Stochastic Transportation-Inventory Network Design Problem

• Published in: Operations research Vol. 53; no. 1; pp. 48 - 60
• Main Authors: Shu, Jia, Teo, Chung-Piaw, Shen, Zuo-Jun Max
• Format: Journal Article
• Language: English
• Published: Linthicum, MD INFORMS 01.01.2005; Institute for Operations Research and the Management Sciences
• Subjects: Algorithms; Applied sciences; Business expenses; Capital costs; Cost allocation; Exact sciences and technology; Facilities planning; facilities/equipment planning:stochastic; Facility management; Facility management systems; Fixed costs; Flows in networks. Combinatorial problems; Inventories; Inventory; Inventory control; Inventory control, production control. Distribution; inventory/production:uncertainty; Methods; Nonlinear programming; Operational research and scientific management; Operational research. Management science; Optimal solutions; programming:nonlinear; Retail stores; Retailing; stochastic; Stochastic analysis; Stochastic models; Studies; Supply chain management; Transportation costs; Uncertainty; United States; Supply chain; facilities/equipment planning: stochastic; inventory/production: uncertainty; stochastic; programming: nonlinear; Retailers; Transportation network; Inventory control; Supplier; Non linear programming; Facility; Distribution network
• ISSN: 0030-364X; 1526-5463
• DOI: 10.1287/opre.1040.0140

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.