MA324      Half Unit
Mathematical Modelling and Simulation

This information is for the 2025/26 session.

Availability

Requisites

Pre-requisites:

Before taking this course, students must have completed: ST107 and (MA213 or MA208)

Additional requisites:

Students should have knowledge of: (1) linear programming, including duality, to the level of Operations Research Techniques (MA213) or Optimisation Theory (MA208); and (2) probability theory to the level of Quantitative Methods (Statistics) (ST107), in particular elementary distribution theory and the Poisson Process.

The course covers some of the most prominent tools in modelling and simulation. Both deterministic and stochastic models are covered. These include 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.

Topics include: formulation of management problems using linear/nonlinear and network models (including linear, integer, binary and convex programming models) as well as solving these problems and analysing the solutions; modelling tricks (including how to deal with fixed costs, modelling logical conditions  and semi-continuous variables); optimisation problems on graphs; quadratic optimisation; second order cone programming problems; generating discrete and continuous random variables using Monte Carlo simulation; discrete event simulation; variance reduction techniques; Markov Chain Monte Carlo methods.

The course will additionally teach students to use modelling and simulation computer packages.

If you have questions in relation to the course content feel free to contact the course convenor.

20 hours of lectures, 10 hours of classes and 5 hours of computer workshops in the Winter Term.

Problem sets

Project

Formative assessment will be in the form of weekly homework and a mock project. Some of the weekly homework will feature questions that are similar in nature to what is expected for the assessed project. There will additionally be a formative mock project given in the second half of WT. This mock project will not contribute towards your final grade, however, it will give you a good indication of what to expect from the final assessment.

Detailed lecture slides will be provided. 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)

Project (100%)

The deliverable is a report of 15-20 pages, along with a copy of any computer code used.