Combinatorial Optimisation

The details
Mathematical Sciences
Colchester Campus
Undergraduate: Level 6
Monday 13 January 2020
Friday 20 March 2020
01 October 2019


Requisites for this module
MA114 and MA205



Key module for

DIP G10109 Mathematics

Module description

The module 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.

Module aims


- 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.
- Unimodularity.

Module learning outcomes

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.

Module information

No additional information available.

Learning and teaching methods

The module runs at 3 hours per week in the Spring term. There are 5 lectures and one class in every fortnight. 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 Description Deadline Weighting
Coursework Coursework 1 14/02/2020
Coursework Coursework 2 20/03/2020
Exam 120 minutes during Summer (Main Period) (Main)

Overall assessment

Coursework Exam
20% 80%


Coursework Exam
0% 100%
Module supervisor and teaching staff
Prof Abdel Salhi, email
Professor Abdel Salhi (



External examiner

Prof Fionn Murtagh
Professor of Data Science
Available via Moodle
Of 33 hours, 33 (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).


Further information
Mathematical Sciences

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