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.