Dr Katerina Papadaki

This course is compulsory on the MSc in Operations Research & Analytics. This course is not available as an outside option.

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.

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.

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.

A mock project will be given to students that resembles the summative project.

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%) in the WT.

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