AMAT 41833: Linear programming and Optimization

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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:

  1. David G. Luenberger, Linear and Nonlinear Programming, (4e) Springer; 2016
  2. Jiri Matousek, Bernd Gärtner, Understanding and Using Linear Programming. Springer Berlin Heidelberg, 2009
  3. F. S. Hillier and G. Lieberman, Introduction to Operations Research, McGraw-Hill, (10e). 2015
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