28 Sep 2010

EMM 5706
DESIGN OF MANUFACTURING SYSTEM
System Modeling
Lecturer:
Assoc. Prof. Datin Dr Napsiah Ismail
Presented by Group 7
Hamidreza Soltani (GS26516)
Masoud Pishdar (GS26514)
Abdollah Omer Ibrahim (GS28223)
1. What is system?
Overview
2. What is modeling and simulation?
3. What is simulation modeling and analysis?
4. What types of problems are suitable for
simulation?
5. How to select simulation software?
6. What are the benefits and pitfalls in
modeling and simulation?
7. References
• SYSTEM MODELING

What is system?
System

A broader definition of a system is, “Any object which has some action
to perform and is dependent on number of objects called entities, is a
system”.

For example a class room, a college, or a university is a system.

University consists of number of colleges (which are entities of the
system called university) and a college has class rooms,
students, laboratories and lot many other objects, as entities. Each
entity has its own attributes or properties.
Also system can be defined as
(i) Continuous: (Fluid flow in a pipe, motion of an aircraft or trajectory of a
projectile)
(ii) Discrete: (a factory where products are produced and marketed in lots)
 modeling

• SYSTEM MODELING

What is modeling and simulation?

5
MODELING AND SIMULATION

Model of a system is the replica of the system, physical or

mathematical, which has all the properties and functions of the
system, whereas simulation is the process which simulates in the
laboratory or on the computer.

In fact, a modeling is the general name whereas simulation is specific

name given to the computer modeling.
Modeling is the process of producing a model which :

• Representation of the construction and working of some system of

interest;
• Similar to but simpler than the system it represents;
• Enable the analyst to predict the effect of changes to the system;
• A close approximation to the real system and incorporate most of its
salient features; and
• Not so complex that it is impossible to understand and experiment with
it.
• A good model is a judicious trade off between realism and simplicity.
• Simulation practitioners recommend increasing the complexity of a
model iteratively.
Five basic steps
While building a model certain basic principles are to be
followed. While making a model one should keep in mind five
basic steps.

• Block building
• Relevance
• Accuracy
• Aggregation
• Validation
Models can be put under three categories, physical
models, mathematical models and computer
models.
All of these types are further defined as static and dynamic
models.
Different types of models
PHYSICAL MODELS

Physical models are of two types, static and dynamic.

Static physical model is a scaled down model of a system

which does not change with time. An architect before
constructing a building, makes a scaled down model of the
building, which reflects all it rooms, outer design and other
important features.

Dynamic physical models are ones which change with time or

which are function of time. In wind tunnel, small aircraft models
(static models) are kept and air is blown over them with
different velocities and pressure profiles are measured with the
help of transducers embedded in the model.
MATHEMATICAL MODELS

Most of the systems can in general be transformed into

mathematical equations. These equations are called the
mathematical model of that system. Since beginning, scientists
have been trying to solve the mysteries of nature by observations
and also with the help of Mathematics.

Equations of fluid flow represent fluid model which is dynamic.

A static model gives relationships between the system attributes

when the system is in equilibrium.
COMPUTER MODELS

With the advent of computers, modeling and simulation concepts

have totally been changed. Now all types of stochastic as well as
continuous mathematical models can be numerically evaluated with
the help of numerical methods using computers. Solution of the
problem with these techniques is called computer modeling.

what is the difference between mathematically obtained solution of

a problem and simulation.
Literal meaning of simulation is to simulate or copy the behavior of a
system or phenomenon under study. Simulation in fact is a computer
model, which may involve mathematical computation, computer graphics
and even discrete modeling.
SIMULATION
 an analysis tool for understanding the system.
 the operation of a model of the system.

Naylor, defines the simulation as follows:

Simulation is a numerical technique for conducting experiments
on a digital computer, which involves certain types of
mathematical and logical models over extended period of real
time.

We thus define system simulation as the technique of solving

problems by the observation of the performance, over time, of a
dynamic model of the system.
In other words, we can define simulation as an experiment of
physical scenario on the computer.
Shannon [1975] defines simulation as an experimental
and applied methodology which seeks to:
i. describe theories or the behavior of systems;.
ii. construct hypotheses that account for the
observed behavior;
iii. use these theories to predict future behavior,
that is, the effects that will be produced by
changes in the system or in its method of
operation.
• Simulation is used before an existing system is
altered or a new system built.

To reduce the chances of

failure to meet specifications
To eliminate unforeseen
bottlenecks
WHY?
To prevent under or over-
utilization of resources
To optimize system performance
 Strengths of Simulation
• Time compression – the potential to simulate years of real
system operation in a few minutes or seconds.
• Component integration – the ability to integrate system
components to study interactions
• Risk avoidance – hypothetical or potentially dangerous systems
can be studied without the financial or physical risks that may be
involved in building and studying a real system
• Physical scaling – the ability to study much larger or smaller
versions of a system
• Repeatability – the ability to study different systems in identical
environments or the same system in different environments
• Control – everything in a simulation can be precisely monitored
and exactly controlled

16
• SYSTEM MODELING

?What is simulation modeling and analysis

 Simulation Modelling

• Simulation is a modeling and analysis tool used for

the purpose of designing planning and control of
manufacturing systems.
• Simulation may be defined as a concise framework
for the analysis and understanding of a system.
• It is an abstract framework of a system that facilitates
imitating the behavior of the system over a period of
time.
• In contrast to mathematical models, simulation
models do not need explicit mathematical functions
to relate variables
• Therefore ,they are suitable for representing complex
systems to get a feeling of real system.
• One of the greatest advantage of a simulation
models is that it can compress or expand time.
• Simulation models can also be used to observe a
phenomenon that cannot be observed at very small
intervals of time.
• Simulation can also stops continuity of the
experiment.
• Simulation modeling techniques are powerful for
manipulation of time system inputs, and logic.
• They are cost effective for modeling a complex
system, and with visual animation capabilities they
provide an effective means of learning,
experimenting, and analyzing real-life complex
systems such as FMS.
• Simulation are capable of taking care of stochastic
variable without much complexity.
• They enable the behavior of the system as a whole to
be predicted.
 Simulation Model
 Consist of the following components:
o system entities
o input variables
o performance measures
o functional relationships

 Almost all simulation software packages

provides constructs to model each of the above
components
 Simulation Model
• Classification of simulation models
– Static vs. dynamic
– Deterministic vs. stochastic
– Continuous vs. discrete
• Most operational models are dynamic,
stochastic, and discrete – will be called
discrete-event simulation models
 DISCRETE-EVENT SIMULATION
 Discrete-event simulation: Modeling of a system as it evolves over
time by a representation where the state variables change
instantaneously at separated points in time
o More precisely, state can change at only a countable number of
points in time
o These points in time are when events occur
 Event: Instantaneous occurrence that may change the state of the
system
o Sometimes get creative about what an “event” is … e.g., end of
simulation, make a decision about a system’s operation
 Can in principle be done by hand, but usually done on
computer
 DISCRETE-EVENT SIMULATION
 Example: Single-server queue
 Estimate expected average delay in queue (line, not service)
 State variables
 Status of server (idle, busy) – needed to decide what to do with an
arrival
 Current length of the queue – to know where to store an arrival that
must wait in line
 Time of arrival of each customer now in queue – needed to compute
time in queue when service starts
 Events
 Arrival of a new customer
 Service completion (and departure) of a customer
 • SYSTEM MODELING

?What types of problems are suitable for simulation

 WHEN SIMULATION IS APPROPRIATE?

• Simulation enables the study of, and experimentation

with, the internal interactions of a complex system,
or of a subsystem within a complex system.
• Informational, organizational, and environmental
changes can be simulated, and the effect of these
alterations on the model’s behavior can be observed.
• The knowledge gained in designing a simulation
model may be of great value toward suggesting
improvement in the system under investigation.
• By changing simulation inputs and observing the
resulting outputs, valuable insight may be obtained
into which variables are most important and how
variables interact
• Simulation can be used as a pedagogical device to reinforce
analytic solution methodologies.
• Simulation can be used to experiment with new designs or
policies prior to implementation, so as to prepare for what
may happen.
• Simulation can be used to verify analytic solutions.
• By simulating different capabilities for a machine,
requirements can be determined.
• Simulation models designed for training allow learning
without the cost and disruption of on-the-job learning.
• Animation shows a system in simulated operation so that he
plan can be visualized.
 WHEN SIMULATION IS NOT APPROPRIATE?

• The Problem is solved by common sense.

• The Problem is solved by analytical means.
• It is easier to perform direct experimentation
• The resources are not available
• The cost exceeds savings
• The time is not available
• No enough time and personal are not available
• Un-reasonable expectations
• The behavior of the system is too complex to define
 Stages in Simulation
Step 1 - Step 2 - Step 3 -
Collect and
Identify the Formulate process real
problem. the problem. system data.

Step 5 - Step 4 -
Validate the Formulate and
model. develop a model.

Step 7 - Step 8 -
Step 6 -
Select appropriate Establish
Document model
experimental experimental
for future use. design. conditions for runs.

Step 10 - Step 9 -
Interpret and Perform
present results. simulation runs.

Step 11 -
Recommend
further course of
action
 Simulation Model
Steps Involved:
1- Identify the problem
Every study should begin with a statement of the problem. If the
statement is provided by the policy makers, or those that have the
problem, the analyst must ensure that the problem being described is
clearly understood. If the problem is being developed by the analyst, it is
important that the policy makers understand and agree with the
formulation
2- Formulate the problem
The objective indicates the questions to be answered by simulation. At
this point a determination should be made concerning whether
simulation is the appropriate methodology for the problem as
formulated and objectives as state. Assuming it is decided that
simulation is appropriate; the overall project plan should include a
statement of the alternative systems to be considered, and a method for
evaluating the effectiveness of these alternatives. It should also include
the plan for the study in terms of the number of people involve, the cost
of the study, and the number of days required to accomplish each phase
of work with the anticipated results at the end of each stage.
3- Collect the process real system data
The construction of a model of the system is problem as much
art as science. The art of modeling is enhanced by an ability to
abstract the essential features of a problem, to select and modify
basic assumptions that characterize the system, and then to
enrich and elaborate the model until a useful approximation
results. Thus it is best to start with a simple model and build
toward greater complexity. However, the model complexity
need not exceed that required to accomplish the purposes for
which the model is intended. It is not necessary to have a one-
to-one mapping between the model and the real system.
4-Formulate & develop a model
There is a constant interplay between the construction of the model and
the collection of the needed input data. As the complexity of the model
changes, the required data elements may also change. Also, since data
collection takes such a large portion of the total time required to
perform a simulation, it necessary to begin it as early as possible,
usually together with early stages of the model building.
 5- Verification

• Is the computer implementation of the conceptual

model correct?
• Procedures
 Structured programming
 Self-document
 Peer-review
 Consistency in input and output data
 Use of IRC and animation
 6- Validation

• Can the conceptual model be substituted, at least

approximately for the real system?
• Procedures
 Standing to criticism/Peer review (Turing)
 Sensitivity analysis
 Extreme-condition testing
 Validation of Assumptions
 Consistency checks
 Validation -contd.

Validating Input-Output transformations

Validating using historical input data
 Experimentation and Output Analysis

• Performance measures
• Statistical Confidence
• Run Length
• Terminating and non-terminating systems.
• Warm-up period.
 Steps in Simulation -contd.

• Production Runs and Analysis

• Documentation/Reporting
• Implementation
 Simulation Experiment
It is a test or series of test, meaningful
changes are made to the input variables
We can observe and identify the reasons of
change in the performance measures.

Steps Involved:
7- Select appropriate experimental design
The alternatives that are to be simulated must be
determined. Often, the decision concerning which
alternatives to simulate may be a function of run that
have been completed and analyzed. For each system
design that is simulated, decision need to be made
concerning the length of the initialization period, the
length of simulation runs, and the number of
replications to be made of each run
8- Establish experimental conditions for runs
Production runs, and their subsequent analysis, are used to
estimate measures of performance for the system designs that are
being simulating.

9-Perform simulation runs

Based on the analysis of the runs that have been
completed, the analyst determines if additional runs
are needed and what design those additional
experiments should follow
10- Documentation and reporting:
There are two types of documentation:
Program documentation is necessary for numerous
reasons. If the program is going to be used again by the
same or different analysts, it may be necessary to
understand how the program operates. This will build
confidence in the program, so the model users and
police makers can make decisions based on the
analysis. Also, if the program is to be modified by the
same or a different analyst, this can be greatly
facilitated by adequate documentation.
11-Recommend further course of action

Progress reports give a chronology of work done and

decisions made. This can prove to be of great value in
keeping the project on course, also it help the
improvement of this simulation in the future.
Procedure for Conducting a Simulation Study

Plan Study

Define System

Build Model

Run Experiments

Analyze Output

Report Results
Use of Simulation in Manufacturing

Manufacturing Manufacturing Issues Performance Measurement

Environments of Manufacturing System
New equipment and buildings Number and type of machines Throughput (number of jobs
are required (called “green for a particular objective. produced per unit of time).
fields”). Location and size of inventory Time in system for jobs
New equipment is required in buffers. (makespan).
an old building. Evaluation of a change in Times jobs spend in queues.
A new product will be product mix (impact of new Time that jobs spend being
produced in all or part of an products). transported.
existing building. Evaluation of the effect of a Sizes of in-process inventories
Upgrading of existing new piece of equipment on an (WIP or queue sizes).
equipment or its operation. existing manufacturing line. Utilization of equipment and
Concerned with producing the Evaluation of capital personnel (i.e., proportion of
same product more efficiently. investments. time busy).
Changes may be in the Manpower requirements Proportion of time that a
equipment (e.g., introduction planning. machine is under fadum,
of a robot) or in operational Throughput analysis. blocked until and starved.
procedures (e.g., scheduling Makespan analysis. Proportion of jobs produced
rule employed). which must be reworked or
Bottleneck analysis.
Evaluation of operational scrapped.
procedures. Return on investment for a
new or modified
Evaluation of policies for
manufacturing system.
component part or raw
material inventory levels.
Evaluation of control strategies
 Areas suitable for simulation
• Applications of simulation abound in the areas of :
government health care
defense ecology and environment
computer and sociological and
communication systems behavioral studies
manufacturing biosciences
transportation (air traffic epidemiology
control)
economics and business services (bank teller
analysis scheduling)
 Simulation language

• describes the operation of a simulation on a computer.

• There are three major types of simulation:

1. Discrete event simulation languages, viewing the
model as a sequence of random events each
causing a change in state. For example Arena.
2. Continuous simulation languages, viewing the
model essentially as a set of differential equations.
For example ACSL.
3. Hybrid, and other. for example AnyLogic multi-
method simulation tool, which supports
System dynamics.
 Types of simulation software

Simulation software is based on the process of imitating a real

phenomenon with a set of mathematical formulas.

Simulation soft ware can be classified to :

1. General simulation fall into two categories: discrete event
and continuous simulation.

2. Electronic simulation utilizes mathematical models to replicate

the behavior of an actual electronic device or circuit.
Examples of simulation software:

 Open Source such as ASCEND and NS2.

 Commercial such as AMESim and Arena.
 SIMULATION SOFTWARE
1st Category 2nd Category 3rd Category Webbased
simulation
Channel Simulation Simulation
purpose language Packages
language
FORTRANC, C + GPSS ARENA JAVASIMWEB-
+VB, VB+ (1965)SIMSCRIPT (1993)AutoMOD BASED
+.......... (1963)SIMULA QUEST EXTEND SIMULATION. . .
............ GASP PROMODEL . . . . . . . .. . . .
(1961)ALGOL
. . . . . . . . . . .. TaylorED . . . . . . .. . . . .
......... SLAM WITNESS. . . . . . . . . . .. . . . . .
(1979)SIMAN
.many other . . . . . .and .....
GPSS/4
oriented (1977)SLAM – many more
languages IIAWESIM
(1995)GEMS
 Simulators

 Facilitates the development of models related to a

specific class of problems.
• Short development cycles.
• Rapid model prototypes.
• Gentle learning curve.
• Lack flexibility to model outside of class.
• Do not handle “unusual” situations.
• Built in assumptions can be problematic.
 Arena simulation software

• Arena is a discrete event simulation software simulation and

automation software developed by Systems Modeling and
acquired by Rockwell Automation in 2000.
• In Arena, the user builds an experiment model by placing
modules (boxes of different shapes) that represent processes or
logic. Connector lines are used to join these modules together
and specifies the flow of entities.

• Arena integrates very well to

Microsoft technologies. It
includes
Visual Basic for Applications so
models can be further automated
if specific algorithms are needed.
 ARENA

• Process hierarchy.
• Integrates with Microsoft desktop tools
• Spreadsheet interface
• Crystal reports
• Free runtime software.
• Fully graphical environment. No programming
required.
• VBA embedded.
• Optimization with Opt Quest for Arena.
• Builds reusable modules.
• $1,000 - $17,000 ($US). Various add-in modules
available
 Manufacturing Systems modeling

 Material Flow Systems

• Assembly lines and Transfer lines
• Flow shops and Job shops
• Flexible Manufacturing Systems and Group
Technology
 Supporting Components
• Setup and sequencing
• Handling systems
• Warehousing
 Goals of Manufacturing Modeling

 Manufacturing Systems
• Identify problem areas
• Quantify system performance
 Supporting Systems
• Effects of changes in order profiles
• Truck/trailer queueing
• Effectiveness of materials handling
• Recovery from surges
METHODOLOGY FOR SELECTION OF SIMULATION SOFTWARE

Need for purchasing simulation

Stage 1 software

Stage 2 Initial software survey

Stage 3
Evaluation

Stage 4
Software selection
Stage 5
Software contract negotiation

Stage 6
Software purchase
56
Figure – 3 : Stages of simulation software selection methodology
 Needfor
Need for
purchasing
purchasing
simulation
simulation
software
software

Purpose Constrai Models Model

of nts to be develope
simulatio simulate rs
n d

“Quick D/C – Previous

Combi Individ exper. in
Educati and ind or Time Discret Contin
ned ual simulation
on dry” - researc e uo. prefere
disc/co
ind h nt nce

Initial
Initial
software
software
survey
survey

57
Continued in the next slide
 Short list of software
for evaluation

Initial
Initial software Initial software Initial software Initial software
software
survey survey survey survey
survey

Initial software
Initial survey
software
survey

Results of Evaluation

Software
Software
selection
selection

Selection of software

Legend:

Software
Software
contract Stages
contract
negotiation
negotiation

Contract acceptable
Intermediate
Results
Software
Software
purchase
purchase Elements
 ProModel

• ProModel is offered by ProModel Corporation

• It is a simulation and animation tool designed to model
manufacturing systems.
• ProModel offers 2-D animation with an optional 3-D like
perspective view.

60
 Promodel
• State-of-the-art simulation
engine
• Graphical user interface
• Distribution-fitting.
• Output analysis module
• Optional optimizer.
• Modules designed for:
– Manufacturing
– Healthcare
– Services
• $17,000 ($US)
61
 Case study
Table – 1 : Machine Area Information

Machine Area (m2)

M1 20 x 20
M2 20 x 20
M3 20 x 20
M4 20 x 20
M5 20 x 20
M6 20 x 20
M7 20 x 20
M8 20 x 20
M9 20 x 20
M10 20 x 20

62
 Table – 2 : Part Job Sequence and Quantity Information

Part Type Job Sequence Quantity

P1 8-6-8-10-4 160
P2 7-9-2 310
P3 6-5 280
P4 3-1-3 265
P5 5-6-7-10 80
P6 7-9-7-8 125
P7 7-9 360
P8 3-4-1-6 240
P9 2-7 175
P10 2-7-9-5 95
P11 10-8-5 100
P12 1-3-10 230
P13 8-10-5-6 285
P14 9-2-7 315
P15 6-8-10 50
P16 4-3 275
P17 6-5 260
P18 4-3-1 150
Table – 3 : Processing Time Information (in minutes)
Machines
Part Type
M1 M2 M3 M4 M5 M6 M7 M8 M9 M10

P1 0 0 0 2 0 3 0 2+ 0 4
1
P2 0 6 0 0 0 0 2 0 3 0
P3 0 0 0 0 4 1 0 0 0 0
P4 2 0 2+ 0 0 0 0 0 0 0
5
P5 0 0 0 0 4 2 1 0 0 5
P6 0 0 0 0 0 0 2+ 2 4 0
1
P7 0 0 0 0 0 0 4 0 1 0
P8 3 0 4 2 0 2 0 0 0 0
P9 0 3 0 0 0 0 2 0 0 0
P10 0 5 0 0 1 0 3 0 1 0
P11 0 0 0 0 2 0 0 2 0 1
P12 1 0 3 0 0 0 0 0 0 3
P13 0 0 0 0 1 2 0 2 0 3
P14 0 2 0 0 0 0 1 0 3 0
P15 0 0 0 0 0 2 0 1 0 2
P16 0 0 4 2 0 0 0 0 0 0
P17 0 0 0 0 5 3 0 0 0 0
P18 4 0 6 2 0 0 0 0 0 0

64
 Here the initial solution for the above case study is obtained using
genetic algorithm as below

Cell Formation
Cell 1 = 3 1 10 4
Cell 2 = 8 6
Cell 3 = 2 9 7 5
 

65
 

(Run Hours 231.57) 66

from above table average process time in percentage of total scheduled
hours = (39.62+14.97+20.04+11.88+11.16+21.7+16.99+22.89+23.89+20.51)/18
= 11.31%=0.1131
67
average process time = 0.1131*231.57*60=1572.05
Run hours 352 The solution for the above case study using heuristic method is as follows
 
Step 1 : Arrange all machines randomly according to the given dimensions of machines. Here machine to machine
clearance of 1 m is also considered.

68
Step 2 : From job sequence of parts, check the minimum sequence (2 machines)
common for all parts e.g. M7 – M9, M5 – M6, M4 – M3, M8 – M6, M8 – M10 and bring
those 2 machines closer or nearer to each other.

(Run Hours 229.37)

 Step 3 : From job sequence, calculate number of times, all parts uses the same
machines.

M1-4
M2-4
M3-6
M4-4
M5-6
M6-7
M7-8
M8-6
M9-5
M10-6

70
  
The least utilized machines are M1,M2 and M4. these machines are kept away from remaining
machines or at periphery so that they will not obstruct other more utilized machines.( e.g. 3-1-3, 1-
3-10, 3-4-1-6 i.e. 3 must be closer to 1 and 2-7, 2-7-9-5, 9-2-7, i.e. 2 must be closer to 7 & 9). In
this step, since the row distance is high, it will take more time for the vehicle to move from one
machine to another machine. So the row distance is reduced from 5 machines to 3 and 4
machines.

(Run hours 223.24) 71

  
The least utilized machines are M1,M2 and M4. these machines are kept away from remaining
machines or at periphery so that they will not obstruct other more utilized machines.( e.g. 3-1-3, 1-
3-10, 3-4-1-6 i.e. 3 must be closer to 1 and 2-7, 2-7-9-5, 9-2-7, i.e. 2 must be closer to 7 & 9). In
this step, since the row distance is high, it will take more time for the vehicle to move from one
machine to another machine. So the row distance is reduced from 5 machines to 3 and 4
machines.

72
(Run hours 223.24)
Step 5: Here M5 is accompanied M6, M7 is accompanied by
M9, M3 is accompanied by M4. These machines are kept at
minimum possible distance.
 
Step 6: now considering maximum number of parts to be
processed and their job sequence.
P7=360, 7-9
P2=310, 7-9-2,
P14=315, 9-2-7
So these machines are at minimum distance in straight line
manner (7-9-2)
In next iteration next lower maximum parts are considered.

73
(Run hours 213) 74
 Step 7: place remaining machines closer to respective machines according
to job sequence.
 

average process time(%) per part =

(42.98+16.24+21.75+12.88+12.10+23.54+18.43+24.83+25.92+2
2.25)/18 = 12.273%=0.1273
average process time per part type =0.1273*213.45*60 = 75

1571.84 min.
average material handling time per part type = (82.26*213.45*60) / (100*18)
= 585.27 min average process time(%) per part =
(42.98+16.24+21.75+12.88+12.10+23.54+18.43+24.83+25.92+22.25)/18 =
12.273%=0.1273 76
average process time per part type =0.1273*213.45*60 = 1571.84 min.
CELL FORMATION 
Cell 1 – 2 9 7
Cell 2 - 10 5 6
77
Cell 3- 4 3 8 1
 CONCLUSIONS

• the application for simulation to address manufacturing problems.

• Developments in the area of simulation – existing softwares for discrete
event simulation and conduction of simulation studies were reviewed.
• The necessity and importance of simulation for modeling and analyzing the
various classes of manufacturing problems was focused in this paper;
• we hope this paper may encourage the extensive use of simulation in
manufacturing and development of simulation technology for addressing
the problems which need serious attention.
78
 References
• Averill M. Law, W. David, Kelton,2000 “Simulation Modeling and Analysis”,
McGraw-Hill
• Charles Harrell, et al., 2000, “Simulation Using ProModel”, McGraw-Hill
• Ramsey Suliman, et al.,2000 “Tools and Techniques for Social Science
Simulation”, Physica Verlag
• Michael Pidd, 1998, “Computer Simulation in Management Science”, John
Wiley & Sons
• Michael Prietula, et al., 1998, “Simulating Organizations: Computational
Models of Institutions and Groups”, Mit. Press
• David Profozich,1997, “Managing Change with Business Process
Simulation”, Pearson Ptr.
• Paul A. Fishwick, Richard B. Modjeski, 1991, “Knowledge-Based
Simulation”,Springer-Verlag
• Klaus G. Troitzsch, et al., 1996, “Social Science Microsimulation”, Springer
Verlag
• Harry A. Pappo, 1998, “Simulations for Skills Training”, Educational
Technology Publications
 Thank you

The end