The parallel stack loading problem of minimizing the exact number of relocations

This study addresses the parallel stack loading problem, a general optimization problem arising in storage facilities such as container yards, slab yards, and warehouses. In this problem, we load incoming items into parallel stacks in the loading phase to minimize the number of relocations in the subsequent retrieval phase. Because of difficulties in treating the nested problem structure originating from the mutual dependence of the two phases, the existing studies approximately minimized the number of relocations using surrogate objective functions. In contrast, this study considers the parallel stack loading problem aiming to minimize the exact number of relocations. We first provide an integer programming formulation and next develop a nested branch-and-bound algorithm. In a computational study, we verify the effectiveness of the proposed branch-and-bound algorithm and evaluate the known surrogate objective functions based on the exact minimization.

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