1 Operations Research and Linear Programming Models

Operations research (OR) is the application of mathematical models to decisions about the operation of systems: how much to produce, how to route, whom to assign, when to order, how many servers to provide. The name dates from the Second World War, when groups of scientists in Britain, such as the one led by P. M. S. Blackett, were attached to the armed forces to study the deployment of radar, the hunting of submarines and the size of convoys. After the war the methods moved to industry and government, and one of them became the core of the subject: linear programming, the optimisation of a linear function subject to linear inequalities. Kantorovich formulated production problems of this kind in 1939; Dantzig invented the simplex method for solving them in 1947; and Koopmans used them in economics. Kantorovich and Koopmans shared the 1975 Nobel prize in economics for this work.

This course develops linear programming and its theory first (the first six sections), then networks and integer programming, then non-linear and dynamic programming, and finally the stochastic models of OR: decisions under uncertainty, games, inventories, queues, Markov chains and simulation. This first section is about the step that comes before any algorithm: turning a description of a problem into a model.

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