IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v53y2006i8p822-841.html
   My bibliography  Save this article

Approximate dynamic programming methods for an inventory allocation problem under uncertainty

Author

Listed:
  • Huseyin Topaloglu
  • Sumit Kunnumkal

Abstract

We propose two approximate dynamic programming methods to optimize the distribution operations of a company manufacturing a certain product at multiple production plants and shipping it to different customer locations for sale. We begin by formulating the problem as a dynamic program. Our first approximate dynamic programming method uses a linear approximation of the value function and computes the parameters of this approximation by using the linear programming representation of the dynamic program. Our second method relaxes the constraints that link the decisions for different production plants. Consequently, the dynamic program decomposes by the production plants. Computational experiments show that the proposed methods are computationally attractive, and in particular, the second method performs significantly better than standard benchmarks. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:53:y:2006:i:8:p:822-841
    DOI: 10.1002/nav.20164
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/nav.20164
    Download Restriction: no
    File URL: https://libkey.io/10.1002/nav.20164?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
    ---><---

    References listed on IDEAS

    as
    1. Uday S. Karmarkar, 1981. "The Multiperiod Multilocation Inventory Problem," Operations Research, INFORMS, vol. 29(2), pages 215-228, April.
    2. Katerina P. Papadaki & Warren B. Powell, 2003. "An adaptive dynamic programming algorithm for a stochastic multiproduct batch dispatch problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(7), pages 742-769, October.
    3. Uday S. Karmarkar, 1987. "The Multilocation Multiperiod Inventory Problem: Bounds and Approximations," Management Science, INFORMS, vol. 33(1), pages 86-94, January.
    4. Kirk A. Yost & Alan R. Washburn, 2000. "The LP/POMDP marriage: Optimization with imperfect information," Naval Research Logistics (NRL), John Wiley & Sons, vol. 47(8), pages 607-619, December.
    5. Anton J. Kleywegt & Vijay S. Nori & Martin W. P. Savelsbergh, 2002. "The Stochastic Inventory Routing Problem with Direct Deliveries," Transportation Science, INFORMS, vol. 36(1), pages 94-118, February.
    6. T. L. Magnanti & R. T. Wong, 1981. "Accelerating Benders Decomposition: Algorithmic Enhancement and Model Selection Criteria," Operations Research, INFORMS, vol. 29(3), pages 464-484, June.
    7. D. P. de Farias & B. Van Roy, 2003. "The Linear Programming Approach to Approximate Dynamic Programming," Operations Research, INFORMS, vol. 51(6), pages 850-865, December.
    8. Raymond K.-M. Cheung & Warren B. Powell, 1996. "Models and Algorithms for Distribution Problems with Uncertain Demands," Transportation Science, INFORMS, vol. 30(1), pages 43-59, February.
    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. Amin Khademi & Burak Eksioglu, 2018. "Spare Parts Inventory Management with Substitution-Dependent Reliability," INFORMS Journal on Computing, INFORMS, vol. 30(3), pages 507-521, August.
    2. Zhou, Jianheng & Luo, Yao, 2023. "Bayes information updating and multiperiod supply chain screening," International Journal of Production Economics, Elsevier, vol. 256(C).
    3. Mochen Yang & Gediminas Adomavicius & Alok Gupta, 2019. "Efficient Computational Strategies for Dynamic Inventory Liquidation," Information Systems Research, INFORMS, vol. 30(2), pages 595-615, June.
    4. Frank Schneider & Ulrich W. Thonemann & Diego Klabjan, 2018. "Optimization of Battery Charging and Purchasing at Electric Vehicle Battery Swap Stations," Transportation Science, INFORMS, vol. 52(5), pages 1211-1234, October.
    5. 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.
    6. Qihang Lin & Selvaprabu Nadarajah & Negar Soheili, 2020. "Revisiting Approximate Linear Programming: Constraint-Violation Learning with Applications to Inventory Control and Energy Storage," Management Science, INFORMS, vol. 66(4), pages 1544-1562, April.
    7. Charles I. Nkeki, 2013. "Dynamic Optimization Technique for Distribution of Goods with Stochastic Shortages," Journal of Optimization, Hindawi, vol. 2013, pages 1-12, December.

    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. Daniel Adelman & Adam J. Mersereau, 2008. "Relaxations of Weakly Coupled Stochastic Dynamic Programs," Operations Research, INFORMS, vol. 56(3), pages 712-727, June.
    2. Yale T. Herer & Michal Tzur, 2001. "The dynamic transshipment problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(5), pages 386-408, August.
    3. Daniel Adelman, 2004. "A Price-Directed Approach to Stochastic Inventory/Routing," Operations Research, INFORMS, vol. 52(4), pages 499-514, August.
    4. 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.
    5. Zheng, Xiaojin & Yin, Meixia & Zhang, Yanxia, 2019. "Integrated optimization of location, inventory and routing in supply chain network design," Transportation Research Part B: Methodological, Elsevier, vol. 121(C), pages 1-20.
    6. 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.
    7. 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.
    8. Sumit Kunnumkal & Huseyin Topaloglu, 2008. "Exploiting the Structural Properties of the Underlying Markov Decision Problem in the Q-Learning Algorithm," INFORMS Journal on Computing, INFORMS, vol. 20(2), pages 288-301, May.
    9. Li, Shuqin & Jia, Shuai, 2019. "A Benders decomposition algorithm for the order fulfilment problem of an e-tailer with a self-owned logistics system," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 122(C), pages 463-480.
    10. Santoso, Tjendera & Ahmed, Shabbir & Goetschalckx, Marc & Shapiro, Alexander, 2005. "A stochastic programming approach for supply chain network design under uncertainty," European Journal of Operational Research, Elsevier, vol. 167(1), pages 96-115, November.
    11. Gutierrez, Genaro J. & Kouvelis, Panagiotis & Kurawarwala, Abbas A., 1996. "A robustness approach to uncapacitated network design problems," European Journal of Operational Research, Elsevier, vol. 94(2), pages 362-376, October.
    12. Meissner, Joern & Strauss, Arne, 2012. "Network revenue management with inventory-sensitive bid prices and customer choice," European Journal of Operational Research, Elsevier, vol. 216(2), pages 459-468.
    13. Moon, Ilkyeong & Feng, Xuehao, 2017. "Supply chain coordination with a single supplier and multiple retailers considering customer arrival times and route selection," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 106(C), pages 78-97.
    14. Lee, Chungmok & Han, Jinil, 2017. "Benders-and-Price approach for electric vehicle charging station location problem under probabilistic travel range," Transportation Research Part B: Methodological, Elsevier, vol. 106(C), pages 130-152.
    15. Nils Rudi & Sandeep Kapur & David F. Pyke, 2001. "A Two-Location Inventory Model with Transshipment and Local Decision Making," Management Science, INFORMS, vol. 47(12), pages 1668-1680, December.
    16. M. Jenabi & S. M. T. Fatemi Ghomi & S. A. Torabi & Moeen Sammak Jalali, 2022. "An accelerated Benders decomposition algorithm for stochastic power system expansion planning using sample average approximation," OPSEARCH, Springer;Operational Research Society of India, vol. 59(4), pages 1304-1336, December.
    17. Peiling Wu & Joseph C. Hartman & George R. Wilson, 2005. "An Integrated Model and Solution Approach for Fleet Sizing with Heterogeneous Assets," Transportation Science, INFORMS, vol. 39(1), pages 87-103, February.
    18. Eike Nohdurft & Elisa Long & Stefan Spinler, 2017. "Was Angelina Jolie Right? Optimizing Cancer Prevention Strategies Among BRCA Mutation Carriers," Decision Analysis, INFORMS, vol. 14(3), pages 139-169, September.
    19. Ogbe, Emmanuel & Li, Xiang, 2017. "A new cross decomposition method for stochastic mixed-integer linear programming," European Journal of Operational Research, Elsevier, vol. 256(2), pages 487-499.
    20. Elisangela Martins de Sá & Ivan Contreras & Jean-François Cordeau & Ricardo Saraiva de Camargo & Gilberto de Miranda, 2015. "The Hub Line Location Problem," Transportation Science, INFORMS, vol. 49(3), pages 500-518, August.

    More about this item

    Statistics

    Access and download statistics

    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:wly:navres:v:53:y:2006:i:8:p:822-841. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    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.