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MA424 Half Unit

Modelling in Operations Research

**This information is for the 2018/19 session.**

**Teacher responsible**

Dr Victor Verdugo

**Availability**

This course is compulsory on the MSc in Management Science (Decision Sciences) and MSc in Operations Research & Analytics. This course is available on the Global MSc in Management, Global MSc in Management (CEMS MiM), Global MSc in Management (MBA Exchange) and MSc in Data Science. This course is available with permission as an outside option to students on other programmes where regulations permit.

**Pre-requisites**

Students must know basics of linear algebra (matrix multiplication, geometric interpretation of vectors) and probability theory (expected value, conditional probability, independence of random events).

Students taking the course as an outside option are also expected to have a basic knowledge of linear programming. For students in the MSc in Operations Research & Analytics this will be covered in MA423 Fundamentals of Operations Research.

**Course content**

The course will be in 2 parts, covering the two most prominent tools in operational research: simulation, the playing-out of real-life scenarios in a (computer-based) modelling environment, and mathematical optimisation, the application of sophisticated mathematical methods to make optimal decisions.

Simulation (8 lecture hours): This part develops simulation modelling skills, understanding of the theoretical basis which underpins the simulation methodology, and an appreciation of practical issues in managing a simulation modelling project. Topics include Monte Carlo simulation, Markov processes, discrete event simulation, and variance reduction. The course will teach students how to use a simulation modelling software package.

Optimisation (12 lecture hours): This part enables students to model and solve real-life management problems as Mathematical Optimisation problems. In providing an overview of the most relevant techniques of the field, it teaches a range of approaches to building Mathematical Optimisation models and shows how to solve them and analyse their solutions. Content includes: The modelling life-cycle and modelling environments; formulation of management problems using linear and network modelsÍ¾ solution of such problems with a special-purpose programming languageÍ¾ interpretation of the solutionsÍ¾ limitations of such models; and formulation and solution of nonlinear models including some or all of binary, integer, convex and stochastic programming models.

**Teaching**

20 hours of lectures, 13 hours and 30 minutes of seminars and 10 hours of computer workshops in the MT. 8 hours of computer workshops in the LT.

Computer workshops are not mandatory. They are help sessions, where an instructor is available to students in the computer cluster while they work on their assignment.

**Formative coursework**

Students will be expected to produce 1 project in the MT.

Feedback will be provided on the weekly homework. Additional feedback will be provided on a one-on-one basis to students attending the optional computer help sessions.

**Indicative reading**

Full lecture notes will be provided to students for both parts.

Recommended readings:

Simulation

- A M Law & W D Kelton, Simulation Modelling and Analysis, McGraw Hill (3rd ed., 2000);
- M Pidd, Computer Simulation in Management Science, Wiley (5th ed., 2006);
- S Ross, Simulation, Academic Press (5th ed., 2012).

Optimisation

- W L Winston, Operations Research: Applications and Algorithms, Brooks/Cole (4th ed., 1998);
- D Bertsimas and J N Tsitsiklis: Introduction to Linear Optimization, Athena Scientific (3rd ed., 1997).

**Assessment**

Project (100%) in the LT.

The project will be on Simulation, Mathematical Optimisation, or a combination of the two. The deliverable is a report of at most 12 pages (main report, excluding executive summary and technical appendices), along with a soft copy of any computer code and solver output.

** Key facts **

Department: Mathematics

Total students 2017/18: 61

Average class size 2017/18: 30

Controlled access 2017/18: No

Lecture capture used 2017/18: Yes (MT)

Value: Half Unit

**Personal development skills**

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