IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v20y2018i3d10.1007_s11009-016-9522-7.html
   My bibliography  Save this article

A Central Limit Theorem for Costs in Bulinskaya’s Inventory Management Problem When Deliveries Face Delays

Author

Listed:
  • Alessandro Arlotto

    (Duke University)

  • J. Michael Steele

    (University of Pennsylvania)

Abstract

It is common in inventory theory to consider policies that minimize the expected cost of ordering and holding goods or materials. Nevertheless, the realized cost is a random variable, and, as the Saint Petersburg Paradox reminds us, the expected value does not always capture the full economic reality of a decision problem. Here we take the classic inventory model of Bulinskaya (Theory of Probability & Its Applications, 9, 3, 389–403, 1964), and, by proving an appropriate central limit theorem, we show in a reasonably rich (and practical) sense that the mean-optimal policies are economically appropriate. The motivation and the tools are applicable to a large class of Markov decision problems.

Suggested Citation

  • Alessandro Arlotto & J. Michael Steele, 2018. "A Central Limit Theorem for Costs in Bulinskaya’s Inventory Management Problem When Deliveries Face Delays," Methodology and Computing in Applied Probability, Springer, vol. 20(3), pages 839-854, September.
    • Handle: RePEc:spr:metcap:v:20:y:2018:i:3:d:10.1007_s11009-016-9522-7
    DOI: 10.1007/s11009-016-9522-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-016-9522-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-016-9522-7?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. Moshe Shaked & Miguel A. Sordo & Alfonso Suárez-Llorens, 2012. "Global Dependence Stochastic Orders," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 617-648, September.
    2. Alessandro Arlotto & Noah Gans & J. Michael Steele, 2014. "Markov Decision Problems Where Means Bound Variances," Operations Research, INFORMS, vol. 62(4), pages 864-875, August.
    3. Alessandro Arlotto & J. Michael Steele, 2016. "A Central Limit Theorem for Temporally Nonhomogenous Markov Chains with Applications to Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 41(4), pages 1448-1468, November.
    4. Alfred Müller, 1997. "How Does the Value Function of a Markov Decision Process Depend on the Transition Probabilities?," Mathematics of Operations Research, INFORMS, vol. 22(4), pages 872-885, November.
    5. James E. Smith & Kevin F. McCardle, 2002. "Structural Properties of Stochastic Dynamic Programs," Operations Research, INFORMS, vol. 50(5), pages 796-809, October.
    6. Muller, Alfred & Scarsini, Marco & Shaked, Moshe, 2002. "The Newsvendor Game Has a Nonempty Core," Games and Economic Behavior, Elsevier, vol. 38(1), pages 118-126, January.
    7. Colangelo, Antonio & Scarsini, Marco & Shaked, Moshe, 2005. "Some notions of multivariate positive dependence," Insurance: Mathematics and Economics, Elsevier, vol. 37(1), pages 13-26, August.
    8. Hartman, Bruce C. & Dror, Moshe & Shaked, Moshe, 2000. "Cores of Inventory Centralization Games," Games and Economic Behavior, Elsevier, vol. 31(1), pages 26-49, April.
    Full references (including those not matched with items on IDEAS)

    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. Ozen, U. & Slikker, M. & Norde, H.W., 2007. "A General Framework for Cooperation under Uncertainty," Discussion Paper 2007-57, Tilburg University, Center for Economic Research.
    2. J. Drechsel & A. Kimms, 2010. "The subcoalition-perfect core of cooperative games," Annals of Operations Research, Springer, vol. 181(1), pages 591-601, December.
    3. Flip Klijn & Marco Slikker, 2004. "Distribution Center Consolidation Games," UFAE and IAE Working Papers 602.04, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    4. Xin Chen & Jiawei Zhang, 2009. "A Stochastic Programming Duality Approach to Inventory Centralization Games," Operations Research, INFORMS, vol. 57(4), pages 840-851, August.
    5. Montrucchio, Luigi & Scarsini, Marco, 2007. "Large newsvendor games," Games and Economic Behavior, Elsevier, vol. 58(2), pages 316-337, February.
    6. Xuan Vinh Doan & Tri-Dung Nguyen, 2019. "Technical Note—Robust Newsvendor Games with Ambiguity in Demand Distributions," Operations Research, INFORMS, vol. 68(4), pages 1047-1062, July.
    7. Daniel R. Jiang & Warren B. Powell, 2015. "An Approximate Dynamic Programming Algorithm for Monotone Value Functions," Operations Research, INFORMS, vol. 63(6), pages 1489-1511, December.
    8. Shoshana Anily & Moshe Haviv, 2010. "Cooperation in Service Systems," Operations Research, INFORMS, vol. 58(3), pages 660-673, June.
    9. Ozen, U. & Fransoo, J. & Norde, H.W. & Slikker, M., 2004. "Cooperation between Multiple Newsvendors with Warehouses," Other publications TiSEM 92a91731-8bec-4c7b-a4bf-7, Tilburg University, School of Economics and Management.
    10. Özen, Ulas & Norde, Henk & Slikker, Marco, 2011. "On the convexity of newsvendor games," International Journal of Production Economics, Elsevier, vol. 133(1), pages 35-42, September.
    11. Peter Borm & Herbert Hamers & Ruud Hendrickx, 2001. "Operations research games: A survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(2), pages 139-199, December.
    12. Ana Meca, 2007. "A core-allocation family for generalized holding cost games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(3), pages 499-517, June.
    13. Karsten, Frank & Basten, Rob J.I., 2014. "Pooling of spare parts between multiple users: How to share the benefits?," European Journal of Operational Research, Elsevier, vol. 233(1), pages 94-104.
    14. Guardiola, Luis A. & Meca, Ana & Puerto, Justo, 2023. "Allocating the surplus induced by cooperation in distribution chains with multiple suppliers and retailers," Journal of Mathematical Economics, Elsevier, vol. 108(C).
    15. Li, Jun & Feng, Hairong & Zeng, Yinlian, 2014. "Inventory games with permissible delay in payments," European Journal of Operational Research, Elsevier, vol. 234(3), pages 694-700.
    16. Michel Beuthe, 2011. "Economics of Transport Logistics," Chapters, in: André de Palma & Robin Lindsey & Emile Quinet & Roger Vickerman (ed.), A Handbook of Transport Economics, chapter 11, Edward Elgar Publishing.
    17. 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.
    18. Özen, Ulaş & Sošić, Greys & Slikker, Marco, 2012. "A collaborative decentralized distribution system with demand forecast updates," European Journal of Operational Research, Elsevier, vol. 216(3), pages 573-583.
    19. Ozen, U. & Slikker, M. & Norde, H.W., 2007. "A General Framework for Cooperation under Uncertainty," Other publications TiSEM 1972d523-d611-4906-a7c1-a, Tilburg University, School of Economics and Management.
    20. M. Mosquera & I. García-Jurado & M. Fiestras-Janeiro, 2008. "A note on coalitional manipulation and centralized inventory management," Annals of Operations Research, Springer, vol. 158(1), pages 183-188, February.

    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:spr:metcap:v:20:y:2018:i:3:d:10.1007_s11009-016-9522-7. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.