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MA231

Operational Research Methods

**This information is for the 2019/20 session.**

**Teacher responsible**

Dr Giacomo Zambelli and Dr Victor Verdugo Silva

**Availability**

This course is available on the BSc in Accounting and Finance, BSc in Business Mathematics and Statistics, BSc in Econometrics and Mathematical Economics, BSc in Economics, BSc in Management, BSc in Mathematics and Economics, BSc in Mathematics with Economics and BSc in Statistics with Finance. This course is available as an outside option to students on other programmes where regulations permit and to General Course students.

**Pre-requisites**

Mathematics, Statistics and Probability Theory to the level of the courses MA107 Quantitative Methods (Mathematics) and ST107 Quantitative Methods (Statistics) is required. In particular, students should have covered elementary distribution theory and the Poisson Process, and have an elementary knowledge of linear algebra. Students must be prepared to use computer packages when required.

**Course content**

An introduction to all the main theoretical techniques of Operational Research.

Linear optimisation: from the most basic introduction to sufficient conditions for optimality; duality; sensitivity of the solution; discovery of the solution to small problems by graphical methods, and proof of optimality by testing the sufficient conditions. The transportation problem. Modelling real world problems using linear optimisation.

Various other operational research techniques including: Shortest Paths, Critical Path Analysis, Markov Chains, Stable Matchings, Queueing Theory, Simulation, Inventory Management, Dynamic Programming, Decision Theory, Game Theory.

The course includes an assessed software component. The software used will be "Microsoft Excel" and the add-on packages "LP solve" to solve linear optimisation problems and "@ risk" to perform Monte Carlo simulation.

Full lecture notes are provided.

**Teaching**

20 hours of lectures and 20 hours of classes in the MT. 10 hours of lectures, 10 hours of classes and 5 hours of computer workshops in the LT. 2 hours of lectures in the ST.

The computer workshops will be non-compulsory.

**Formative coursework**

Students will be expected to produce 10 problem sets in the MT and 1 project and 5 problem sets in the LT.

The formative coursework comprises weekly problem sets. A mock project will be given, similar in format to the summative project, to be carried out by the same groups that will work on the final project. This is meant as a trial run of the group project, with a similar level of work but with no summative mark.

**Indicative reading**

Comprehensive lecture notes will be provided. The course content largely follows the following textbook:

- F S Hillier, G J Liebermann, Introduction to Operations Research, McGraw-Hill Series in Industrial Engineering and Management Science. Any edition from 7th onward.

Further reading includes:

- W L Winston, Operations Research, Duxbury Press (2004).
- W L Winston, S C Albright: Practical Management Science, Cengage Learning. 4th edition or later.
- H P Williams, Model Building in Mathematical Programming, Wiley (2013).

**Assessment**

Exam (80%, duration: 2 hours and 45 minutes) in the summer exam period.

Case analysis (20%) in the LT.

The group project will consist of a case study developed by the lecturer and presenting a (simplified version of a) real world problem that is amenable to optimisation and simulation techniques that are taught in the course. The students will need to choose the appropriate techniques, develop a mathematical model, implement it using the software taught in the course, and write a report describing the approach and reporting critically the results obtained from the solution of the model.

The group project will be in randomly allocated groups of at most 3, and students will need to submit a teamwork evaluation form to assess whether the workload was fair and balanced.

** Key facts **

Department: Mathematics

Total students 2018/19: 86

Average class size 2018/19: 14

Capped 2018/19: No

Value: One Unit

**Personal development skills**

- Self-management
- Team working
- Problem solving
- Application of information skills
- Communication
- Application of numeracy skills
- Specialist skills