Course Book
Operations Research
4th Year Mathematics Department
Academic Year: 2011-2012
3 Hours per Week
Operations Research
Soran University/College of Science/Mathematics Departments
Lecturer: Farhad Djannaty
Email: fdjanaty@yahoo.com
Course coordinator: Nowzad M. A.
Email: nowzad.a@soranu.com
The Aim of the Course :
The student is expected to get familiar with the history of operations research and its
Origin. He should learn that whatever he studies is a miniature of what is happening
In the computer. One should understand that any operation taking place in his living
Environment is possible to be done in a better way and very likely in the best way.
He should fully learn the masterpiece of George B Dantzig, that is, simplex method
And the great role it has played in saving billions of dollars in the large incorporations
Around the world. The impact of computer on the progress of the field of operations
Research should be appreciated by the class. They should learn how to work with a
number of software available to solve the linear programming problems, including
Matlab. Since the second world war simplex has gone under a tremendous upgrades
Which is an integral part of the study of operations research and are to be learned by
The readers. The award winning work of Karmarkar, that is, interior point method,
Which can solve a very large linear programming problems, which took place in 1986
And many of the lecturers and students of the Kurdistan Region are not aware of it
Is a must in studying operations research. The students should be acquainted with
The real life applications of the operations research such as Transportation problem
Network problems and how to solve them.
Course Description:
The course starts with a lengthy history of operations research and the impact of
operations research on the society. A number of award winning researches are raised
To encourage the students to take the course more seriously. A prototype example is
initiating the important the linear programming chapter. This example is repeated over
And over throughout the course. The simplex method is explained both algebraically
and in tabular form and the interior point method is shortly considered. Postoptimality
Analysis and computer implementation of the simplex method are mentioned in
summary. The theoretical foundation of the simplex method and the revised simplex
method along with a fundamental insight which is the basics of duality theory are
brought up. Duality theory and dual simplex and sensitivity analysis are thoroughly
described. A number of special simplex methods such as transportation problem and
network optimization are discussed. There will be some computer lab hours as well
which teaches the students how to solve large linear programming problem by
computer. Tutoring is an integral part of the course which encourages the students to
solve problems and assignments.
1st week
The Origins of Operations Research, The Nature of Operations Research, The
Impact of Operations Research, Algorithms and OR Courseware
Defining the Problem and Gathering Data, Formulating a Mathematical Model
2nd week
Deriving Solutions from the Model, Testing the Model, Preparing to Apply the
Model.
3rd week
4th week
Model Implementation, Prototype Example, The Linear Programming Model ,
Assumptions of Linear Programming
Problem solving sessions
Some Case Studies, Displaying and Solving Linear Programming Models using
5th week
Matlab, Additional Examples, Formulating Very Large Linear Programming
Models
6th week
Answering questions about the first exam.
First examination
Case study 1 Auto Assembly
7th week
Case study 2 Cutting Cafeteria Costs
Case study 3 Staffing a Call Center
8th week
9th week
Problem solving sessions
Foundations of the Simplex Method, The Revised Simplex Method, A
Fundamental Insight , Conclusions
10th week
11th week
12th week
The Essence of Duality Theory, Economic Interpretation of Duality, PrimalDual Relationships, Adapting to Other Primal Forms
Answering questions about the second exam
Second examination
The Role of Duality Theory in Sensitivity Analysis, The Essence of Sensitivity
Analysis, Applying Sensitivity Analysis
Case study 1 Controlling Air Pollution,
13th week
Case study 2 Farm Management
Case study 3 Assigning Students to Schools
14th week
The Dual Simplex Method, Parametric Linear Programming
15th week
The Upper Bound Technique, The Upper Bound Technique
16th week
Problem solving sessions
17th week
Answering questions about the third exam.
Third examination
18th week
An Interior-Point Algorithm
19th week
Problem solving sessions
20th week
21st week
22nd week
23rd week
The Transportation Problem, North west method, Russell Method, Vogel
Method
A Streamlined Simplex Method for the Transportation Problem
Answering questions about the forth exam
Forth examination
A Streamlined Simplex Method for the Transportation Problem
The Assignment Problem
Hungarian method, Shipping
24th week
Case study 1 Wood to Market
Case study 2 Project Pickings
25th week
26th week
27th week
Network Optimization Models, Prototype Example, The Terminology of
Networks, The Shortest-Path Problem
The Minimum Spanning Tree Problem, The Maximum Flow Problem,
The Minimum Cost Flow Problem, The Network Simplex Method
Problem solving
Fifth examination
References:
1. Hillier, S.H. and Lieberman, G. J. "Introduction to Operations Research", Mc
Graw Hill, 2007
2. Bazaraa, M.S., Jarvis, J.J., "Linear Programming and Network Flows",
Johan Wiley, 2005
3. Taha H.. "Operations research: An Introduction 9th Edition", Printice Hall,
2010
4. Bronson R., Naadimuthu, G "Schaum's Outline of Operations Research"
Mc-Graw Hill 1997