Spring semester

Unit(s) of Assessment	Weighting Towards Module Mark( %)
Coursework: One take-home assignment and one class test	25%
Exam: 2 hours, unseen	75%
Qualifying Condition(s)

MS102 Vector Calculus
MS113 Linear Algebra

This module introduces a variety of commonly-used techniques in Operational Research.

Linear programming, the simplex method and the transportation algorithm are covered, including some theoretical material on duality.

Non-linear optimization with equality constraints is also considered, with particular application to convex and concave functions.

By the end of the module, students should

• be familiar with standard techniques of linear and non-linear optimisation,
• be able to formulate simple OR and optimization problems mathematically, and apply standard methods to solve them,
• understand the concept of convexity and its rôle in optimization theory,
• understand and be able to prove results concerning duality and conditions for optimality.

Linear programming: problem formulation, the Simplex method, sensitivity analysis, duality and complementary slackness.

The transportation algorithm: theory and applications.

Convex sets. Convex and concave functions. Gradient vector and Hessian matrix.

Non-linear optimization: Lagrange multipliers, necessary and sufficient conditions for local and global optima.

Teaching is by lectures and tutorials. Learning takes place through lectures, tutorials, exercises and class tests.

3 hours per week for 10 weeks.

H.A. Taha : Operations Research, An Introduction, Prentice Hall (2007), ISBN 0131889230.

F.S. Hillier and G.J. Lieberman : Introduction to Operations Research, McGraw Hill (2002), ISBN 0072535105.

R. Bronson : Schaum’s Outline of Operations Research, McGraw-Hill (1997), ISBN 0070080208.

Wayne L. Winston : Operations Research, Applications and Algorithms, Thomson (2004), ISBN 0534423620.

31 July 2007