PLANT LOCATION UNDER ECONOMIES OF SCALE FOR THE STOCHASTIC WORLD OF A MULTI-NATIONAL MANUFACTURER.
CARNEGIE-MELLON UNIV PITTSBURGH PA MANAGEMENT SCIENCES RESEARCH GROUP
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There are M national markets each with a target demand known only to a probability distribution. If this target demand is not supplied, a penalty is imposed, quadratically increasing in the amount of shortage. Conversely product can be supplied in excess of target demand, but the revenue it earns is quadratically decreasing in the amount dumped. P possible plant sites are under consideration, and at each the economies of scale are represented as a fixed cost plus a linear incremental cost in plant capacity. There is a probability that each plant will become unavailable due to strikes, sabotage, etc.. The cost on each transportation route is similarly known only to a probability distribution due to changes in import tariffs, and the occasional closing of routes such as Suez. The problem is formulated as a stochastic program with recourse in which the first stage decision is the choice of plant capacities, and the second stage decision sets production levels and distribution patterns. The second stage transportation problem has quadratic costs on variables depicting the penalties of failing to meet a markets target demand, and the revenue from dumping excess product in a market. A branch and bound approach handles the fixed costs of opening a plant, though an exhaustive search would unusually be replaced by simplifying heuristics. Author
- Administration and Management
- Operations Research