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2010/1 Module Catalogue
Module Provider: Mathematics Short Name: MS221
Level: HE2 Module Co-ordinator: RAYMAN JF Dr (Maths)
Number of credits: 15 Number of ECTS credits: 7.5
Module Availability
Assessment Pattern

                        Unit(s) of Assessment


                        Weighting Towards Module Mark( %)


Coursework:  one take-home assignment and one class test





Exam:  2 hours, unseen





Qualifying Condition(s) 


A weighted aggregate mark of 40% is required to pass this module.



Module Overview
MAT1015 Calculus and MAT1016 Linear Algebra
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.
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.
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.
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.
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.
Last Updated
September 10