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The Multiperiod Multilocation Inventory Problem

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  • Uday S. Karmarkar

    (University of Rochester, Rochester, New York)

Abstract

This paper studies the structure of optimal policies in general multiperiod, multilocation inventory problems with proportional costs. It is shown that the multiperiod problem has the same generic form in each period as a one-period problem Hence, properties of the one-period problem are inherited by the multiperiod formulation; in particular the form of the optimal policy can be characterized. In the special case of a Leontief system structure (and for a somewhat more general class) it is shown that base-stock policies are optimal for certain initial states. For the stationary problem some results are derived about the monotonicity of the sequence of base stock vectors.

Suggested Citation

  • Uday S. Karmarkar, 1981. "The Multiperiod Multilocation Inventory Problem," Operations Research, INFORMS, vol. 29(2), pages 215-228, April.
    • Handle: RePEc:inm:oropre:v:29:y:1981:i:2:p:215-228
    DOI: 10.1287/opre.29.2.215
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    Cited by:

    1. Jian Yang & Zhaoqiong Qin, 2007. "Capacitated Production Control with Virtual Lateral Transshipments," Operations Research, INFORMS, vol. 55(6), pages 1104-1119, December.
    2. Hossein Abouee-Mehrizi & Oded Berman & Shrutivandana Sharma, 2015. "Optimal Joint Replenishment and Transshipment Policies in a Multi-Period Inventory System with Lost Sales," Operations Research, INFORMS, vol. 63(2), pages 342-350, April.
    3. Rong Li, 2020. "Reinvent Retail Supply Chain: Ship‐from‐Store‐to‐Store," Production and Operations Management, Production and Operations Management Society, vol. 29(8), pages 1825-1836, August.
    4. Daniel Kuhn, 2009. "An Information-Based Approximation Scheme for Stochastic Optimization Problems in Continuous Time," Mathematics of Operations Research, INFORMS, vol. 34(2), pages 428-444, May.
    5. Bhatnagar, Rohit & Lin, Bing, 2019. "The joint transshipment and production control policies for multi-location production/inventory systems," European Journal of Operational Research, Elsevier, vol. 275(3), pages 957-970.
    6. Qi Feng & Chengzhang Li & Mengshi Lu & Jeyaveerasingam George Shanthikumar, 2022. "Dynamic Substitution for Selling Multiple Products under Supply and Demand Uncertainties," Production and Operations Management, Production and Operations Management Society, vol. 31(4), pages 1645-1662, April.
    7. Sumit Kunnumkal & Huseyin Topaloglu, 2010. "Computing Time-Dependent Bid Prices in Network Revenue Management Problems," Transportation Science, INFORMS, vol. 44(1), pages 38-62, February.
    8. Van der Heide, G. & Buijs, P. & Roodbergen, K.J. & Vis, I.F.A., 2018. "Dynamic shipments of inventories in shared warehouse and transportation networks," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 118(C), pages 240-257.
    9. Anil Kukreja & Charles P. Schmidt & David M. Miller, 2001. "Stocking Decisions for Low-Usage Items in a Multilocation Inventory System," Management Science, INFORMS, vol. 47(10), pages 1371-1383, October.
    10. E. Angelelli & R. Mansini & M. Vindigni, 2009. "Exploring greedy criteria for the dynamic traveling purchaser problem," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 17(2), pages 141-158, June.
    11. Yale T. Herer & Michal Tzur, 2001. "The dynamic transshipment problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(5), pages 386-408, August.
    12. Kumar Satyendra & Venkata Rao, V. & Tirupati Devanath, 2003. "Multiple products, multiple constraints, single period inventory problem: A Hierarchical solution procedure," IIMA Working Papers WP2003-11-03, Indian Institute of Management Ahmedabad, Research and Publication Department.
    13. 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.
    14. Yiwei Huang & Yunxia Zhu & Subodha Kumar & Bala Shetty & Chelliah Sriskandarajah, 2020. "A Framework for Analyzing the U.S. Coin Supply Chain," Production and Operations Management, Production and Operations Management Society, vol. 29(12), pages 2736-2759, December.
    15. Satya S. Malladi & Alan L. Erera & Chelsea C. White, 2021. "Managing mobile production-inventory systems influenced by a modulation process," Annals of Operations Research, Springer, vol. 304(1), pages 299-330, September.
    16. Robert A. Shumsky & Fuqiang Zhang, 2009. "Dynamic Capacity Management with Substitution," Operations Research, INFORMS, vol. 57(3), pages 671-684, June.
    17. Sumit Kunnumkal & Huseyin Topaloglu, 2008. "A duality‐based relaxation and decomposition approach for inventory distribution systems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 55(7), pages 612-631, October.
    18. Huseyin Topaloglu & Sumit Kunnumkal, 2006. "Approximate dynamic programming methods for an inventory allocation problem under uncertainty," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(8), pages 822-841, December.
    19. García-Benito, Juan Carlos & Martín-Peña, María-Luz, 2021. "A redistribution model with minimum backorders of spare parts: A proposal for the defence sector," European Journal of Operational Research, Elsevier, vol. 291(1), pages 178-193.
    20. Ying Rong & Lawrence V. Snyder & Yang Sun, 2010. "Inventory sharing under decentralized preventive transshipments," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(6), pages 540-562, September.
    21. Herer, Yale T. & Tzur, Michal & Yucesan, Enver, 2002. "Transshipments: An emerging inventory recourse to achieve supply chain leagility," International Journal of Production Economics, Elsevier, vol. 80(3), pages 201-212, December.
    22. Jason Acimovic & Stephen C. Graves, 2017. "Mitigating Spillover in Online Retailing via Replenishment," Manufacturing & Service Operations Management, INFORMS, vol. 19(3), pages 419-436, July.

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