The forward reserve warehouse sizing and dimensioning problem

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Gu, Jinxiang
Goetschalckx, Marc
McGinnis, Leon F.
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This research addresses sizing and dimensioning of a forward-reserve warehouse, a strategic design problem that has important implications on warehouse life cycle costs including construction, inventory holding and replenishment, and material handling. Large mixed integer nonlinear models are developed that capture the complex tradeoffs among the different costs in order to achieve a global optimal design satisfying throughput requirements. We first consider the situation where the forward area includes all SKUs so that order picking is performed only in the forward area. In this case, the problem can be decomposed. The resulting sub-problem is convex and can be solved very efficiently based on the Karush-Kuhn-Tucker (KKT) conditions. This property enables the use of a Generalized Benders Decomposition (GBD) method to solve the sizing and dimensioning problem exactly. We then extend the problem to more general situations where the forward area contains a subset of SKUs. This requires integrating the sizing and dimensioning decisions with the decision to assign SKUs to the forward area based on their flow characteristics (i.e., the forward reserve allocation). A similar decomposition strategy can be employed, but the sub-problem (incorporating the forward reserve allocation) is no longer convex. A bi-level hierarchical heuristic approach is proposed that integrates a pattern search method for the master problem and optimal and heuristic algorithms for the sub-problems. Numerical results demonstrate that the proposed solution methods can efficiently find optimal or near optimal solutions for the sizing and dimensioning problem, and the resulting solutions are robust with regards to possible forecasting errors in design parameters.
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