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

  • Xiaobei Shen
  • , Yimin Yu*
  • , Woonghee Tim Huh
    • *Corresponding author for this work

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

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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.
Original languageEnglish
Pages (from-to)1953-1968
JournalOperations Research
Volume70
Issue number4
Online published19 Nov 2021
DOIs
Publication statusPublished - Jul 2022

Research Keywords

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

RGC Funding Information

  • RGC-funded

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  • TBRS: Safety, Reliability, and Disruption Management of High Speed Rail and Metro Systems

    XIE, M. (Principal Investigator / Project Coordinator), BENSOUSSAN, A. (Co-Principal Investigator), LO, S. M. (Co-Principal Investigator), SHOU, B. (Co-Principal Investigator), SINGPURWALLA, N. D. (Co-Principal Investigator), TSE, W. T. P. (Co-Principal Investigator), TSUI, K. L. (Co-Principal Investigator), YU, Y. (Co-Principal Investigator), YUEN, K. K. R. (Co-Principal Investigator), CHAN, A. B. (Co-Investigator), CHAN, N.-H. (Co-Investigator), CHIN, K. S. (Co-Investigator), CHOW, H. A. (Co-Investigator), Chow, W. K. (Co-Investigator), EDESESS, M. (Co-Investigator), GOLDSMAN, D. M. (Co-Investigator), Huang, J. (Co-Investigator), LEE, W. M. (Co-Investigator), LI, L. (Co-Investigator), LI, C. L. (Co-Investigator), LING, M. H. A. (Co-Investigator), LIU, S. (Co-Investigator), MURAKAMI, J. (Co-Investigator), NG, S. Y. S. (Co-Investigator), NI, M. C. (Co-Investigator), TAN, M.H.-Y. (Co-Investigator), Wang, W. (Co-Investigator), Wang, J. (Co-Investigator), WONG, C. K. (Co-Investigator), WONG, S. Y. Z. (Co-Investigator), WONG, S. C. (Co-Investigator), Xu, Z. (Co-Investigator), ZHANG, Z. (Co-Investigator), Zhang, D. (Co-Investigator), ZHAO, J. L. (Co-Investigator) & Zhou, Q. (Co-Investigator)

    1/01/16 → 31/12/21

    Project: Research

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