operational research i

Core Syllabus

This subject introduces the fundamental theory, techniques and algorithms for linear programming, nonlinear programming and statistical computation problems. 

Prerequisite

Mathematics, Statistics and Probability Theory to the level of an introductory course is required. In particular, students should have covered elementary distribution theory and the Poisson process, and have knowledge of linear algebra sufficient to handle matrix inversion. Students must be prepared to use computer packages when required. 

Objectives

This subject introduces the fundamental theory, techniques and algorithms for linear programming, nonlinear programming and statistical computation problems. The subject addresses both the basic as well as advanced topics in linear programming and nonlinear programming. Numerous examples will be adopted to demonstrate the use of various 
algorithms and techniques involved. The emphasis is not only on mastering these algorithms and techniques but also on the applications of them on various practical problems. 

Subject Content in Outline

Linear Programming

1. Linear Programming models. 
   
2. Simplex method. 
   
3. M-Method. 
   
4. Generalized Simplex method. 
   
5. Duality theory. 
   
6. Interior point methods for linear programming. 
   

Optimality Conditions

1. Unconstrained optimization. 
   
2. Constrained optimization. 
   
3. Convex programming. 
   

Unconstrained and Constrained Methods

1. Numerical methods for unconstrained problems. 
   
2. Numerical methods for constrained problems. 
   
3. Penalty methods. 
   

Network Models

1. Minimal Spanning Tree Algorithm. 
2. Shortest-Route Problem. 
3. Maximal Flow Model. 
4. Minimum Cost Flow Problem