Postgraduate: Level 7
Monday 13 January 2020
Friday 20 March 2020
01 October 2019
Requisites for this module
MSC G10112 Mathematics,
MSC G10124 Mathematics,
DIP GN1309 Mathematics and Finance,
MSC GN1312 Mathematics and Finance,
MSC GN1324 Mathematics and Finance,
DIP G20109 Statistics and Operational Research,
MSC G20312 Statistics and Operational Research
The module aims to provide an understanding at postgraduate level of combinatorial optimisation. It aims to understand the mathematical underpinnings of algorithms commonly used in the solution of mathematical programming models where some or all
of the variables are integer. The focus is on applying such algorithms to solve integer and mixed integer models.
- Scope of integer and combinatorial programming.
- Polyhedral theory.
- General integer programming. Theory of valid inequalities.
- Strong valid inequalities and facets for structured problems.
- Duality and relaxation.
- General integer programming algorithms.
- Special purpose algorithms and their applications.
On completion of the module, students should be able to:
- formulate planning and scheduling problems as integer programs;
- describe feasible sets as polyhedra using facets, rays and vertices;
- generate valid inequalities for feasible sets;
- use linear programming relaxation and duality to generate upper bounds for integer programs' objective values;
- solve integer programs with cutting-plane algorithms;
- solve integer and mixed integer programs with Branch-and-Bound;
- apply Benders' decomposition algorithm to mixed integer programs.
No additional information available.
There are 5 lectures and two classes in every fortnight. There will be regular assessed material at postgraduate level which will be discussed in one of the fortnightly classes. In the Summer term 3 revision lectures are given.
- Winston, Wayne L. (c2004) Operations research: applications and algorithms, Australia: Thomson Brooks/Cole.
- Wolsey, Laurence A. (c1998) Integer programming, New York: Wiley. vol. Wiley-Interscience series in discrete mathematics and optimization
- Nemhauser, George L.; Wolsey, Laurence A. (c1988) Integer and combinatorial optimization, New York: Wiley. vol. Wiley-Interscience series in discrete mathematics and optimization
- Williams, H. P. (2015) Model building in mathematical programming, Chichester: Wiley.
The above list is indicative of the essential reading for the course. The library makes provision for all reading list items, with digital provision where possible, and these resources are shared between students. Further reading can be obtained from this module's reading list.
Assessment items, weightings and deadlines
|Coursework / exam
||120 minutes during Summer (Main Period) (Main)
Module supervisor and teaching staff
Prof Abdel Salhi, email email@example.com
Professor Abdel Salhi (firstname.lastname@example.org)
Prof Fionn Murtagh
Professor of Data Science
Available via Moodle
Of 38 hours, 38 (100%) hours available to students:
0 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).
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