Course Details

1. Outline the scope of Operations Research, the impact it has, and the core underlying technologies it involves
2. Formulate optimization problems in Mathematical Programming (linear and integer)
3. Apply the Simplex method to solve small LP formulations
4. Use spreadsheet software packages to solve small to medium size MP problems and perform sensitivity analysis.
5. Discuss the limitations of MP models and its application in real world settings
6. List and briefly describe alternative (non mathematical programming) approaches to optimization

Introduction to Operations Research

What is Operations Research. Scope, applications and impact

Role of Optimization in OR

Data acquisition and model development

Linear Programming systems. The Simplex Method

          Structure of a Linear Program.

          Solving a simple LP visually

          The Simplex method. Solving a linear program

          Main characteristics of the Simplex method

          Modelling problems as LP

          Use spreadsheet software to practically solve LP systems.

          Overview of large scale solvers

Practical Sensitivity Analysis

          Overview of the dual model

          Reduced costs and shadow prices

Limitations of LP and extensions.

          Integer variables. MIP programming techniques. Advanced models

          Limitations of MILP programs. Overview of branch and bound approach

          Other extensions: Stochastic Programming, Nonlinear Programming

Dynamic Programming.

          The dynamic programming approach and applications

Non MP optimization.

          Ill defined and complex problems.

          Near optimality. Heuristic and metaheuristics (SA, GA, VNS)

• F Hillier Introduction to Operations Research, McGraw-Hill

• H Taha Operations Research: An Introduction, Prentice Hall

The course is delivered in three-hour lectures per week. Two cover the theoretical aspects of the course. A period per week is reserved for delivering the lecture in computer laboratories. This is used for practical experimentation with the concepts and demonstration of various programming paradigm examples.

Students are handed out a series of assignments and exercises. MS Excel will be used for demonstration purposes.

The course material (notes, exercises, forum, etc) is maintained on the university’s e-learning platform.