Optimisation and Operations Research

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Description

Operations Research (OR) is the application of mathematical techniques and analysis to problem solving in business and industry, in particular to carrying out more efficiently tasks such as scheduling, or optimising the provision of services. OR is an interdisciplinary topic drawing from mathematical modelling, optimisation theory, game theory, decision analysis, statistics, and simulation to help make decisions in complex situations. This first course in OR concentrates on mathematical modelling and optimisation: for example maximising production capacity, or minimising risk. It focuses on linear optimisation problems involving both continuous, and integer variables. The course covers a variety of mathematical techniques for linear optimisation, and the theory behind them. It will also explore the role of heuristics in such problems. Examples will be presented from important application areas, such as the emergency services, telecommunications, transportation, and manufacturing. Students will undertake a team project based on an actual Adelaide problem.

Objective

Content

Topics covered are: formulating a linear program; the Simplex Method; duality and Complementary slackness; sensitivity analysis; an interior point method; alternative means to solve some linear and integer programs, such as primal-dual approaches methods from a complete solution (such as Greedy Methods, and Simulated Annealing), methods from a partial solution (such as Dijkstra's shortest path algorithm, and branch-and-bound).