This document provides an introduction to operations research and the management science process. It discusses how operations research uses mathematical modeling to help organizations optimize their resources and decision-making. The management science process involves three main steps: 1) defining the problem, 2) building a mathematical model to represent the problem quantitatively, and 3) solving the model to identify optimal solutions. An example problem demonstrates how to formulate an operations research model to maximize profit subject to resource constraints.

1. Mjdah Al Shehri
Introduction
Hamdy A. Taha, Operations Research: An
introduction, 8th
Edition

2. Mute ur call

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What is management sciences/
Operation Research (OR)?
• In general, the organization goal is to optimize
the use of available resources.
• Management science/OR is a discipline that
adapts the scientific approach to problem solving
to decision making.

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• Mathematical Modeling
– A process that translates observed phenomena into
mathematical expressions.
Mathematical Modeling and the
Management Science/Operation
Research Process

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• The Management Science/OR Process
– By and large, the Management Science/OR process
can be described by the following steps procedure.

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• Basic Steps of the Management Science/OR
Process
1- Defining the Problem.
2- Building a Mathematical Model.
3- Solving a Mathematical Model.

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1- Defining the Problem
• Management Science/ OR is Applied When -
– Designing and implementing new operations.
– Evaluating ongoing Operations and Procedures.
– Determining and recommending corrective actions.

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How to Start and How to Proceed
– Identify the problem.
– Observe the problem from various points of view.
– Keep things simple.
– Identify constraints.
– Work with management, get feedback .

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2- Building a Mathematical Model
• Identify Decision Variables
–Which factors are controllable?
• Quantify the Objective and Constraints
– Formulate the function to be optimized (profit, cost).
– Formulate the requirements and/or restrictions.
• Construct a Model Shell
– Help focus on the exact data required.
• Gather Data --
– Consider time / cost issues.

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Mathematical modeling formulation: The general OR model can
be organized in the following general format:-
T. Doua Nassar 10
Maximize or minimize Objective Function
subject to
Constraints

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3- Solving a Mathematical Model
• Choose an Appropriate Solution Technique
– An optimization algorithm.
– A heuristic algorithm.
• Generate Model Solutions
• Test / Validate Model Results
– Is the solution reasonable?
– Are radical changes needed?
– Does it fit present and future plans?
– Unacceptable results? Return to modeling.
• Perform “What--If” Analyses

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EXAMPLES
• Example 1:
Wilson company produces three products: desk,
chairs, and molded steel. It is trying to decide on
the number of desks (D), chair (C), and pound of
model steels (M)

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Assumption :
1- If the nets $ 50 profit on each desk produced, $30
on each chair produced, and $ 6 per pound of
modeled steel produced. What the total profit?
The answer :
Total profit for production run can be modeled by the
expression
50 D + 30 C + 6 M

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2- if 7 pounds of raw steel are needed to manufacture
a desk, 3 pounds to manufacture a chair, and 1.15
pounds to produce a pound of model steel. What the
amount of raw steel used during the production?
The answer:
The amount of raw steel used during the production
run is modeled by the expression:
7D + 3C + 1.5 M

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3- Wilson has only 2000 pounds of raw steel available.
And at least 100 desk must be produced to satisfy
contract commitment.
The answer:
The function constraint can be modeled as :
7 D + 3C + 1.5 M <= 2000 (raw steel)
D >= 100 (contract)

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The Mathematical model for this problem is
formulated as :
MAXIMIZE 50 D + 30 C + 6 M
SUBJECT TO
7D + 3C + 1.5M <= 2000 (Raw steel)
D >= 100 (contract)