|Delivery Type||Delivery length / details|
|Lecture||19 Hours. (19 x 1 hour lectures)|
|Seminars / Tutorials||3 Hours. (3 x 1 hour example classes)|
|Assessment Type||Assessment length / details||Proportion|
|Semester Exam||2 Hours (written examination)||100%|
|Supplementary Exam||2 Hours (written examination)||100%|
On completion of this module, a student should be able to:
1. describe the scope of linear programming;
2. formulate real situations as linear programming problems;
3. solve such problems by the Simplex Method;
4. apply appropriate modifications to the basic technique.
5. interpret the results of computer generated linear programming solutions.
The basic problem of Linear Programming is to maximise or minimise a linear function of several variables, subject to constraints expressed as linear inequalities or equations. The theory of Linear Programming is now well established to the extent that the technique often appears as an option in widely available business computer packages such as spreadsheets. This module provides a balance between the theory and applications of the subject and considers the interpretation of problem solutions.
To introduce an important and widely used application of Mathematics in the real world.
2. THE SIMPLEX METHOD: Overall idea; geometrical and algebraic characterisation. Fundamental Theorem of Linear Programming. Artificial variables; big-M method, two-phase method, Dual Simplex method. Unsigned variables. What can go wrong.
3. SENSITIVITY ANALYSIS: Interpreting the simplex tableau, including economic interpretations where relevant. Dual prices. Marginal change and return.
4. DUALITY: The dual problem and its motivation. Fundamental Theorem of Duality. Relationships between solutions to the primal and dual problems. Complementary slackness. Interpretations of the Dual problem.
5. SPECIAL TOPICS: A selection of topics from: Zero-sum games, Integer programming, Assignment problems, Transportation problems.
Reading ListSupplementary Text
H A Taha (2003) Operations research: an introduction 7th Prentice Hall Primo search J G Ecker & M Kupferschmid (1988) Introduction to operations research Wiley Primo search W L Winston (1995) Introduction to mathematical programming: applications and algorithms 2nd OWS-Kent Primo search
This module is at CQFW Level 6