Dr Katerina Papadaki

Dr Grammateia Kotsialou

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.

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 (12 lecture hours): 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 (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: generating discrete and continuous random variables; Monte Carlo simulation; variance reduction techniques; and other topics such as, for example discrete event simulation, 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 classes and lectures totalling a minimum of 30 hours across Michaelmas Term and a minimum of 18 hours of computer workshop sessions delivered in Michaelmas Term and Lent Term. Lectures and solutions to exercises will be delivered as online videos; classes will be delivered as a combination of virtual and on campus question and answer sessions. Computer workshops are help sessions, where an instructor is available to students virtually to answer questions while they work on their computer assignment (computer workshops are not mandatory).

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

Feedback will be provided in the virtual/on campus weekly classes (question and answer sessions), where the weekly homework will be discussed. Additional feedback on programming assignments will be provided to students attending the virtual optional computer workshops.

The reading will be a combination of lecture notes 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)
• A M Law and W D Kelton, Simulation Modelling and Analysis, McGraw Hill (3rd ed., 2000)
• M Pidd, Computer Simulation in Management Science, Wiley (5th ed., 2006)

Project (100%) in the LT.

The project will be on Mathematical Optimisation, Simulation, 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.