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

Xiaobei Shen (), Yimin Yu () and Woonghee Tim Huh ()
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Xiaobei Shen: International Institute of Finance, School of Management, University of Science and Technology of China, Hefei, China
Yimin Yu: Department of Management Sciences, College of Business, City University of Hong Kong, Hong Kong SAR, China
Woonghee Tim Huh: Sauder School of Business, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada

Operations Research, 2022, vol. 70, issue 4, 1953-1968

Abstract: 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 notion 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.

Keywords: Operations and Supply Chains; capacitated serial system; permutation-dependent separability; optimal replenishment policy (search for similar items in EconPapers)
Date: 2022
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