Operations Research ILO 7015: Pro Jay Goy
Operations Research ILO 7015: Pro Jay Goy
Operations Research ILO 7015: Pro Jay Goy
ILO 7015
Lecture1
Introduction to Operations Research
Lecture by
Pro Jay Goy
Department of Mechanical Engineering
2. Classification by Behavior
a) Static Models: These models do not consider the impact of changes that
takes place during the planning horizon (independent of time).
b) Dynamic Models: I these models time is considered as one of the
important variables and admit the impact of changes generated by time.
A series of interdependent decisions are required during planning
Classification of Models
3. Classification by Method of Solution
a) Analytical Models: These models have a specific mathematical structure
and thus can be solved by known analytical or mathematical
techniques. Ex. LPP, assignment or transportation model.
b) Simulation Models: They also have a mathematical structure but they
can not be solved by purely using the tools and techniques of
mathematics. A simulation model is essentially computer assisted
experimentation on a mathematical structure of a real time structure in
order to study the system under a variety of assumptions.
-Simulation modelling has the advantage of being more flexible than
mathematical modeling and hence can be used to represent complex
systems.
Structure of Mathematical Model
We can look at any situation as a decision making problem
whose solution requires identifying three components:
1) What are decision alternatives?
2) Under what restrictions is the decision made?
3) What is an appropriate objective criterion for evaluating the
alternatives?
Example:
Imagine that you have to plan 5 weeks business trips between Mumbai
and Delhi. You are required to fly on Monday and return on Thursday
every week. A round trip ticket cost 7000 INR, but a 20% discount is
granted if the dates of the return ticket span at least a weekend. A one
way ticket in either direction cost 75% of the regular price. How
should you buy the tickets for the 5 week period?
Structure of Mathematical Model
• Three alternatives are considered as follows:
1. Buy 5 regular return tickets MUM-DEL-MUM.
2. Buy 1 MUM-DEL, Four DEL-MUM-DEL that span weekends, and 1 DEL-MUM
3. Buy 1 MUM-DEL-MUM to cover first Monday and return on last Thursday and
Four DEL-MUM-DEL that span weekends. (Each ticket in this way will span a
weekend)
2. Model Construction
Translating the problem definition into mathematical relationships.
3. Model Solution
Computation of the value of decision variables that maximize (or
minimize) the objective function.
4. Model Validation
Checks whether or not the proposed model does what it is supposed
to do? The model is considered valid if, under similar input
conditions, it reproduces past performances.
5. Implementation
Translation of the results into operating instructions.
Solving the OR Model
• In OR, we do not have a single general technique that solves all
mathematical models that arise in practice.
• Instead, the type and complexity of the mathematical model dictate
the nature of the solution method.
• The most prominent OR technique is linear programming (designed
for strict linear objective and constraint function). Other techniques
include integer programming (in which variable assume integer
values); dynamic programming (original model can be decomposed
in smaller sub problems); network programming (problem can be
modelled as a network); and non-linear programming ( functions
of the model are nonlinear).
• The solutions obtained using OR techniques are not generally
obtained in (formula like) closed forms. Instead, they are determined
by ‘Algorithms’. An algorithm provides fixed computational rules
that are applied repetitively to the problem, with each repetition
(called iteration) moving the solution closer to the optimum.
• Iterations are typically tedious, it is imperative that these algorithms
Scope of Operations Research
• In Agriculture
– Optimum allocation of land to various crops
– Optimum distribution of water from various resources
• In Finance
– To find out the profit plan for the company
– To determine best replacement policies
• In Marketing
– To minimize the cost of transportation
– To determine size of stock to meet future demand
• In Production Management
– To determine the quantity to be produced
– Allocation of machines
– To determine optimum product mix
• In Personnel Management
– Selection of suitable personnel on minimum salary
– Mixes of ages and skills
Limitations of Operations Research
• Dependence on a Computer
OR techniques try to find out an optimal solution taking into account all the factors.
In the modern society these factors are enormous and expressing them in quantity
and establishing relationships among these require voluminous calculations that
can only be handled by computers.
• Non-Quantifiable Factors
All relevant variables do not lend themselves to quantification (qualitative or
emotional factors). Factors that cannot be quantified find no place in OR models.
• Implementation
Implementation of OR model is a delicate task. It must take into account the
complexities of human relations and behavior. (due to conventional thinking,
changes face lot of resistance from workers)
Introduction to Linear Programming Problem
Introduction to Linear Programming Problem
Requirements of Linear Programming
1. Decision variables and their relationship
The decision variables refer to candidates that are competing with one another for
sharing the given limited resources. These variables are usually interrelated in terms
of utilization of resources and need simultaneous solutions. Decision variables should
have linear relationship
5. Non-Negative Restriction
Any Questions