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Semester 1

Fundamentals of Operational Research (MATH10065)

Mathematics

SCE

10

4

2022/2023

Pre-requisites

Visiting students are advised to check that they have studied the material covered in the syllabus of each prerequisite course before enrolling.

Course Summary

This course covers some core areas of Operational Research, namely Dynamic Optimisation, Integer Optimisation and Game Theory. Emphasis will be placed both on the mathematical techniques and on problem formulation through examples from applications.

Course Description

Dynamic Optimisation is a neat way of solving sequential decision problems based on recursion. Its power comes from the fact that some important classes of optimisation problems that "ought to be difficult" can be reformulated as a recursive optimisation problem and thus made tractable. Examples are network optimisation problems, allocation problems and inventory problems.Integer Optimisation provides a general method of solving problems with logical or integrality constraints. Solution methods include Branch-and-Bound and Gomory Cuts. Much emphasis will be placed on how to express various types of restrictions that may appear in optimisation problems (like logical conditions) can be expressed using integer variables.Game Theory is concerned with mathematical modelling of behaviour and optimal decision making in competitive strategic situations in which the success of strategic choices of one individual (person, company, server, ...) depends on the choices of other (intelligent) "players" that each have their own (possibly conflicting) agenda.Note that Dynamic Optimisation and Integer Optimisation were historically called "Dynamic Programming" and "Integer Programming" respectively (the term "programming" in these words did not mean "computer programming" but rather decision making). Dynamic OptimisationMultistage decision processes; principle of optimality. Applications: network problems; inventory problem; resource allocation problem; knapsack problem; stochastic problems.Integer OptimisationModelling: set-up costs, batch production, limited number of production methods. Logical constraints; set covering problems; systematic conversion of logical expression to IP constraints. Solution techniques: branch and bound; Gomory pure integer cuts.Game TheoryOptimal strategies in face of uncertainty (minimax and maximin). Two-person zero sum games, dominated strategies, saddle points, non=zero sum games, reaction curves and Nash equilibria.

Assessment Information

Written Exam 80%, Coursework 20%, Practical Exam 0%