AMAT 41423: Linear Programming and Nonlinear Programming

Course Unit Code : AMAT  41423

Course Title           : Linear programming and Nonlinear Programming

Pre-requisites        : PMAT 21263

Learning outcomes:

Upon successful completion of the course unit the student will be able to:

• develop a linear programming model from problem description

• solve linear programming problems using graphical method, simplex method, revised simplex method, big M method, two-phase method

• obtain the solution of the dual of a linear programming using the solution of the primal problem

• analyze sensitivity of the model parameters

• solve transportation problems, assignment problems and transshipment problems

• solve problems using non-linear programming methods

• obtain the solution of various applications of linear programming problems using Excel, TORA and other appropriate software and analyze the solutions for decision making

Course Content:

Introduction: 

• Optimization, types of optimization problems

Linear Programming: 

• Formulation of linear programming problem, extreme points, basic feasible solutions, solutions using graphical methods, simplex method, revised simplex method, big Method, two-phase method, solution behavior, duality theory, primal and dual problems, sensitivity analysis, reduction of linear inequalities.

Applications of Linear Programming Problems: 

• Transportation problem, assignment problem and transshipments problems

Non-Linear programming: 

• Graphical illustration of nonlinear programming problems, types of nonlinear programming problems, one-variable unconstrained optimization, multivariable unconstrained optimization, the Karush-Kuhn-Tucker (KKT) conditions for constrained optimization, applications of nonlinear programming

Software: 

• Solve Linear programming problems using Excel, TORA computer packages and other appropriate computer software.

Method of Teaching and Learning :  A combination of lectures, group projects, case studies, tutorial discussions and presentations.

Assessment : A combination of lectures, group projects, case studies, tutorial discussions and presentations.

Recommended Textbook:

1. Luenberger, D.G. (4th Ed., 2016). Linear and Nonlinear Programming, Springer.

2. Matousek, J. & Gärtner, B. (2009). Understanding and Using Linear Programming. Springer Berlin Heidelberg.

3. Hillier, F.S. & Lieberman, G. (11th Ed., 2021). Introduction to Operations Research, McGraw-Hill.

4. Taha, H.A. (10th Ed., 2017). Operations Research: An Introduction, Pearson.