Course Unit Code : AMAT 41833
Course Title : Linear programming and Optimization
Pre-requisites : PMAT 21553
Learning outcomes:
Upon successful completion of the course unit the student will be able to:
- develop a linear programming model from problem description,
- use the simplex method for solving linear programming problems,
- use the revised simplex method to solve linear programming problems,
- interpret the dual of a linear programming problem and solve the resulting dual problem using the dual simplex method,
- obtain the solution to the primal problem from the solution of the dual problem
- use methods of linear programming for solving assignment problems and transportation problems
- identify the convex functions
- solve optimization problems in various areas using linear and non-linear programming methods
Course Content:
Optimization, Types of optimization problems,
Linear Programming: Formulate linear programming problem: Extreme Points, Basic Feasible Solutions, Solutions using graphical methods, Simplex method, Revised simplex method, Duality theory, Primal and dual problems, Reduction of linear inequalities, Hungarian method, Big m method.
Non Linear programming: Types of non-linear programing, Convex and concave functions, one variable unconstrained optimization, multivariable unconstrained optimization, Convex programming
Applications of Linear Programming Problems: Transportation problem and Assignment problem
Implement Linear programming problems using Excel
Method of Teaching and Learning: A combination of lectures, group projects, case studies, tutorial discussions and presentations.
Assessment: Based on tutorials, group project, tests, presentations and end of course examination
Recommended Textbook:
- David G. Luenberger, Linear and Nonlinear Programming, (4e) Springer; 2016
- Jiri Matousek, Bernd Gärtner, Understanding and Using Linear Programming. Springer Berlin Heidelberg, 2009
- F. S. Hillier and G. Lieberman, Introduction to Operations Research, McGraw-Hill, (10e). 2015