Optimisation (Linear Programming)

The details
Mathematical Sciences
Colchester Campus
Undergraduate: Level 5
Monday 13 January 2020
Friday 20 March 2020
04 October 2019


Requisites for this module


MA305, MA306

Key module for

BSC L1G2 Economics and Mathematics (Including Placement Year),
BSC LG11 Economics and Mathematics,
BSC LG18 Economics and Mathematics (Including Foundation Year),
BSC LG1C Economics and Mathematics (Including Year Abroad),
BSC L1G1 Economics with Mathematics,
BSC L1G3 Economics with Mathematics (Including Placement Year),
BSC L1G8 Economics with Mathematics (Including Foundation Year),
BSC L1GC Economics with Mathematics (Including Year Abroad),
BSC G100 Mathematics,
BSC G102 Mathematics (Including Year Abroad),
BSC G103 Mathematics (Including Placement Year),
BSC G104 Mathematics (Including Foundation Year),
BSC 5B43 Statistics (Including Year Abroad),
BSC 9K12 Statistics,
BSC 9K13 Statistics (Including Placement Year),
BSC 9K18 Statistics (Including Foundation Year),
BSC G1G4 Mathematics with Computing (Including Year Abroad),
BSC G1G8 Mathematics with Computing (Including Foundation Year),
BSC G1GK Mathematics with Computing,
BSC G1IK Mathematics with Computing (Including Placement Year),
BSC I1G3 Data Science and Analytics,
BSC I1GB Data Science and Analytics (Including Placement Year),
BSC I1GC Data Science and Analytics (Including Year Abroad),
BSC I1GF Data Science and Analytics (Including Foundation Year)

Module description

An introduction to the methods of linear programming, including both theoretical and computational aspects.

Module aims

Formulation of linear programming models
Graphical solution
The Simplex Algorithm, Two-Phase Simplex and Revised Simplex
Duality, Complementary Slackness and Dual Simplex
Sensitivity Analysis
Transportation Problem
Implementation of some of these ideas using MATLAB.

Module learning outcomes

On completion of the course students will be able to:
- formulate an appropriate linear programming model, from a written description of a problem environment, whose solution would actually solve the problem;
- recognise the scope and limitations of linear programming modelling and appreciate its position within the Operational Research discipline;
- solve any (small) linear programming problem using an appropriate version of the Simplex Algorithm;
- perform sensitivity analysis on an optimal solution;
- use Duality Theory to prove basic theorems of Linear Programming and apply Duality Theory to recognize optimality, infeasibility or unboundedness in a linear program;
- apply the Transportation Simplex Algorithm under a variety of scenarios.
-make use of the MATLAB computer package to solve linear programming problems.

Module information

No additional information available.

Learning and teaching methods

This module has two one hour lectures each week, an additional lecture in even-numbered weeks and a class in odd-numbered weeks. In the Summer term 3 hours of revision lectures are given.


  • Winston, Wayne L. (c2004) Operations research: applications and algorithms, Australia: Thomson Brooks/Cole.

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   Homework 1     
Coursework   Homework 2     
Exam  180 minutes during Summer (Main Period) (Main) 

Overall assessment

Coursework Exam
20% 80%


Coursework Exam
0% 100%
Module supervisor and teaching staff
Prof Abdellah Salhi, email:
Prof Abdel Salhi, email, Dr Georgios Papamikos (
Professor Abdel Salhi (, Dr Georgios Papamikos (



External examiner

Prof Fionn Murtagh
University of Huddersfield
Professor of Data Science
Available via Moodle
Of 34 hours, 32 (94.1%) hours available to students:
2 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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