Module Code: MAT2009 
Module Title: OPERATIONS RESEARCH AND OPTIMIZATION 

Module Provider: Mathematics

Short Name: MS221

Level: HE2

Module Coordinator: RAYMAN JF Dr (Maths)

Number of credits: 15

Number of ECTS credits: 7.5




Module Availability 
Autumn 


Assessment Pattern 
Unit(s) of Assessment

Weighting Towards Module Mark( %)


Coursework: one takehome assignment and one class test

25


Exam: 2 hours, unseen

75


Qualifying Condition(s)
A weighted aggregate mark of 40% is required to pass this module.





Module Overview 



Prerequisites/Corequisites 
MAT1015 Calculus and MAT1016 Linear Algebra 


Module Aims 
This module introduces a variety of commonlyused techniques in Operational Research.
Linear programming, the simplex method and the transportation algorithm are covered, including some theoretical material on duality.
Nonlinear 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 nonlinear 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.
Nonlinear 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, McGrawHill (1997), ISBN 0070080208.
Wayne L. Winston : Operations Research, Applications and Algorithms, Thomson (2004), ISBN 0534423620. 


Last Updated 
September 10 


