IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v53y2007i1p78-87.html
   My bibliography  Save this article

Shipment Consolidation: Who Pays for It and How Much?

Author

Listed:
  • Moshe Dror

    (Management Information Systems Department, Eller College of Management, University of Arizona, Tucson, Arizona 85721)

  • Bruce C. Hartman

    (Department of Business Administration, California State University-Maritime, Vallejo, California 94590 and Department of Management and Finance, College of Business and Economics, California State University-East Bay, Hayward, California 94542)

Abstract

This paper examines the subject of cost allocation in a multiple product inventory system, allowing for consolidation of shipments. If we order multiple items using an economic order quantity (EOQ) policy, and consolidate shipments, part of the ordering cost is shared, and part is specific to each item; we want to find the consolidation choice with optimal total cost and divide the cost fairly among the individual items. Such a fair division is central to a costing system in which no group of items subsidizes the others; there are no free riders! We use a cooperative inventory game to determine when this can be done. This game is usually not concave, so we want to know what consolidation combinations determine when this cost can be fairly divided, using the core of the game. We prove that consolidation of all the items is cheaper exactly if there are fair cost allocations (core of the game is not empty), which happens when the portion of the ordering cost common to all items is not too small. We further show how sensitive the nonempty core result is to adjustments in the cost parameters and show how to determine a threshold value for the shared ordering cost, which assures the existence of a fair cost allocation.

Suggested Citation

  • Moshe Dror & Bruce C. Hartman, 2007. "Shipment Consolidation: Who Pays for It and How Much?," Management Science, INFORMS, vol. 53(1), pages 78-87, January.
    • Handle: RePEc:inm:ormnsc:v:53:y:2007:i:1:p:78-87
    DOI: 10.1287/mnsc.1060.0607
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.1060.0607
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.1060.0607?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. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. 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.
    3. 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.
    4. Robin O. Roundy, 1990. "Computing Nested Reorder Intervals for Multi-Item Distribution Systems," Operations Research, INFORMS, vol. 38(1), pages 37-52, February.
    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. M Dror & B C Hartman, 2011. "Survey of cooperative inventory games and extensions," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(4), pages 565-580, April.
    2. Dror, Moshe & Hartman, Bruce C. & Chang, Wei, 2012. "The cost allocation issue in joint replenishment," International Journal of Production Economics, Elsevier, vol. 135(1), pages 242-254.
    3. 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.
    4. Guardiola, Luis A. & Meca, Ana & Puerto, Justo, 2009. "Production-inventory games: A new class of totally balanced combinatorial optimization games," Games and Economic Behavior, Elsevier, vol. 65(1), pages 205-219, January.
    5. Yea, Minyoung & Kim, Daeki & Cheong, Taesu & Moon, Joon & Kang, Sungho, 2022. "Baking and slicing the pie: An application to the airline alliance's profit-sharing based on cooperative game theory," Journal of Air Transport Management, Elsevier, vol. 102(C).
    6. Drechsel, J. & Kimms, A., 2010. "Computing core allocations in cooperative games with an application to cooperative procurement," International Journal of Production Economics, Elsevier, vol. 128(1), pages 310-321, November.
    7. Nagarajan, Mahesh & Sosic, Greys, 2008. "Game-theoretic analysis of cooperation among supply chain agents: Review and extensions," European Journal of Operational Research, Elsevier, vol. 187(3), pages 719-745, June.
    8. 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.
    9. J. Drechsel & A. Kimms, 2010. "The subcoalition-perfect core of cooperative games," Annals of Operations Research, Springer, vol. 181(1), pages 591-601, December.
    10. 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).
    11. Xin Chen & Jiawei Zhang, 2009. "A Stochastic Programming Duality Approach to Inventory Centralization Games," Operations Research, INFORMS, vol. 57(4), pages 840-851, August.
    12. Montrucchio, Luigi & Scarsini, Marco, 2007. "Large newsvendor games," Games and Economic Behavior, Elsevier, vol. 58(2), pages 316-337, February.
    13. 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.
    14. Shoshana Anily & Moshe Haviv, 2010. "Cooperation in Service Systems," Operations Research, INFORMS, vol. 58(3), pages 660-673, June.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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).
    20. 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.

    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:inm:ormnsc:v:53:y:2007:i:1:p:78-87. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.