IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v302y2022i3p1175-1188.html
   My bibliography  Save this article

The joint replenishment problem: Optimal policy and exact evaluation method

Author

Listed:
  • Creemers, Stefan
  • Boute, Robert

Abstract

We propose a new method to evaluate any stationary joint replenishment policy under compound Poisson demand. The method makes use of an embedded Markov chain that only considers the state of the system after an order is placed. The resulting state space reduction allows exact analysis of instances that until now could only be evaluated using approximation procedures. In addition, the size of the state space is not affected if we include nonzero lead times, backlog, and lost sales. We characterize the optimal joint replenishment policy, and use these characteristics to develop a greedy-optimal algorithm that generalizes the can-order policy, a well-known family in the class of joint replenishment policies. We numerically show that this generalized can-order policy only marginally improves the best conventional can-order policy. For sizeable systems with multiple items, the latter can now be found using our exact embedded Markov-chain method. Finally, we use our method to improve and extend the well-known decomposition approach.

Suggested Citation

  • Creemers, Stefan & Boute, Robert, 2022. "The joint replenishment problem: Optimal policy and exact evaluation method," European Journal of Operational Research, Elsevier, vol. 302(3), pages 1175-1188.
    • Handle: RePEc:eee:ejores:v:302:y:2022:i:3:p:1175-1188
    DOI: 10.1016/j.ejor.2022.02.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221722000911
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2022.02.005?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Stefan Creemers & Gert Woumans & Robert Boute & Jeroen Beliën, 2017. "Tri-Vizor Uses an Efficient Algorithm to Identify Collaborative Shipping Opportunities," Interfaces, INFORMS, vol. 47(3), pages 244-259, June.
    2. Khouja, Moutaz & Goyal, Suresh, 2008. "A review of the joint replenishment problem literature: 1989-2005," European Journal of Operational Research, Elsevier, vol. 186(1), pages 1-16, April.
    3. Edward Ignall, 1969. "Optimal Continuous Review Policies for Two Product Inventory Systems with Joint Setup Costs," Management Science, INFORMS, vol. 15(5), pages 278-283, January.
    4. A. Federgruen & H. Groenevelt & H. C. Tijms, 1984. "Coordinated Replenishments in a Multi-Item Inventory System with Compound Poisson Demands," Management Science, INFORMS, vol. 30(3), pages 344-357, March.
    5. Padilla Tinoco, Silvia Valeria & Creemers, Stefan & Boute, Robert N., 2017. "Collaborative shipping under different cost-sharing agreements," European Journal of Operational Research, Elsevier, vol. 263(3), pages 827-837.
    6. Melchiors, Philip, 2002. "Calculating can-order policies for the joint replenishment problem by the compensation approach," European Journal of Operational Research, Elsevier, vol. 141(3), pages 587-595, September.
    7. Joseph L. Balintfy, 1964. "On a Basic Class of Multi-Item Inventory Problems," Management Science, INFORMS, vol. 10(2), pages 287-297, January.
    8. Silvia Valeria Padilla Tinoco & Stefan Creemers & Robert Boute, 2017. "Collaborative shipping under different cost-sharing agreements," Post-Print hal-01745266, HAL.
    9. Yu-Shen Zheng, 1994. "Optimal Control Policy for Stochastic Inventory Systems with Markovian Discount Opportunities," Operations Research, INFORMS, vol. 42(4), pages 721-738, August.
    10. S. Viswanathan, 2007. "An Algorithm for Determining the Best Lower Bound for the Stochastic Joint Replenishment Problem," Operations Research, INFORMS, vol. 55(5), pages 992-996, October.
    11. Stefan Creemers & Gert Woumans & Robert Boute & Jeroen Beliën, 2017. "Tri-Vizor Uses an Efficient Algorithm to Identify Collaborative Shipping Opportunities," Post-Print hal-01745271, HAL.
    12. Schultz, Helle & Johansen, Soren Glud, 1999. "Can-order policies for coordinated inventory replenishment with Erlang distributed times between ordering," European Journal of Operational Research, Elsevier, vol. 113(1), pages 30-41, February.
    13. Goyal, Suresh K. & Satir, Ahmet T., 1989. "Joint replenishment inventory control: Deterministic and stochastic models," European Journal of Operational Research, Elsevier, vol. 38(1), pages 2-13, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Park, Hyungjun & Choi, Dong Gu & Min, Daiki, 2023. "Adaptive inventory replenishment using structured reinforcement learning by exploiting a policy structure," International Journal of Production Economics, Elsevier, vol. 266(C).
    2. De Moor, Bram J. & Creemers, Stefan & Boute, Robert N., 2023. "Breaking truck dominance in supply chains: Proactive freight consolidation and modal split transport," International Journal of Production Economics, Elsevier, vol. 257(C).
    3. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. De Moor, Bram J. & Creemers, Stefan & Boute, Robert N., 2023. "Breaking truck dominance in supply chains: Proactive freight consolidation and modal split transport," International Journal of Production Economics, Elsevier, vol. 257(C).
    2. Padilla Tinoco, Silvia Valeria & Creemers, Stefan & Boute, Robert N., 2017. "Collaborative shipping under different cost-sharing agreements," European Journal of Operational Research, Elsevier, vol. 263(3), pages 827-837.
    3. Kouki, Chaaben & Babai, M. Zied & Jemai, Zied & Minner, Stefan, 2016. "A coordinated multi-item inventory system for perishables with random lifetime," International Journal of Production Economics, Elsevier, vol. 181(PA), pages 226-237.
    4. S G Johansen & P Melchiors, 2003. "Can-order policy for the periodic-review joint replenishment problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(3), pages 283-290, March.
    5. Banu Yüksel Özkaya & Ülkü Gürler & Emre Berk, 2006. "The stochastic joint replenishment problem: A new policy, analysis, and insights," Naval Research Logistics (NRL), John Wiley & Sons, vol. 53(6), pages 525-546, September.
    6. Kiesmüller, G.P., 2010. "Multi-item inventory control with full truckloads: A comparison of aggregate and individual order triggering," European Journal of Operational Research, Elsevier, vol. 200(1), pages 54-62, January.
    7. Stefanny Ramirez & Laurence H. Brandenburg & Dario Bauso, 2023. "Coordinated Replenishment Game and Learning Under Time Dependency and Uncertainty of the Parameters," Dynamic Games and Applications, Springer, vol. 13(1), pages 326-352, March.
    8. Larsen, Christian, 2009. "The Q(s,S) control policy for the joint replenishment problem extended to the case of correlation among item-demands," International Journal of Production Economics, Elsevier, vol. 118(1), pages 292-297, March.
    9. Kiesmüller, G.P., 2009. "A multi-item periodic replenishment policy with full truckloads," International Journal of Production Economics, Elsevier, vol. 118(1), pages 275-281, March.
    10. Melchiors, Philip, 2002. "Calculating can-order policies for the joint replenishment problem by the compensation approach," European Journal of Operational Research, Elsevier, vol. 141(3), pages 587-595, September.
    11. Lee, Loo Hay & Chew, Ek Peng, 2005. "A dynamic joint replenishment policy with auto-correlated demand," European Journal of Operational Research, Elsevier, vol. 165(3), pages 729-747, September.
    12. Yu Zhang & Vidyadhar Kulkarni, 2018. "Automated Teller Machine Replenishment Policies with Submodular Costs," Manufacturing & Service Operations Management, INFORMS, vol. 20(3), pages 517-530, July.
    13. Tsai, Chieh-Yuan & Tsai, Chi-Yang & Huang, Po-Wen, 2009. "An association clustering algorithm for can-order policies in the joint replenishment problem," International Journal of Production Economics, Elsevier, vol. 117(1), pages 30-41, January.
    14. Larsen, Christian, 2019. "A heuristic joint replinishment policy for the case of heterogeneity among items," International Journal of Production Economics, Elsevier, vol. 209(C), pages 164-171.
    15. Dellaert, Nico & van de Poel, Erik, 1996. "Global inventory control in an academic hospital," International Journal of Production Economics, Elsevier, vol. 46(1), pages 277-284, December.
    16. Pundoor, Guruprasad & Chen, Zhi-Long, 2009. "Joint cyclic production and delivery scheduling in a two-stage supply chain," International Journal of Production Economics, Elsevier, vol. 119(1), pages 55-74, May.
    17. Liu, Liming & Yuan, Xue-Ming, 2000. "Coordinated replenishments in inventory systems with correlated demands," European Journal of Operational Research, Elsevier, vol. 123(3), pages 490-503, June.
    18. Khouja, Moutaz & Goyal, Suresh, 2008. "A review of the joint replenishment problem literature: 1989-2005," European Journal of Operational Research, Elsevier, vol. 186(1), pages 1-16, April.
    19. Nielsen, Christina & Larsen, Christian, 2005. "An analytical study of the Q(s,S) policy applied to the joint replenishment problem," European Journal of Operational Research, Elsevier, vol. 163(3), pages 721-732, June.
    20. Saeed Poormoaied, 2022. "Inventory decision in a periodic review inventory model with two complementary products," Annals of Operations Research, Springer, vol. 315(2), pages 1937-1970, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:302:y:2022:i:3:p:1175-1188. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.