This paper studies 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.
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