Inventory placement in acyclic supply chain networks

The strategic safety stock placement problem is a constrained separable concave minimization problem and so is solvable, in principle, as a sequence of mixed-integer programming problems using a successive piecewise linear approximation approach. Unfortunately, direct implementation of this approach proves to be very time consuming, and so the research community has focused on other problem specific techniques, most notably a dynamic programming approach proposed by Graves and Willems (2000) for situations when the underlying network is a spanning tree. We examine a new successive piecewise linear approximation approach to this problem. By adding a set of redundant constraints to the formulation and by iteratively refining the piecewise linear approximations, we show that a commercial solver (CPLEX) is able to routinely solve moderate-size supply chain safety stock placement problems to optimality. For a random 100-stage sparse acyclic supply chain network, the algorithm typically fin...

• Type: Journal
• Year: 2006
• Where: ORL
• Authors: Thomas L. Magnanti, Zuo-Jun Max Shen, Jia Shu, David Simchi-Levi, Chung-Piaw Teo
• Keywords: Linear Approximation Approach, ORL 2006, Piecewise Linear Approximations, Successive Piecewise Linear