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A Power-of-Two Ordering Policy for One-Warehouse Multiretailer Systems with Stochastic Demand

Marshall School of Business, University of Southern California, Los Angeles, California 90089
Department of Industrial Engineering and Operations Research, University of California, Berkeley, California 94720
leonyzhu{at}marshall.usc.edu
shen{at}ieor.berkeley.edu

We study a two-echelon supply chain with one warehouse and N (nonidentical) retailers facing stochastic demand. An easy-to-implement inventory policy, the so-called power-of-two (POT) policy, is proposed to manage inventory for the system. To maintain a certain service level, safety stocks are kept at the warehouse and each retailer outlet to buffer random demand. Our analysis highlights the important role of the warehouse safety stock level, which, in addition to the length of the warehouse order interval, significantly affects the lengths of the retailers' order intervals. By combining the length of the warehouse order interval with the warehouse safety stock level, we introduce a plane partition method and develop a polynomial time algorithm to find a POT policy for arbitrary target service levels. The long-run average cost of the proposed POT policy is guaranteed to be no more than 1.26 times the optimal POT policy cost. We also show that our proposed policy can be computed in O(N³).

Subject classifications: one-warehouse multiretailer system; approximation algorithm; analysis of algorithms.
History: Received January 2008; revision received December 2008; accepted December 2008.