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Coordination of Production/Distribution Networks with Unbalanced Leadtimes

Graduate School of Business, Columbia University, New York, New York 10027
Graduate School of Business, Columbia University, New York, New York 10027
The Fuqua School of Business, Duke University, Durham, North Carolina 27708
jdb8{at}columbia.edu

We investigate multiproduct, multilocation production/distribution networks with deterministic, stationary demands. Most research on such systems assumes zero leadtimes. Methods using fixed reorder intervals that are power-of-two multiples of a base planning period have proved to be very successful for such systems. The same methods apply to networks with positive leadtimes, provided the leadtimes are balanced in a specific sense. We explore networks with general, unbalanced leadtimes. A key result is a lower bound on the cost of any feasible policy. Other results concern policy heuristics and their performance. For a large class of networks, we construct a policy whose cost is within 45% of the lower bound. For general networks, the performance guarantee is 1:02(1+), where is a number dependent on the network topology only. In general, the best performance bound is obtained by systematically reducing the order intervals derived from the corresponding zero-leadtime system.

Subject classifications: Inventory/production: multi-item/echelon/stage, approximations/heuristics.
History: Received June 1996; revision received February 1997; revision received April 1998; revision received January 1999; accepted May 1999.