Technical Note-A Permutation-Dependent Separability Approach for Capacitated Two-Echelon Inventory Systems

作者：Shen, Xiaobei; Yu, Yimin^*; Huh, Woonghee Tim

来源：Operations Research, 2022, 70(4).

DOI：10.1287/opre.2021.2194

• capacitated serial system
• permutation-dependent separability
• optimal replenishment policy

We consider optimal inventory replenishment policies for capacitated 2-echelon serial inventory systems, where the capacity of upstream echelon can be the bottleneck. We show that the optimal replenishment decisions in each period can be made one echelon at a time by introducing a procedure that can sequentially decompose a multidimensional optimization problem to a series of one-dimensional problems. We also introduce the no-tion of permutation-dependent separability. A permutation-dependent separable function is a function that can be decomposed as a sum of single-variable component functions under each nondecreasing order of variables. We find that the value function for the capacitated 2-echelon system in each period is permutation-dependent separable, and that, for each echelon, a permutation-dependent echelon base stock policy is optimal.

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