Aims & Learning Objectives:
Aims: To present methods of optimisation commonly used in OR, to explain their theoretical basis and give an appreciation of the variety of areas in which they are applicable.
On completing the course, students should be able to
* Recognise practical problems where optimisation methods can be used effectively
* Implement appropriate algorithms, and understand their procedures
* Understand the underlying theory of linear programming problems, especially duality.
The Nature of OR: Brief introduction.
Linear Programming: Basic solutions and the fundamental theorem. The simplex algorithm, two phase method for an initial solution. Interpretation of the optimal tableau. Applications of LP. Duality.
Topics selected from:
Sensitivity analysis and the dual simplex algorithm. Brief discussion of Karmarkar's method. The transportation problem and its applications, solution by Dantzig's method. Network flow problems, the Ford-Fulkerson theorem.
Non-linear Programming: Revision of classical Lagrangian methods. Kuhn-Tucker conditions, necessity and sufficiency. Illustration by application to quadratic programming.