An introduction to the methods of linear programming, including both theoretical and computational aspects.
Syllabus:
Formulation of linear programming models
Graphical solution
The Simplex Algorithm, Two-Phase Simplex and Revised Simplex
Duality, Complementary Slackness and Dual Simplex
Sensitivity Analysis
Transportation Problem
Implementation of some of these ideas using MATLAB.
On completion of the course students will be able to:
- formulate an appropriate linear programming model, from a written description of a problem environment, whose solution would actually solve the problem;
- recognise the scope and limitations of linear programming modelling and appreciate its position within the Operational Research discipline;
- solve any (small) linear programming problem using an appropriate version of the Simplex Algorithm;
- perform sensitivity analysis on an optimal solution;
- use Duality Theory to prove basic theorems of Linear Programming and apply Duality Theory to recognize optimality, infeasibility or unboundedness in a linear program;
- apply the Transportation Simplex Algorithm under a variety of scenarios.
-make use of the MATLAB computer package to solve linear programming problems.
- Module Supervisor: Abdellah Salhi