An introduction to the methods of linear programming, including both theoretical and computational aspects.
Formulation of linear programming models
The Simplex Algorithm, Two-Phase Simplex and Revised Simplex
Duality, Complementary Slackness and Dual Simplex
Implementation of some of these ideas using MATLAB/Python.
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/Python/Google OR Tools computer packages to solve linear programming problems.
- Module Supervisor: Felipe Maldonado