IDEAS home Printed from https://ideas.repec.org/a/eee/jomega/v116y2023ics0305048322002067.html
   My bibliography  Save this article

An alternating direction method of multipliers for optimizing (s, S) policies in a distribution system with joint replenishment volume constraints

Author

Listed:
  • Dai, Bo
  • Chen, Haoxun
  • Li, Yuan
  • Zhang, Yidong
  • Wang, Xiaoqing
  • Deng, Yuming

Abstract

In this paper, we study a two-echelon distribution system in which multiple products are jointly replenished at each stocking location and the inventory of each product at each location is controlled by an (s, S) policy. The transportation capacity in volume of products for each joint replenishment is limited, and linear rationing policies are used for both on-hand inventory and transportation capacity allocation in the system in case of shortage. We propose a novel scenario-based model for the optimization of the (s, S) policies in the system that considers the rationing policies. Because of its high complexity when the number of scenarios is large, an Alternating Direction Method of Multipliers is proposed to solve the model. Based on real data, forty instances were generated and tested to evaluate the model and the solution method. Our numerical experiments show that for these instances this method could find a better solution in a much shorter computation time compared with CPLEX 12.9, whereas the latter often runs out of memory for large-size instances on a personal computer. Moreover, the inventory policies found by this scenario-based optimization approach can reduce costs by 5.1% and improve fill rates by 9.7% on average compared with those currently used in Alibaba.

Suggested Citation

  • Dai, Bo & Chen, Haoxun & Li, Yuan & Zhang, Yidong & Wang, Xiaoqing & Deng, Yuming, 2023. "An alternating direction method of multipliers for optimizing (s, S) policies in a distribution system with joint replenishment volume constraints," Omega, Elsevier, vol. 116(C).
    • Handle: RePEc:eee:jomega:v:116:y:2023:i:c:s0305048322002067
    DOI: 10.1016/j.omega.2022.102800
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0305048322002067
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.omega.2022.102800?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. Carvajal, Jimmy & Castaño, Fabian & Sarache, William & Costa, Yasel, 2020. "Heuristic approaches for a two-echelon constrained joint replenishment and delivery problem," International Journal of Production Economics, Elsevier, vol. 220(C).
    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. de Kok, Ton & Grob, Christopher & Laumanns, Marco & Minner, Stefan & Rambau, Jörg & Schade, Konrad, 2018. "A typology and literature review on stochastic multi-echelon inventory models," European Journal of Operational Research, Elsevier, vol. 269(3), pages 955-983.
    4. M. Fattahi & M. Mahootchi & S.M. Moattar Husseini & E. Keyvanshokooh & F. Alborzi, 2015. "Investigating replenishment policies for centralised and decentralised supply chains using stochastic programming approach," International Journal of Production Research, Taylor & Francis Journals, vol. 53(1), pages 41-69, January.
    5. Noordhoek, Marije & Dullaert, Wout & Lai, David S.W. & de Leeuw, Sander, 2018. "A simulation–optimization approach for a service-constrained multi-echelon distribution network," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 114(C), pages 292-311.
    6. 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.
    7. Hamed Jalali & Inneke Van Nieuwenhuyse, 2015. "Simulation optimization in inventory replenishment: a classification," IISE Transactions, Taylor & Francis Journals, vol. 47(11), pages 1217-1235, November.
    8. Haoxun Chen & Bo Dai & Yuan Li & Yidong Zhang & Xiaoqing Wang & Yuming Deng, 2022. "Stock allocation in a two-echelon distribution system controlled by (s, S) policies," International Journal of Production Research, Taylor & Francis Journals, vol. 60(3), pages 894-911, February.
    9. Al-Rifai, Mohammad H. & Rossetti, Manuel D., 2007. "An efficient heuristic optimization algorithm for a two-echelon (R, Q) inventory system," International Journal of Production Economics, Elsevier, vol. 109(1-2), pages 195-213, September.
    10. Hill, R.M. & Seifbarghy, M. & Smith, D.K., 2007. "A two-echelon inventory model with lost sales," European Journal of Operational Research, Elsevier, vol. 181(2), pages 753-766, September.
    11. Seifbarghy, Mehdi & Jokar, Mohammad Reza Akbari, 2006. "Cost evaluation of a two-echelon inventory system with lost sales and approximately Poisson demand," International Journal of Production Economics, Elsevier, vol. 102(2), pages 244-254, August.
    12. Andrew J. Clark & Herbert Scarf, 2004. "Optimal Policies for a Multi-Echelon Inventory Problem," Management Science, INFORMS, vol. 50(12_supple), pages 1782-1790, December.
    13. Bijvank, Marco & Vis, Iris F.A., 2011. "Lost-sales inventory theory: A review," European Journal of Operational Research, Elsevier, vol. 215(1), pages 1-13, November.
    14. Awi Federgruen & Paul Zipkin, 1984. "Allocation policies and cost approximations for multilocation inventory systems," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 31(1), pages 97-129, March.
    15. Tsai, Shing Chih & Chen, Sin Ting, 2017. "A simulation-based multi-objective optimization framework: A case study on inventory management," Omega, Elsevier, vol. 70(C), pages 148-159.
    16. Axsater, Sven & Zhang, Wen-Fa, 1999. "A joint replenishment policy for multi-echelon inventory control," International Journal of Production Economics, Elsevier, vol. 59(1-3), pages 243-250, March.
    17. Qiu, Ruozhen & Sun, Yue & Sun, Minghe, 2022. "A robust optimization approach for multi-product inventory management in a dual-channel warehouse under demand uncertainties," Omega, Elsevier, vol. 109(C).
    18. Forsberg, Rolf, 1997. "Exact evaluation of (R, Q)-policies for two-level inventory systems with Poisson demand," European Journal of Operational Research, Elsevier, vol. 96(1), pages 130-138, January.
    19. Bollapragada, rinivas & Akella, Ram & Srinivasan, Ramesh, 1998. "Centralized ordering and allocation policies in a two-echelon system with non-identical warehouses," European Journal of Operational Research, Elsevier, vol. 106(1), pages 74-81, April.
    20. Zhou, Yong-Wu & Lau, Hon-Shiang & Yang, Shan-Lin, 2004. "A finite horizon lot-sizing problem with time-varying deterministic demand and waiting-time-dependent partial backlogging," International Journal of Production Economics, Elsevier, vol. 91(2), pages 109-119, September.
    21. Jula, Payman & Leachman, Robert C., 2011. "A supply-chain optimization model of the allocation of containerized imports from Asia to the United States," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 47(5), pages 609-622, September.
    22. Avci, Mualla Gonca & Selim, Hasan, 2018. "A multi-objective simulation-based optimization approach for inventory replenishment problem with premium freights in convergent supply chains," Omega, Elsevier, vol. 80(C), pages 153-165.
    23. Teunter, Ruud H. & Kuipers, Stefan, 2022. "Inventory control with demand substitution: new insights from a two-product Economic Order Quantity analysis," Omega, Elsevier, vol. 113(C).
    24. van der Heijden, M. C. & Diks, E. B. & de Kok, A. G., 1997. "Stock allocation in general multi-echelon distribution systems with (R, S) order-up-to-policies," International Journal of Production Economics, Elsevier, vol. 49(2), pages 157-174, April.
    25. Andersson, Jonas & Melchiors, Philip, 2001. "A two-echelon inventory model with lost sales," International Journal of Production Economics, Elsevier, vol. 69(3), pages 307-315, February.
    26. Lagodimos, A.G. & Koukoumialos, S., 2008. "Service performance of two-echelon supply chains under linear rationing," International Journal of Production Economics, Elsevier, vol. 112(2), pages 869-884, April.
    27. S. Viswanathan, 1997. "Note. Periodic Review (s, S) Policies for Joint Replenishment Inventory Systems," Management Science, INFORMS, vol. 43(10), pages 1447-1454, October.
    28. Berling, Peter & Johansson, Lina & Marklund, Johan, 2023. "Controlling inventories in omni/multi-channel distribution systems with variable customer order-sizes," Omega, Elsevier, vol. 114(C).
    29. Dai, B. & Chen, H.X. & Li, Y.A. & Zhang, Y.D. & Wang, X.Q. & Deng, Y.M., 2021. "Inventory replenishment planning of a distribution system with storage capacity constraints and multi-channel order fulfilment," Omega, Elsevier, vol. 102(C).
    30. Balkhi, Zaid T., 2001. "On a finite horizon production lot size inventory model for deteriorating items: An optimal solution," European Journal of Operational Research, Elsevier, vol. 132(1), pages 210-223, July.
    31. Diks, E. B. & de Kok, A. G., 1998. "Optimal control of a divergent multi-echelon inventory system," European Journal of Operational Research, Elsevier, vol. 111(1), pages 75-97, November.
    32. 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.
    33. Yue Wang & Joseph Geunes & Xiaofeng Nie, 2022. "Optimising inventory placement in a two-echelon distribution system with fulfillment-time-dependent demand," International Journal of Production Research, Taylor & Francis Journals, vol. 60(1), pages 48-72, January.
    34. Lin, Yizhong & Leung, Janny M.Y. & Zhang, Lianmin & Gu, Jia-Wen, 2020. "Single-item repairable inventory system with stochastic new and warranty demands," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 142(C).
    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. Sunyu Tao & Shenglin Liu & Huijie Zhou & Xiaoyan Mao, 2024. "Research on Inventory Sustainable Development Strategy for Maximizing Cost-Effectiveness in Supply Chain," Sustainability, MDPI, vol. 16(11), pages 1-23, May.

    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. Bo Dai & Fenfen Li, 2021. "Joint Inventory Replenishment Planning of an E-Commerce Distribution System with Distribution Centers at Producers’ Locations," Logistics, MDPI, vol. 5(3), pages 1-14, July.
    2. de Kok, Ton & Grob, Christopher & Laumanns, Marco & Minner, Stefan & Rambau, Jörg & Schade, Konrad, 2018. "A typology and literature review on stochastic multi-echelon inventory models," European Journal of Operational Research, Elsevier, vol. 269(3), pages 955-983.
    3. Huaxiao Shen & Tian Tian & Han Zhu, 2019. "A Two-Echelon Inventory System with a Minimum Order Quantity Requirement," Sustainability, MDPI, vol. 11(18), pages 1-22, September.
    4. Kaynov, Illya & van Knippenberg, Marijn & Menkovski, Vlado & van Breemen, Albert & van Jaarsveld, Willem, 2024. "Deep Reinforcement Learning for One-Warehouse Multi-Retailer inventory management," International Journal of Production Economics, Elsevier, vol. 267(C).
    5. Gioia, Daniele Giovanni & Minner, Stefan, 2023. "On the value of multi-echelon inventory management strategies for perishable items with on-/off-line channels," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 180(C).
    6. Haji, Rasoul & Neghab, Mohammadali Pirayesh & Baboli, Armand, 2009. "Introducing a new ordering policy in a two-echelon inventory system with Poisson demand," International Journal of Production Economics, Elsevier, vol. 117(1), pages 212-218, January.
    7. Rau, Hsin & Wu, Mei-Ying & Wee, Hui-Ming, 2003. "Integrated inventory model for deteriorating items under a multi-echelon supply chain environment," International Journal of Production Economics, Elsevier, vol. 86(2), pages 155-168, November.
    8. Gumus, Alev Taskin & Guneri, Ali Fuat & Ulengin, Fusun, 2010. "A new methodology for multi-echelon inventory management in stochastic and neuro-fuzzy environments," International Journal of Production Economics, Elsevier, vol. 128(1), pages 248-260, November.
    9. Alvarez, Elisa & van der Heijden, Matthieu, 2014. "On two-echelon inventory systems with Poisson demand and lost sales," European Journal of Operational Research, Elsevier, vol. 235(1), pages 334-338.
    10. Noordhoek, Marije & Dullaert, Wout & Lai, David S.W. & de Leeuw, Sander, 2018. "A simulation–optimization approach for a service-constrained multi-echelon distribution network," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 114(C), pages 292-311.
    11. Carole Camisullis & Vincent Giard, 2010. "Détermination des stocks de sécurité dans une chaîne logistique-amont dédiée à une production de masse de produits fortement diversifiés," Working Papers hal-00876986, HAL.
    12. 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.
    13. van der Heijden, Matthieu, 2000. "Near cost-optimal inventory control policies for divergent networks under fill rate constraints," International Journal of Production Economics, Elsevier, vol. 63(2), pages 161-179, January.
    14. Gabor, Adriana F. & van Ommeren, Jan-Kees & Sleptchenko, Andrei, 2022. "An inventory model with discounts for omnichannel retailers of slow moving items," European Journal of Operational Research, Elsevier, vol. 300(1), pages 58-72.
    15. Güllü, Refik & Erkip, Nesim, 2024. "Risk pooling under demand and price uncertainty," European Journal of Operational Research, Elsevier, vol. 315(1), pages 120-129.
    16. Howard, Christian & Marklund, Johan, 2011. "Evaluation of stock allocation policies in a divergent inventory system with shipment consolidation," European Journal of Operational Research, Elsevier, vol. 211(2), pages 298-309, June.
    17. repec:dau:papers:123456789/3720 is not listed on IDEAS
    18. 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.
    19. Bijvank, Marco & Vis, Iris F.A., 2011. "Lost-sales inventory theory: A review," European Journal of Operational Research, Elsevier, vol. 215(1), pages 1-13, November.
    20. Olof Stenius & Ayşe Gönül Karaarslan & Johan Marklund & A. G. de Kok, 2016. "Exact Analysis of Divergent Inventory Systems with Time-Based Shipment Consolidation and Compound Poisson Demand," Operations Research, INFORMS, vol. 64(4), pages 906-921, August.
    21. Kanchanasuntorn, Kanchana & Techanitisawad, Anulark, 2006. "An approximate periodic model for fixed-life perishable products in a two-echelon inventory-distribution system," International Journal of Production Economics, Elsevier, vol. 100(1), pages 101-115, March.

    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:jomega:v:116:y:2023:i:c:s0305048322002067. 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/wps/find/journaldescription.cws_home/375/description#description .

    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.