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

Author

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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)

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.

Suggested Citation

  • Xiaobei Shen & Yimin Yu & Woonghee Tim Huh, 2022. "Technical Note—A Permutation-Dependent Separability Approach for Capacitated Two-Echelon Inventory Systems," Operations Research, INFORMS, vol. 70(4), pages 1953-1968, July.
    • Handle: RePEc:inm:oropre:v:70:y:2022:i:4:p:1953-1968
    DOI: 10.1287/opre.2021.2194
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