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Stochastic Transportation-Inventory Network Design Problem

High Performance Computation for Engineered Systems, Singapore-MIT Alliance, and Department of Decision Sciences, National University of Singapore, Singapore
High Performance Computation for Engineered Systems, Singapore-MIT Alliance, and Department of Decision Sciences, National University of Singapore, Singapore
Department of Industrial Engineering and Operations Research, University of California, Berkeley, California 94720
tlisj{at}nus.edu.sg
bizteocp{at}nus.edu.sg
shen{at}ieor.berkeley.edu

We study the stochastic transportation-inventory network design problem involving one supplier and multiple retailers. Each retailer faces some uncertain demand, and safety stock must be maintained to achieve suitable service levels. However, risk-pooling benefits may be achieved by allowing some retailers to serve as distribution centers for other retailers. The problem is to determine which retailers should serve as distribution centers and how to allocate the other retailers to the distribution centers. Shen et al. (2003) formulated this problem as a set-covering integer-programming model. The pricing problem that arises from the column generation algorithm gives rise to a new class of the submodular function minimization problem. In this paper, we show that by exploiting certain special structures, we can solve the general pricing problem in Shen et al. efficiently. Our approach utilizes the fact that the set of all lines in a two-dimension plane has low VC-dimension. We present computational results on several instances of sizes ranging from 40 to 500 retailers. Our solution technique can be applied to a wide range of other concave cost-minimization problems.

Subject classifications: facilities/equipment planning:stochastic; inventory/production:uncertainty; stochastic; programming:nonlinear.
History: Received October 2001; revision received December 2002; accepted September 2003.

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