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Bounds, Heuristics, and Approximations for Distribution Systems

Columbia University, 500 West 120th Street, MC 4704, New York, New York 10027
Stanford University, Terman 314, 380 Panama Way, Stanford, California 94305
Fuqua School of Business, Duke University, Durham, North Carolina 27708
ggallego{at}ieor.columbia.edu
oozer{at}stanford.edu
paul.zipkin{at}duke.edu

This paper develops simple approximate methods to analyze a two-stage distribution system consisting of one warehouse and multiple retailers with stochastic demand. We consider local and central control schemes. The main ideas are based on relaxing and or decomposing the system into more manageable newsvendor-type subsystems. We also provide bounds on the optimal policy and the optimal expected cost. We show that one of the heuristics is asymptotically optimal in the number of retailers. These results provide practically useful techniques as well as insights into stock-positioning issues and the drivers of system performance.

Subject classifications: inventory; production; multi-item; echelon; stage; approximation; heuristics; uncertainty; stochastic; operating characteristics.
History: Received June 2003; revision received July 2006; accepted July 2006.