Optimizing Strategic Safety Stock Placement in General Acyclic Networks.

Abstract

We present two significant enhancements to the guaranteed-service (GS) model for multiechelon safety stock placement. First, we let each stage’s expected inventory cost be a generalized nonconcave non-closed-form function of its incoming and outgoing service time. This allows the GS model to incorporate important phenomena such as variable stage times and nonnested review periods, which previous GS literature has not allowed. Second, we optimize the generalized cost GS model for directed acyclic networks, rather than assembly/distribution networks or trees. For the resulting NP-hard optimization problem, we present a provably optimal algorithm that runs within minutes for 29 chains from a data set of 38 real-world supply chains ranging from 8 to 2,025 stages. We also present two significantly faster yet near-optimal heuristics. One heuristic is motivated by the structure of the formulation’s dual space, whereas the other heuristic simply terminates the optimization algorithm after a fixed number of iterations. As a performance benchmark, on the 38 chains, the first heuristic has an average optimality gap of approximately 1.1 % and average run time of 88 seconds, whereas the second heuristic has an average optimality gap of 2.8 % and an average run time of 5.9 seconds. Subject classifications: multiechelon inventory system; safety stock optimization; dynamic programming application; general acyclic networks.

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