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What is OR? |
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Many businesses and all large complex organizations face difficult decisions on a daily basis. For example, a manufacturing company must decide how much of each product it should be making at each point in time, how many products of each type it should keep in inventory, by what modes of transport and what routes it should distribute its product, which combination of new product development projects it should fund in the next year, which workers should be rostered on which shifts, how much overtime will be required of each worker, when it should replace or repair its equipment, and so on. The decisions made interact with each other and may have complex repercussions that are difficult to evaluate. Each decision involves making a trade-off between competing activities, often vying for limited resources. For example, a decision to maintain steady production levels may reduce production costs but increase inventory costs, while a decision to produce a large quantity of one product may deplete stock of a component needed for the timely production of another product.
The mathematical techniques used in Operations Research are drawn from areas of mathematics such as Optimization, Optimal Control and Probability and Statistics. The area of Optimization, which is concerned with the mathematical problem of minimizing or maximizing a function or functions subject to constraints, plays a particularly important role since the objective of many decision making problems is to determine the minimum or maximum out of a set of alternatives; for example a production company might wish to make decisions so as to minimize its transportation costs or to maximize its workers' job satisfaction.
Major subfields of Optimization which are critical in solving Operations Research problems are Mathematical Programming, Dynamic Programming and Combinatorial Optimization, all of which are the subject of active research by members and graduate students of the Operations Research Group in the Department of Mathematics and Statistics.
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