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Optimal division of inventory between depot and bases

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  • Hadar Amrani
  • Eugene Khmelnitsky

Abstract

We consider a problem of optimal division of stock between a logistic depot and several geographically dispersed bases, in a two‐echelon supply chain. The objective is to minimize the total cost of inventory shipment, taking into account direct shipments between the depot and the bases, and lateral transshipments between bases. We prove the convexity of the objective function and suggest a procedure for identifying the optimal solution. Small‐dimensional cases, as well as a limit case in which the number of bases tends to infinity, are solved analytically for arbitrary distributions of demand. For a general case, an approximation is suggested. We show that, in many practical cases, partial pooling is the best strategy, and large proportions of the inventory should be kept at the bases rather than at the depot. The analytical and numerical examples show that complete pooling is obtained only as a limit case in which the transshipment cost tends to infinity. © 2017 Wiley Periodicals, Inc. Naval Research Logistics, 64: 3–18, 2017

Suggested Citation

  • Hadar Amrani & Eugene Khmelnitsky, 2017. "Optimal division of inventory between depot and bases," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(1), pages 3-18, February.
    • Handle: RePEc:wly:navres:v:64:y:2017:i:1:p:3-18
    DOI: 10.1002/nav.21733
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    2. Zhou, Zihan & Wang, Xinhui, 2023. "Replenishment and transshipment in periodic-review systems with a fixed order cost," European Journal of Operational Research, Elsevier, vol. 307(3), pages 1240-1247.
    3. Yongchang Wei & Fangyu Chen & Feng Xiong, 2018. "Dynamic Complexities in a Supply Chain System with Lateral Transshipments," Complexity, Hindawi, vol. 2018, pages 1-15, June.
    4. Brandimarte, Paolo & Craparotta, Giuseppe & Marocco, Elena, 2024. "Inventory reallocation in a fashion retail network: A matheuristic approach," European Journal of Operational Research, Elsevier, vol. 317(2), pages 603-615.
    5. Silbermayr, Lena & Gerchak, Yigal, 2019. "Partial pooling by independent firms with allocation according to contribution to pool," International Journal of Production Economics, Elsevier, vol. 218(C), pages 375-385.
    6. Somarin, Aghil Rezaei & Sharma, Pankaj & Tiwari, Sunil & Chen, Songlin, 2023. "Stock reallocation policy for repairable service parts in case of supply disruptions due to extreme weather events," International Journal of Production Economics, Elsevier, vol. 256(C).

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