This course is compulsory on the MSc in Operations Research & Analytics. This course is available on the CEMS Exchange, Global MSc in Management, Global MSc in Management (CEMS MIM), Global MSc in Management (MBA Exchange), MBA Exchange and MPA in Data Science for Public Policy. This course is available with permission as an outside option to students on other programmes where regulations permit. This course uses controlled access as part of the course selection process. For information on controlled access courses, including eligibility, application processes, deadlines, and departmental contact details, please refer to the Controlled Access Courses webpage.

This course has a limited number of places (it is controlled access). Priority is given to MSc students in the Department of Mathematics.

Pre-requisites: Familiarity at undergraduate level with linear algebra (matrix multiplication, geometric interpretation of vectors, linear independence).

The course covers the theory of mathematical optimisation and its practical application in Operations Research.

On the theory side, the course presents linear programming including the notion of duality and the simplex algorithm, integer programs and how to solve them, dynamic programming, optimisation methods on graphs, and nonlinear optimisation techniques.

On the application side, the course presents modelling techniques in integer linear programming, sensitivity analysis, column generation, solution of optimisation problems with special-purpose programming languages, and interpretation of the solutions.

10 hours of seminars and 20 hours of lectures in the Autumn Term.
2 hours of lectures in the Spring Term.

Students will be expected to submit coursework, covering theory and modelling, for feedback.

The course has its own set of lecture notes, provided at the beginning of the term. The course will be taught from these notes, as well as lecture slides provided weekly during the term.

In addition to the textbook, students may also wish to consult:

• F S Hillier & G J Lieberman, Introduction to Operations Research, 9th edition (2009) (7th edition of Hillier & Lieberman (2000) is also acceptable). 
• Wayne Winston, Operational Research; Applications and Algorithms, Fourth/International Student Edition.
• 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)

Exam (80%), duration: 120 Minutes in the Spring exam period.

Project (20%).

Students will be expected to submit a combination of homework and projects, covering theory and modelling.