributed Data
ject Database Design
Structures for Database Management
1 Abbreviations:
SIKS - Dutch Research School for Information and Knowledge Systems; CWI - Centrum
voor Wiskunde en Informatica, Amsterdam; EUR - Erasmus Universiteit, Rotterdam; KUB - Katholieke
Universiteit Brabant, Tilburg; KUN - Katholieke Universiteit Nijmegen; OU - Open Universiteit; RUL
- Rijksuniversiteit Leiden; RUN - Radboud Universiteit Nijmegen; TUD - Technische Universiteit Delft;
TU/e - Technische Universiteit Eindhoven; UL - Universiteit Leiden; UM - Universiteit Maastricht; UT
- Universiteit Twente, Enschede; UU - Universiteit Utrecht; UvA - Universiteit van Amsterdam; UvT Universiteit van Tilburg; VU - Vrije Universiteit, Amsterdam.
148
2001
1 Silja Renooij (UU) Qualitative Approaches to
Quantifying Probabilistic Networks
2 Koen Hindriks (UU) Agent Programming Languages: Programming with Mental Models
3 Maarten van Someren (UvA) Learning as Problem Solving

9 Willem-Jan van den Heuvel (KUB) Integrating
Modern Business Applications with Objectified
Legacy Systems
10 Brian Sheppard (UM) Towards Perfect Play of
Scrabble
11 Wouter C.A. Wijngaards (VU) Agent Based
Modelling of Dynamics: Biological and Organisational Applications
4 Evgueni Smirnov (UM) Conjunctive and Dis- 12 Albrecht Schmidt (UvA) Processing XML in
junctive Version Spaces with Instance-Based
Database Systems
Boundary Sets
13 Hongjing Wu (TU/e) A Reference Architecture
5 Jacco van Ossenbruggen (VU) Processing Strucfor Adaptive Hypermedia Applications
tured Hypermedia: A Matter of Style
14 Wieke de Vries (UU) Agent Interaction: Ab6 Martijn van Welie (VU) Task-Based User Interstract Approaches to Modelling, Programming
face Design
and Verifying Multi-Agent Systems
7 Bastiaan Schonhage (VU) Diva: Architectural 15 Rik Eshuis (UT) Semantics and Verification of
Perspectives on Information Visualization
UML Activity Diagrams for Workflow Modelling
8 Pascal van Eck (VU) A Compositional Semantic
16 Pieter van Langen (VU) The Anatomy of DeStructure for Multi-Agent Systems Dynamics
sign: Foundations, Models and Applications
9 Pieter Jan t Hoen (RUL) Towards Distributed
17 Stefan Manegold (UvA) Understanding, ModDevelopment of Large Object-Oriented Models,
eling, and Improving Main-Memory Database
Views of Packages as Classes
Performance
10 Maarten Sierhuis (UvA) Modeling and Simulating Work Practice BRAHMS: a Multiagent 2003
Modeling and Simulation Language for Work
1 Heiner Stuckenschmidt (VU) Ontology-Based
Practice Analysis and Design
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ment: The Role of Mental Models in Business
2 Jan Broersen (VU) Modal Action Logics for ReaSystems Design
soning About Reactive Systems
2002
1 Nico Lassing (VU) Architecture-Level Modifiability Analysis
2 Roelof van Zwol (UT) Modelling and Searching
Web-based Document Collections
3 Henk Ernst Blok (UT) Database Optimization
Aspects for Information Retrieval
4 Juan Roberto Castelo Valdueza (UU) The Discrete Acyclic Digraph Markov Model in Data
Mining
5 Radu Serban (VU) The Private Cyberspace
Modeling Electronic Environments Inhabited by
Privacy-Concerned Agents
3 Martijn Schuemie (TUD) Human-Computer Interaction and Presence in Virtual Reality Exposure Therapy
4 Milan Petkovic (UT) Content-Based Video Retrieval Supported by Database Technology
5 Jos Lehmann (UvA) Causation in Artificial Intelligence and Law A Modelling Approach
6 Boris van Schooten (UT) Development and Specification of Virtual Environments
7 Machiel Jansen (UvA) Formal Explorations of
Knowledge Intensive Tasks
8 Yong-Ping Ran (UM) Repair-Based Scheduling
9 Rens Kortmann (UM) The Resolution of Visually Guided Behaviour
6 Laurens Mommers (UL) Applied Legal Epistemology; Building a Knowledge-based Ontology of 10 Andreas Lincke (UT) Electronic Business Negothe Legal Domain
tiation: Some Experimental Studies on the Interaction between Medium, Innovation Context
7 Peter Boncz (CWI) Monet: A Next-Generation
and Cult
DBMS Kernel For Query-Intensive Applications
8 Jaap Gordijn (VU) Value Based Requirements 11 Simon Keizer (UT) Reasoning under Uncertainty in Natural Language Dialogue using
Engineering: Exploring Innovative E-Commerce
Bayesian Networks
Ideas
149
12 Roeland Ordelman (UT) Dutch Speech Recogni- 14 Paul Harrenstein (UU) Logic in Conflict. Logical Explorations in Strategic Equilibrium
tion in Multimedia Information Retrieval
13 Jeroen Donkers (UM) Nosce Hostem Searching 15 Arno Knobbe (UU) Multi-Relational Data Mining
with Opponent Models
14 Stijn Hoppenbrouwers (KUN) Freezing Lan- 16
guage: Conceptualisation Processes across ICTSupported Organisations
17
15 Mathijs de Weerdt (TUD) Plan Merging in
Multi-Agent Systems
18
16 Menzo Windhouwer (CWI) Feature Grammar
Systems - Incremental Maintenance of Indexes 19
to Digital Media Warehouse
Federico Divina (VU) Hybrid Genetic Relational

Search for Inductive Learning
Mark Winands (UM) Informed Search in Complex Games
Vania Bessa Machado (UvA) Supporting the
Construction of Qualitative Knowledge Models
Thijs Westerveld (UT) Using generative probabilistic models for multimedia retrieval
17 David Jansen (UT) Extensions of Statecharts 20 Madelon Evers (Nyenrode) Learning from Dewith Probability, Time, and Stochastic Timing
sign: facilitating multidisciplinary design teams
18 Levente Kocsis (UM) Learning Search Decisions
2005
2004
1 Floor Verdenius (UvA) Methodological Aspects

of Designing Induction-Based Applications
1 Virginia Dignum (UU) A Model for Organizational Interaction: Based on Agents, Founded
in Logic
2 Erik van der Werf (UM) AI techniques for the

game of Go
2 Lai Xu (UvT) Monitoring Multi-party Contracts

for E-business
3 Perry Groot (VU) A Theoretical and Empirical
Analysis of Approximation in Symbolic Problem
Solving
4 Chris van Aart (UvA) Organizational Principles
for Multi-Agent Architectures
5 Viara Popova (EUR) Knowledge Discovery and
Monotonicity
6 Bart-Jan Hommes (TUD) The Evaluation of
Business Process Modeling Techniques
7 Elise Boltjes (UM) VoorbeeldIG Onderwijs;
Voorbeeldgestuurd Onderwijs, een Opstap naar
Abstract Denken, vooral voor Meisjes
3 Franc Grootjen (RUN) A Pragmatic Approach

to the Conceptualisation of Language
4 Nirvana Meratnia (UT) Towards Database Support for Moving Object data
5 Gabriel Infante-Lopez (UvA) Two-Level Probabilistic Grammars for Natural Language Parsing
6 Pieter Spronck (UM) Adaptive Game AI
7 Flavius Frasincar (TU/e) Hypermedia Presentation Generation for Semantic Web Information
Systems
8 Richard Vdovjak (TU/e) A Model-driven Approach for Building Distributed Ontology-based
Web Applications
9 Jeen Broekstra (VU) Storage, Querying and Inferencing for Semantic Web Languages
8 Joop Verbeek (UM) Politie en de Nieuwe In- 10 Anders Bouwer (UvA) Explaining Behaviour:
ternationale Informatiemarkt, Grensregionale
Using Qualitative Simulation in Interactive
Politi
ele Gegevensuitwisseling en Digitale ExLearning Environments
pertise
11 Elth Ogston (VU) Agent Based Matchmaking
9 Martin Caminada (VU) For the Sake of the Arand Clustering - A Decentralized Approach to
gument; Explorations into Argument-based ReaSearch
soning
12 Csaba Boer (EUR) Distributed Simulation in In10 Suzanne Kabel (UvA) Knowledge-rich Indexing
dustry
of Learning-objects
13 Fred Hamburg (UL) Een Computermodel voor
11 Michel Klein (VU) Change Management for Dishet Ondersteunen van Euthanasiebeslissingen
tributed Ontologies
14 Borys Omelayenko (VU) Web-Service configura12 The Duy Bui (UT) Creating Emotions and Facial Expressions for Embodied Agents
tion on the Semantic Web; Exploring how semantics meets pragmatics
13 Wojciech Jamroga (UT) Using Multiple Models 15 Tibor Bosse (VU) Analysis of the Dynamics of
of Reality: On Agents who Know how to Play
Cognitive Processes
150
16 Joris Graaumans (UU) Usability of XML Query 16 Carsten Riggelsen (UU) Approximation Methods
Languages
for Efficient Learning of Bayesian Networks
17 Boris Shishkov (TUD) Software Specification 17 Stacey Nagata (UU) User Assistance for Multitasking with Interruptions on a Mobile Device
Based on Re-usable Business Components
18 Danielle Sent (UU) Test-selection strategies for 18 Valentin Zhizhkun (UvA) Graph transformation
for Natural Language Processing
probabilistic networks
19 Michel van Dartel (UM) Situated Representation 19 Birna van Riemsdijk (UU) Cognitive Agent Programming: A Semantic Approach
20 Cristina Coteanu (UL) Cyber Consumer Law,
20 Marina Velikova (UvT) Monotone models for
State of the Art and Perspectives
prediction in data mining
21 Wijnand Derks (UT) Improving Concurrency
and Recovery in Database Systems by Exploit- 21 Bas van Gils (RUN) Aptness on the Web
ing Application Semantics
22 Paul de Vrieze (RUN) Fundaments of Adaptive
2006
1
2
3
4
5
6
Personalisation
23 Ion Juvina (UU) Development of Cognitive

Samuil Angelov (TU/e) Foundations of B2B
Model for Navigating on the Web
Electronic Contracting
24 Laura Hollink (VU) Semantic Annotation for
Cristina Chisalita (VU) Contextual issues in the
Retrieval of Visual Resources
design and use of information technology in or25 Madalina Drugan (UU) Conditional logganizations
likelihood MDL and Evolutionary MCMC
Noor Christoph (UvA) The role of metacognitive
26
Vojkan Mihajlovic (UT) Score Region Algebra:
skills in learning to solve problems
A Flexible Framework for Structured InformaMarta Sabou (VU) Building Web Service Ontion Retrieval
tologies
27 Stefano Bocconi (CWI) Vox Populi: generatCees Pierik (UU) Validation Techniques for
ing video documentaries from semantically anObject-Oriented Proof Outlines
notated media repositories
Ziv Baida (VU) Software-aided Service Bundling 28 Borkur Sigurbjornsson (UvA) Focused Informa- Intelligent Methods & Tools for Graphical Sertion Access using XML Element Retrieval
vice Modeling
7 Marko Smiljanic (UT) XML schema matching

balancing efficiency and effectiveness by means
of clustering
2007
8 Eelco Herder (UT) Forward, Back and Home

Again - Analyzing User Behavior on the Web
2 Wouter Teepe (RUG) Reconciling Information

Exchange and Confidentiality: A Formal Approach
9 Mohamed Wahdan (UM) Automatic Formulation of the Auditors Opinion

10 Ronny Siebes (VU) Semantic Routing in Peerto-Peer Systems
1 Kees Leune (UvT) Access Control and ServiceOriented Architectures
3 Peter Mika (VU) Social Networks and the Semantic Web
11 Joeri van Ruth (UT) Flattening Queries over

Nested Data Types
4 Jurriaan van Diggelen (UU) Achieving Semantic Interoperability in Multi-agent Systems: a

dialogue-based approach
12 Bert Bongers (VU) Interactivation - Towards

an e-cology of people, our technological environment, and the arts
5 Bart Schermer (UL) Software Agents, Surveillance, and the Right to Privacy: a Legislative
Framework for Agent-enabled Surveillance
13 Henk-Jan Lebbink (UU) Dialogue and Decision

Games for Information Exchanging Agents
6 Gilad Mishne (UvA) Applied Text Analytics for

Blogs
14 Johan Hoorn (VU) Software Requirements: Update, Upgrade, Redesign - towards a Theory of
Requirements Change
7 Natasa Jovanovic (UT) To Whom It May Concern - Addressee Identification in Face-to-Face

Meetings
15 Rainer Malik (UU) CONAN: Text Mining in the

Biomedical Domain
8 Mark Hoogendoorn (VU) Modeling of Change in

Multi-Agent Organizations
151
9 David Mobach (VU) Agent-Based Mediated Service Negotiation
3 Vera Hollink (UvA) Optimizing hierarchical

menus: a usage-based approach
10 Huib Aldewereld (UU) Autonomy vs. Conformity: an Institutional Perspective on Norms and
Protocols
4 Ander de Keijzer (UT) Management of Uncertain Data - towards unattended integration
11 Natalia Stash (TU/e) Incorporating Cognitive/Learning Styles in a General-Purpose

Adaptive Hypermedia System
12 Marcel van Gerven (RUN) Bayesian Networks
for Clinical Decision Support: A Rational Approach to Dynamic Decision-Making under Uncertainty
5 Bela Mutschler (UT) Modeling and simulating

causal dependencies on process-aware information systems from a cost perspective
6 Arjen Hommersom (RUN) On the Application of
Formal Methods to Clinical Guidelines, an Artificial Intelligence Perspective
7 Peter van Rosmalen (OU) Supporting the tutor
in the design and support of adaptive e-learning
13 Rutger Rienks (UT) Meetings in Smart Environments; Implications of Progressing Technology
8 Janneke Bolt (UU) Bayesian Networks: Aspects

of Approximate Inference
14 Niek Bergboer (UM) Context-Based Image

Analysis
9 Christof van Nimwegen (UU) The paradox of the

guided user: assistance can be counter-effective
15 Joyca Lacroix (UM) NIM: a Situated Computa- 10 Wauter Bosma (UT) Discourse oriented Summarization
tional Memory Model
11
Vera Kartseva (VU) Designing Controls for Net16 Davide Grossi (UU) Designing Invisible Handwork Organizations: a Value-Based Approach
cuffs. Formal investigations in Institutions and
12 Jozsef Farkas (RUN) A Semiotically oriented
Organizations for Multi-agent Systems
Cognitive Model of Knowlegde Representation
17 Theodore Charitos (UU) Reasoning with Dy13
Caterina Carraciolo (UvA) Topic Driven Access
namic Networks in Practice
to Scientific Handbooks
18 Bart Orriens (UvT) On the development and
management of adaptive business collaborations 14 Arthur van Bunningen (UT) Context-Aware
Querying; Better Answers with Less Effort
19 David Levy (UM) Intimate relationships with
15
Martijn van Otterlo (UT) The Logic of Adaptive
artificial partners
Behavior: Knowledge Representation and Algo20 Slinger Jansen (UU) Customer Configuration
rithms for the Markov Decision Process FrameUpdating in a Software Supply Network
work in First-Order Domains
21 Karianne Vermaas (UU) Fast diffusion and 16 Henriette van Vugt (VU) Embodied Agents from
broadening use: A research on residential adopa Users Perspective
tion and usage of broadband internet in the 17 Martin Opt Land (TUD) Applying Architecture
Netherlands between 2001 and 2005
and Ontology to the Splitting and Allying of En22 Zlatko Zlatev (UT) Goal-oriented design of value
and process models from patterns
18
23 Peter Barna (TU/e) Specification of Application 19
Logic in Web Information Systems
terprises
Guido de Croon (UM) Adaptive Active Vision
Henning Rode (UT) From document to entity retrieval: improving precision and performance of
focused text search
24 Georgina Ramrez Camps (CWI) Structural Features in XML Retrieval

20 Rex Arendsen (UvA) Geen bericht, goed bericht.
Een onderzoek naar de effecten van de intro25 Joost Schalken (VU) Empirical Investigations in
ductie van elektronisch berichtenverkeer met een
Software Process Improvement
overheid op de administratieve lasten van bedrijven
2008
21 Krisztian Balog (UvA) People search in the en1 Katalin Boer-Sorb
an (EUR) Agent-Based Simterprise
ulation of Financial Markets: A modular,
22 Henk Koning (UU) Communication of ITcontinuous-time approach
architecture
2 Alexei Sharpanskykh (VU) On Computer-Aided
23
Stefan Visscher (UU) Bayesian network modMethods for Modeling and Analysis of Organiels for the management of ventilator-associated
zations
pneumonia
152
24 Zharko Aleksovski (VU) Using background

knowledge in ontology matching
9 Benjamin Kanagwa (RUN) Design, Discovery

and Construction of Service-oriented Systems
25 Geert Jonker (UU) Efficient and Equitable ex- 10

change in air traffic management plan repair using spender-signed currency
11
26 Marijn Huijbregts (UT) Segmentation, diarization and speech transcription: surprise data un12
raveled
Jan Wielemaker (UvA) Logic programming for

knowledge-intensive interactive applications
Alexander Boer (UvA) Legal Theory, Sources of
Law & the Semantic Web
Peter Massuthe (TU/e, Humboldt-Universt
at zu
Berlin) Operating Guidelines for Services
27 Hubert Vogten (OU) Design and implementa13 Steven de Jong (UM) Fairness in Multi-Agent
tion strategies for IMS learning design
Systems
28 Ildiko Flesh (RUN) On the use of independence
14 Maksym Korotkiy (VU) From ontology-enabled
relations in Bayesian networks
services to service-enabled ontologies (making
29 Dennis Reidsma (UT) Annotations and subjecontologies work in e-science with ONTO-SOA)
tive machines- Of annotators, embodied agents,
15 Rinke Hoekstra (UvA) Ontology Representation
users, and other humans
- Design Patterns and Ontologies that Make
30 Wouter van Atteveldt (VU) Semantic network
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13
Xiaoyu Mao (UvT) Airport under Control. MulInter-Organizational Business-ICT Alignment
tiagent Scheduling for Airport Ground Handling
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Challenges, Techniques, Examples
TiCC Ph.D. Series

1
Pashiera Barkhuysen. Audiovisual prosody in interaction. Promotores: M.G.J. Swerts, E.J. Krahmer. Tilburg, 3 October 2008
Ben Torben-Nielsen. Dendritic morphology: function shapes structure. Promotores: H.J. van den
Herik, E.O. Postma. Copromotor: K.P. Tuyls. Tilburg, 3 December 2008
Hans Stol. A framework for evidence-based policy making using IT. A systems approach. Promotor:
H.J. van den Herik. Tilburg, 21 January 2009
Jeroen Geertzen. Act recognition and prediction. Explorations in computational dialogue modelling.
Promotor: H.C. Bunt. Copromotor: J.M.B. Terken. Tilburg, 11 February 2009
Sander Canisius. Structural prediction for natural language processing: a constraint satisfaction
approach. Promotores: A.P.J. van den Bosch, W.M.P. Daelemans. Tilburg, 13 February 2009
Fritz M.H. Reul. New Architectures in Computer Chess. Promotor: H.J. van den Herik. Copromotor: J.W.H.M. Uiterwijk. Tilburg, 17 June 2009
Laurens van der Maaten. Feature Extraction from Visual Data. Promotores: E.O. Postma, H.J.
van den Herik. Copromotor: A.G. Lange. Tilburg, 23 June 2009
Stephan Raaijmakers. Multinomial Language Learning: Investigations into the Geometry of Language. Promotores: W.M.P. Daelemans, A.P.J. van den Bosch. Tilburg, 1 December 2009
Igor Berezhnoy. Digital Analysis of Paintings. Promotores: E.O. Postma, H.J. van den Herik.
Tilburg, 7 December 2009
10
Toine Bogers. Recommender Systems for Social Bookmarking. Promotor: A.P.J. van den Bosch.
Tilburg, 8 December 2009
11
Sander Bakkes. Rapid Adaptation of Video Game AI. Promotor: H.J. van den Herik. Copromotor:
P.H.M. Spronck. Tilburg, 3 March 2010
12
Maria Mos. Complex Lexical Items. Promotor: A.P.J. van den Bosch. Copromotores: A. Vermeer,
A. Backus. Tilburg, 12 May 2010
13
Marieke van Erp. Accessing Natural History. Discoveries in data cleaning, structuring, and retrieval. Promotor: A.P.J. van den Bosch. Tilburg, 30 June 2010
14
Edwin Commandeur. Implicit causality and implicit consequentially in language comprehension.

Promotores: L.G.M. Noordman, W. Vonk. Copromotor: R. Cozijn. Tilburg, 30 June 2010
156
TiCC Ph.D. Series
15
Bart Bogaert. Cloud Content Contention. Promotores: H.J. van den Herik, E.O. Postma. Tilburg,
30 March 2011
16
Xiaoyu Mao. Airport under Control. Multiagent Scheduling for Airport Ground Handling. Promotores: H.J. van den Herik, E.O. Postma. Copromotores: N. Roos, A.H. Salden. Tilburg, 25 May
2011

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Airport under Control

Multiagent Scheduling for Airport Ground Handling

Airport under Control

ter verkrijging van de graad van doctor

Dutch Ministry of Economic Affairs

SIKS Dissertation Series No. 2011-13

TiCC Ph.D. Series No. 16

enjoyable working partnership but also a life-long valuable friendship.

2 AGH Scheduling Problem

3 A Review of Existing Solution Methods

4 A Lease-based Multiagent Model

5 Online Iterative Scheduling

A Airport Ground-Handling Operations

B Properties of the 80 Chosen MPSPLib Instances

SIKS Dissertation Series

TiCC Ph.D. Series

Activity-dependent Slack Time Window

Minimum time lag between the start of activity ai and aj

Project due time

Multi-project Scheduling Problem

ith project in an RCMPSP

Delay cost per time unit for project Pi

Maximum capacity of resource type Rk

Agent-based Model for AGH Scheduling

lth aggregated offer for scheduling ai,j

Project delay time given a schedule i

Set of edged in resource flow network Gk

Set of aggregated offers for scheduling ai,j

Resource quantity of Rk passing on from activity ai,j to activity ai0 ,j 0

Resource flow network of resource type Rk

Marginal delay caused by the scheduling of activity ai,j

Project agent representing project Pi

Project-agent schedule of project Pi

Complete set of all project-agent schedules

Project-agent utility given project-agent schedule i and project unit

Resource agent representing resource type Rk

Resource-agent schedule of resource type Rk

Complete set of all resource-agent schedules

Resource-agent utility given resource-agent schedule k and resource

Resource load of Rk at time t given a resource-agent schedule k

Request for quotations

Total cost of aggregated offer oi,j,l

Length of slack time window inserted after activity schedule i,j

Vector of ni lengths of slack time windows inserted after activities of

Amount of Rk scheduled to be used at time t

Vertex representing activity ai,j in resource flow network Gk

Set of vertices in resource flow network Gk

An example of Boeing 747 turnaround schedule in Gantt chart . . . . . .

AoN representation of a project . . . . . . . . . . . . . . . . . . . . . . .

An example of super AoN network for RCMPSP . . . . . . . . . . . . . .

Agent encapsulation approaches . . . . . . . . . . . . . . . . . . . . . . . .

AoN network of an example project P1 . . . . . . . . . . . . . . . . . . .

A resource flow network of R1 and the corresponding resource profile . . .

Offers sent by RA1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Comparison of three heuristics on total project stability over 100 simulations106

Scheduling of all aircraft turnaround processes at an airport is a complex task. The

Airport Ground Handling

Delay is an experience shared by almost anyone who ever travelled. Arguably, it is an

the thesis, we indicate organisation names with small capitals.

1.1. Airport Ground Handling