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/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