Optimization models, especially nonlinear optimization models,
have been widely used to solve integrated supply chain design
problems. In integrated supply chain design, the decision maker
needs to take into consideration inventory costs and distribution
costs when the number and locations of the facilities are
determined. The objective is to minimize the total cost that
includes location costs and inventory costs at the facilities, and
distribution costs in the supply chain. We provide a survey of
recent developments in this research area.

https://www.aimsciences.org/article/exportPdf?id=9658ccc3-d6fd-4f9c-a4bf-cb0ec01dee46

Integrated supply chain design models: a survey and future research directions

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

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Stochastic Transportation-Inventory Network Design Problem

We consider a multi-commodity supply chain design problem in which we need to determine where to locate facilities and how to allocate customers to facilities so as to minimize total costs. The cost associated with each facility exhibits economies of scale. We show that this problem can be formulated as a nonlinear integer program and propose a Lagrangian-relaxation solution algorithm. By exploiting the structure of the problem, we find a low-order polynomial algorithm for the nonlinear integer program that must be solved in solving the Lagrangian relaxation subproblems. We also compare our approach with an existing algorithm. Contributed by the Location and Transportation Modeling Department

A multi-commodity supply chain design problem

A profit-maximizing supply chain network design model with demand choice flexibility

Integrating effective flexibility measures into a strategic supply chain planning model

Standard approaches to classical inventory control problems treat satisfying a predefined demand level as a constraint. In many practical contexts, however, total demand is comprised of separate demands from different markets or customers. It is not always clear that constraining a producer to satisfy all markets is an optimal approach. Since the inventory-related cost of an item depends on total demand volume, no clear method exists for determining a market's profitability a priori, based simply on per unit revenue and cost. Moreover, capacity constraints often limit a producer's ability to meet all demands. This paper presents models to address economic ordering decisions when a producer can choose whether to satisfy multiple markets. These models result in a set of nonlinear binary integer programming problems that, in the uncapacitated case, lend themselves to efficient solution due to their special structure. The capacitated versions can be cast as nonlinear knapsack problems, for which we propose a heuristic solution approach that is asymptotically optimal in the number of markets. The models generalize the classical EOQ and EPQ problems and lead to interesting optimization problems with intuitively appealing solution properties and interesting implications for inventory and pricing management. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2004.

Zuo-Jun Shen

Papers

Economic ordering decisions with market choice flexibility