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MA424 Half Unit

Modelling in Operations Research

**This information is for the 2023/24 session.**

**Teacher responsible**

Dr Katerina Papadaki and Dr Grammateia Kotsialou

**Availability**

This course is compulsory on the 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), linear programming, and probability theory (expected value, conditional probability, independence of random events). For students in the MSc in Operations Research & Analytics, MA423 and ST447 more than cover the prerequisites.

**Course content**

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

Optimisation: This part enables students to formulate, 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. Topics include: formulation of management problems using linear and network models; solution of such problems with a special-purpose programming language; interpretation of the solutions; and formulation and solution of nonlinear models including some or all of binary, integer, convex and stochastic programming models.

Simulation: 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: generating discrete and continuous random variables; Monte Carlo simulation; discrete event simulation; variance reduction techniques; Markov Chain Monte Carlo methods. The course will teach students how to use a simulation modelling software package.

**Teaching**

This course is delivered through a combination of seminars and lectures totalling a minimum of 30 hours across Autumn Term.

Further, there is a minimum of 6 hours of computer workshop sessions delivered in Autumn Term. Computer workshops are not mandatory.

**Formative coursework**

Students will be expected to produce 2 projects in the AT.

Two mock projects will be given to students that resemble the summative projects. Students are asked to submit only selected parts of the mock projects for feedback.

**Indicative reading**

The reading will be a combination of lecture slides and chapters from the following list of books.

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)
- George B. Dantzig and Mukund N. Thapa, Linear Programming 2: Theory and extensions, Springer (2003)

Simulation

- S Ross, Simulation, Academic Press (5th ed., 2012)
- Joseph K. Blitzstein, Jessica Hwang, Introduction to Probability, Chapman and Hall/CRC Press (2014)

**Assessment**

Project (50%) and project (50%) in the WT.

There will be one project on Mathematical Optimisation and another on Simulation. The deliverable is a report along with a soft copy of any computer code and solver output.

** Key facts **

Department: Mathematics

Total students 2022/23: 29

Average class size 2022/23: 15

Controlled access 2022/23: Yes

Lecture capture used 2022/23: Yes (MT)

Value: Half Unit

**Course selection videos**

Some departments have produced short videos to introduce their courses. Please refer to the course selection videos index page for further information.

**Personal development skills**

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