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| Module Availability |
| Autumn |
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| Assessment Pattern |
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Unit(s) of Assessment
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Weighting Towards Module Mark( %)
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Coursework: one take-home assignment and one class test
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25
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Exam: 2 hours, unseen
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75
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Qualifying Condition(s)
A weighted aggregate mark of 40% is required to pass this module.
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| Module Overview |
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| Prerequisites/Co-requisites |
| MAT1015 Calculus and MAT1016 Linear Algebra |
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| Module Aims |
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. |
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| Learning Outcomes |
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. |
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| Module Content |
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. |
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| Methods of Teaching/Learning |
Teaching is by lectures and tutorials. Learning takes place through lectures, tutorials, exercises and class tests.
Autumn semester: 3 hours per week for 10 weeks. |
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| Selected Texts/Journals |
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. |
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| Last Updated |
| September 10 |
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