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.
Objectives:
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.
Content:
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.
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