Topic 1 Introduction to Operations Research

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Topic 1: Introduction to Operations Research

• The first formal activities of Operations Research
(OR) were initiated in England during World War II,
when a team of British scientists set out to make
scientifically based decisions regarding the best
utilization of war materiel.
• After the war, the ideas advanced in military
operations were adapted to improve efficiency and
d ti it in the i ili       t
productivity i th civilian sector.
• This chapter will familiarize you with the basic
terminology of operations research, including
mathematical modeling, feasible solutions,
optimization, and iterative computations.

Dr Muhammad Al‐Salamah, Industrial Engineering, KFUPM
Read Section 1.1 OPERATIONS RESEARCH MODELS

Imagine that you have a 5
• I      i th t      h             k business
5-week b i
commitment between City A and City B. You fly out
of A on Saturdays and return on Mondays. A
l       d t i ticket    t SR400 but the i
regular round-trip ti k t costs SR400, b t th price
is SR 320 if the dates of the ticket span a
weekend. A one-way ticket in either direction costs
300. How should you b th ti k t f th 5
SR 300 H        h ld        buy the tickets for the 5-
week period?
• This is a decision-making problem which requires
1. What are the decision alternatives?
2.
2 Under what restrictions is the decision made?
3. What is an appropriate objective criterion for
evaluating the alternatives?

Dr Muhammad Al‐Salamah, Industrial Engineering, KFUPM
• Consider the alternatives:
y        g                  p
– Buy five regular A-B-A for departure on
Saturday and return on Monday of the same
week.
A-B,      B-A-B            weekends
– Buy one A B four B A B that span weekends,
and one B-A.
y                              y
– Buy one A-B-A to cover Saturday of the first
week and Monday of the last week and four B-
A-B to cover the remaining legs. All tickets in
weekend.
this alternative span at least one weekend
• The restriction on these options is that you should
be able to leave A on Saturday and return on
Monday of the same week.
Dr Muhammad Al‐Salamah, Industrial Engineering, KFUPM
• The objective criterion for evaluating the proposed
alternative is the price of the tickets. The
alternative that yields the smallest cost is the best:
– Alternative 1 cost = 5 X 400 = SR2000
– Alternative 2 cost = 300 + 4 X 320 + 300 =
SR1880
– Alternative 3 cost = 5 X 320 = SR1600
• Choose alternative 3.

Dr Muhammad Al‐Salamah, Industrial Engineering, KFUPM
• The three main components of an operations
research model are
1. Alternatives
2. objective criterion
3. constraints

Dr Muhammad Al‐Salamah, Industrial Engineering, KFUPM
• Another Example: what would be the width and
the height of the maximum-area rectangle formed
out of a piece of wire of length L inches?
• The number of alternatives is infinite.
• We can define the width and height as continuous
(algebraic) variables
g
w= width of the rectangle in inches
h = height of the rectangle in inches
• The restrictions can be expressed as
1. Width + Height = Half the length of the wire.
2. Width and height cannot be negative.

Dr Muhammad Al‐Salamah, Industrial Engineering, KFUPM
• These restrictions are translated algebraically as
1. 2( w + h) = L
2. w ≥ 0, h ≥ 0

• The objective of the problem is the maximization of
the area of the rectangle.
• Let z be the area of the rectangle:
Maximize z = wh
bj t t
subject to
2( w + h) = L
w, h ≥ 0

Dr Muhammad Al‐Salamah, Industrial Engineering, KFUPM
• The general OR model can be organized in the
following general format:

Maximize or minimize Objective Function
Maximize or minimize Objective Function
Subject to
Constraints

Dr Muhammad Al‐Salamah, Industrial Engineering, KFUPM
• A solution of the model is feasible if it satisfies all
the constraints.
• It is optimal if, in addition to being feasible, it yields
the best (maximum or minimum) value of the
function.
objective function

Dr Muhammad Al‐Salamah, Industrial Engineering, KFUPM
Read Section 1.2 SOLVING THE OR MODEL

l ti techniques i l d
• OR solution t h i     include
– Linear programming
– Integer programming
– Dynamic programming
et o programming
– Network p og a      g
– Nonlinear programming

Dr Muhammad Al‐Salamah, Industrial Engineering, KFUPM
Read Section 1.4 ART OF MODELING

Dr Muhammad Al‐Salamah, Industrial Engineering, KFUPM
Read Section 1.6 PHASES OF AN OR STUDY

The i i l h            for implementing OR i
• Th principal phases f i l          ti      in
practice include:
1. Definition of the problem
2. Construction of the model
3. Solution of the model
4. Validation of the model
5. Implementation of the solution.

Dr Muhammad Al‐Salamah, Industrial Engineering, KFUPM

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