Stochastic Transportation-Inventory Network Design Problem

By Jia Shu, Chung-Piaw Teo, Zuo-Jun Max Shen. Operational Research, 2005

307 citations recorded by the source corpus.

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.

Subfields: Industrial and Manufacturing Engineering, Organizational Behavior and Human Resource Management, Transportation

View Paper: https://www.semanticscholar.org/paper/85667cd8bfce400e981d92028937400945e2a089

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In Industrial and Manufacturing Engineering

In Organizational Behavior and Human Resource Management

In Transportation

Zuo-Jun Max Shen

Citations in the corpus

Facility location and supply chain management - A review (2009, background): “Multi-layer models are restricted to two types of facilities and only the intermediate layer is subject to location decisions (see [25,33,86,112]).”
Integrated supply chain design models: a survey and future research directions (2007, methodology): “Shu et al. [ 70 ] show that the above problem can be solved efficiently through a corresponding concave minimization problem defined on a polyhedron.”
A multi-commodity supply chain design problem (2005, methodology): “Shu et al. (2004) recently provided an O(n2 log n) algorithm to solve problem (P′′l (j)), which enables us to solve problem (P) efficiently.”
A multi-objective optimization for green supply chain network design (2011, background): “The problem covers a wide range of formulations ranged from linear deterministic models [20,24,28] to complex non-linear stochastic ones [30,33].”
Robust supply chain network design with service level against disruptions and demand uncertainties: A real-life case (2013, unknown): “demand-side uncertainty (Daskin et al., 2002; Shen and Qi, 2006; Shen and Daskin, 2005; Shu et al., 2005; Shen et al., 2003; Salema et al., 2007; Tsiakis et al., 2001; Leung et al., 2007; Romeijn et al., 2007; Pan and Nagi, 2010; Cardona-Valdés et al., 2011).”