APP MTH 7105 - Optimisation and Operations Research

Every business in the world needs to make complex decisions. These decisions -- what to make, how to do it cheaply, how to schedule production, whether to outsource, how to get their goods to market, and so on -- dramatically affect their profitability. However, in the modern world, the factors affecting these choices are too complex to manage by hand. Operations Research (OR) provides the tools needed to make these decisions rigorously and effectively. This first course in OR will present some of the basic tools, concentrating on mathematical modelling and optimisation. But OR is an interdisciplinary topic drawing from game theory, statistics, and computer science as well as applied mathematics, and we will show some of these connections. The course focusses on linear optimisation problems involving both continuous and integer variable, because these are used in a vast range of real situations. It will present techniques for optimisation and the theory behind them, but will also show how to use these techniques on real problems, for example, minimising cost, maximising production capacity, or minimising risk. Topics covered are: formulating a linear program; the Simplex Method; duality and complementary slackness; sensitivity analysis; primal-dual approaches; brand-and-bound; and heuristics such as the greedy method and simulated annealing. Examples will be presented from important application areas, such as the emergency services, telecommunications, transportation, and manufacturing.