introduction

 
INTRODUCTION
 

The Operational Research (OR) specialization is designed for students who want to use mathematical techniques to model and analyze decision problems. It aims to apply the scientific method to decision making. Operational Research is the discipline of applying advanced analytical methods to help make better decisions. By using techniques such as problem structuring methods and mathematical modeling to analyze complex situations, operational research gives executives the power to make more effective decisions and build more productive systems based on: a better understanding of the problems,  More complete data,  Consideration of all available options,  Careful predictions of outcomes, estimates of risk, and The latest decision tools and techniques.
OR helps in allocating scarce resources across competing activities in order to improve performance and efficiency. It studies the analysis and planning of complex systems. This course will focus on the optimization of deterministic systems using Linear Programming.
   The program includes theory and applications (models) for linear programming, integer  programming, network analysis, Modeling and simulation. This course will introduce the computer science students to deterministic models in Operational Research. they will learn to formulate, analyze, and solve mathematical models that represent real-world problems. This course will cover linear programming and the simplex algorithm, as well as related analytical topics. It will also introduce other types of mathematical models, including transportation, network, game theory and integer programming. At the end of the course, students will have the skills to build their own formulations, to critically evaluate the impact of assumptions and to choose an appropriate solution technique

Upon completion of this course, the student will be able to:
1. Build an idea about the fundamentals and principles of Operational Research and its applications.
2. Interpret and apply the results of an operational research model.
3. Define terms: Decision variable, objective functions, constraints.
4. Acquire the skills to formulate LP problem.
5. Identify feasible regions.
6. Obtain Graphical Solutions.
7. Acquire General idea of the Simplex method.
8. Identify and define the terms slack variables.
9. Classify basic variables, non- basic variables.
10.  Obtain Initial Basic feasible solution.
11.  Represent Initial solution in a tableau form.
12.  Stepwise improvement using pivot operation to obtain optimal solution.
13.  Find unique, multiple solution and unbounded solution.
14.  Solve General LP problems using two-phased and Big M methods.
15.  Identify infeasibility.
16. Use developed or available software to solve LP problems.
17.  Constructing Objective Functions and Constraints.
18.  Formulate the required Assumptions.
19.  Formulate a real-world problem as a mathematical programming model.
20.  Develop the theoretical workings of the simplex method for linear programming and perform iterations. 
21.  Solve specialized linear programming problems like the transportation and assignment problems.
22.  Identify the situation in which minimum spanning tree algorithm can be used.
23.  Discuss  the situation in which shortest path algorithm can be used.
24.  Deals with  the situation in which maximal flow algorithm can be used.
25.  Draw network diagram.
26.  Analyze the network using Earliest Start Time(ES) Latest Start Time (LS) , Earliest Event Time(ET), Latest Event Time(LT).
27.  Apply PERT using Optimistic, Most likely, pessimistic times of activities.
28.  Indicate the applications of, basic methods for, and challenges in integer programming.
29.  Build and apply the  game theory and its applications.
 To communicate the results of an operational research project through a written report and an oral summary

contents   
 Origins of Operational Research
 Impacts of Operational Research
 Model Formulation
 Mathematical Models
 linear  Model Components   
 Formulation Examples
 Graphical Method
 Simplex Solution Technique
  Tableau Method
  Algebraic Representation
  Geometric Interpretation 
Transportation and Assignment Problems
Network models
   Shortest Path Problem
   Minimum Spanning Tree Problem
 Critical Path Method (CPM), Program Evaluation and Review Technique  (PERT)
 Integer Programming
Game theory And its applications
Problem Formulation Examples and case studies.
(3-4)

  1.  The readings in the above schedule  are from the texts ( given and discusses as lectures)
  2.  Additional material will be drawn from other sources, explained during the class lectures .
  3.  No homework will be accepted after the class period in which it is due.
  4. Quizzes are generally unannounced, no make-up quizzes will be given.
  5.  All work must be shown to receive full or partial credit on any assignment (tests, quizzes, etc.).

Your final grade will be based on the following:
(1) Lecture Notes and active participation (with no absence)    5 %
(2) Case Studies and computer Projects   10 %
(2) Tests (3)                     35%    
(3) Final exam                  50%

REFERENCES

  1. Wayne L. Winston, Operations Research, 4th edition , Duxbury Press, 2004.
  2. WinQSB v. 2.0: Decision Support Software for MS/OM . (Windows 95/98/NT) Yih-Long Chang, Wiley, 2003.
  3. Hillier, F. S. and Lieberman, G. J. Introduction to Operations Research, 8th ed., New York: McGraw-Hill, 2005.
 4.  Hamdy A. Taha, “Operations Research”, Fifth edn. , Macmillan Publishing company, 1992