IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v59y2011i4p866-881.html
   My bibliography  Save this article

Managing a Noncooperative Supply Chain with Limited Capacity

Author

Listed:
  • Rodney P. Parker

    (The University of Chicago, Chicago, Illinois 60637)

  • Roman Kapuściński

    (The University of Michigan, Ann Arbor, Michigan 48109)

Abstract

We consider a two-stage serial supply chain with capacity limits, where each installation is operated by managers attempting to minimize their own costs. A multiple-period model is necessitated by the multiple stages, capacity limits, stochastic demand, and the explicit consideration of inventories. With appropriate salvage value functions, a Markov equilibrium policy is found. Intuitive profit dominance allows for existence of a unique equilibrium solution, which is shown to be a modified echelon base-stock policy. This equilibrium policy structure is sustained in the infinite horizon. A numerical study compares the behavior of the decentralized system with the first-best integrated capacitated system. The performance of this decentralized system relative to the integrated system across other parameters can be very good over a broad range of values. This implies that an acceptable system performance may be attained without the imposition of a contract or other coordinating mechanism, which themselves may encounter difficulties in implementation in the form of negotiation, execution, or enforcement of these agreements. We find instances where tighter capacities may actually enhance channel efficiency. We also examine the effect of capacity utilization on the system suboptimality.

Suggested Citation

  • Rodney P. Parker & Roman Kapuściński, 2011. "Managing a Noncooperative Supply Chain with Limited Capacity," Operations Research, INFORMS, vol. 59(4), pages 866-881, August.
    • Handle: RePEc:inm:oropre:v:59:y:2011:i:4:p:866-881
    DOI: 10.1287/opre.1110.0927
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.1110.0927
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.1110.0927?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. Evan L. Porteus, 2000. "Responsibility Tokens in Supply Chain Management," Manufacturing & Service Operations Management, INFORMS, vol. 2(2), pages 203-219, October.
    2. 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.
    3. Drew Fudenberg & David Levine, 2008. "Subgame–Perfect Equilibria of Finite– and Infinite–Horizon Games," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 1, pages 3-20, World Scientific Publishing Co. Pte. Ltd..
    4. Ganesh Janakiraman & John A. Muckstadt, 2009. "A Decomposition Approach for a Class of Capacitated Serial Systems," Operations Research, INFORMS, vol. 57(6), pages 1384-1393, December.
    5. Fangruo Chen, 1999. "Decentralized Supply Chains Subject to Information Delays," Management Science, INFORMS, vol. 45(8), pages 1076-1090, August.
    6. Kirman, Alan P & Sobel, Matthew J, 1974. "Dynamic Oligopoly with Inventories," Econometrica, Econometric Society, vol. 42(2), pages 279-287, March.
    7. A. Federgruen & P. Zipkin, 1986. "An Inventory Model with Limited Production Capacity and Uncertain Demands II. The Discounted-Cost Criterion," Mathematics of Operations Research, INFORMS, vol. 11(2), pages 208-215, May.
    8. Gérard P. Cachon & Paul H. Zipkin, 1999. "Competitive and Cooperative Inventory Policies in a Two-Stage Supply Chain," Management Science, INFORMS, vol. 45(7), pages 936-953, July.
    9. Paul Glasserman & Sridhar Tayur, 1994. "The Stability of a Capacitated, Multi-Echelon Production-Inventory System Under a Base-Stock Policy," Operations Research, INFORMS, vol. 42(5), pages 913-925, October.
    10. Barry Alan Pasternack, 1985. "Optimal Pricing and Return Policies for Perishable Commodities," Marketing Science, INFORMS, vol. 4(2), pages 166-176.
    11. Joseph Hall & Evan Porteus, 2000. "Customer Service Competition in Capacitated Systems," Manufacturing & Service Operations Management, INFORMS, vol. 2(2), pages 144-165, November.
    12. A. Federgruen & P. Zipkin, 1986. "An Inventory Model with Limited Production Capacity and Uncertain Demands I. The Average-Cost Criterion," Mathematics of Operations Research, INFORMS, vol. 11(2), pages 193-207, May.
    13. Tava Lennon Olsen & Rodney P. Parker, 2008. "Inventory Management Under Market Size Dynamics," Management Science, INFORMS, vol. 54(10), pages 1805-1821, October.
    14. Karen L. Donohue, 2000. "Efficient Supply Contracts for Fashion Goods with Forecast Updating and Two Production Modes," Management Science, INFORMS, vol. 46(11), pages 1397-1411, November.
    15. Awi Federgruen & Paul Zipkin, 1984. "Computational Issues in an Infinite-Horizon, Multiechelon Inventory Model," Operations Research, INFORMS, vol. 32(4), pages 818-836, August.
    16. Roman Kapuściński & Sridhar Tayur, 1998. "A Capacitated Production-Inventory Model with Periodic Demand," Operations Research, INFORMS, vol. 46(6), pages 899-911, December.
    17. Maskin, Eric & Tirole, Jean, 2001. "Markov Perfect Equilibrium: I. Observable Actions," Journal of Economic Theory, Elsevier, vol. 100(2), pages 191-219, October.
    18. Steven A. Lippman & Kevin F. McCardle, 1997. "The Competitive Newsboy," Operations Research, INFORMS, vol. 45(1), pages 54-65, February.
    19. Rodney P. Parker & Roman Kapuscinski, 2004. "Optimal Policies for a Capacitated Two-Echelon Inventory System," Operations Research, INFORMS, vol. 52(5), pages 739-755, October.
    20. Mahmut Parlar, 1988. "Game theoretic analysis of the substitutable product inventory problem with random demands," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(3), pages 397-409, June.
    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. Tuni, Andrea & Rentizelas, Athanasios, 2019. "An innovative eco-intensity based method for assessing extended supply chain environmental sustainability," International Journal of Production Economics, Elsevier, vol. 217(C), pages 126-142.
    2. Fiestras-Janeiro, M.G. & García-Jurado, I. & Meca, A. & Mosquera, M.A., 2015. "Cooperation on capacitated inventory situations with fixed holding costs," European Journal of Operational Research, Elsevier, vol. 241(3), pages 719-726.
    3. Nie, Jiajia & Xu, Xiaoxuan & Yue, Xiaohang & Guo, Qiang & Zhou, Yu, 2023. "Less is more: A strategic analysis of 3D printing with limited capacity," International Journal of Production Economics, Elsevier, vol. 258(C).
    4. Meng, Mingyou & Deng, Shiming & Zhou, Pin & Xu, He, 2023. "The effects of subsidy programs in byproduct synergy operations," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 175(C).

    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. Woonghee Tim Huh & Ganesh Janakiraman & Mahesh Nagarajan, 2016. "Capacitated Multiechelon Inventory Systems: Policies and Bounds," Manufacturing & Service Operations Management, INFORMS, vol. 18(4), pages 570-584, October.
    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. Qingkai Ji & Lijun Sun & Xiangpei Hu & Jing Hou, 2016. "Optimal policies of a two-echelon serial inventory system with general limited capacities," International Journal of Production Research, Taylor & Francis Journals, vol. 54(20), pages 6142-6155, October.
    4. Gavirneni, Srinagesh, 2006. "Price fluctuations, information sharing, and supply chain performance," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1651-1663, November.
    5. Rodney P. Parker & Roman Kapuscinski, 2004. "Optimal Policies for a Capacitated Two-Echelon Inventory System," Operations Research, INFORMS, vol. 52(5), pages 739-755, October.
    6. Tava Lennon Olsen & Rodney P. Parker, 2014. "On Markov Equilibria in Dynamic Inventory Competition," Operations Research, INFORMS, vol. 62(2), pages 332-344, April.
    7. Ioannis Ch. Paschalidis & Yong Liu, 2003. "Large Deviations-Based Asymptotics for Inventory Control in Supply Chains," Operations Research, INFORMS, vol. 51(3), pages 437-460, June.
    8. Jordan Tong & Gregory DeCroix & Jing-Sheng Song, 2020. "Modeling Payment Timing in Multiechelon Inventory Systems with Applications to Supply Chain Coordination," Manufacturing & Service Operations Management, INFORMS, vol. 22(2), pages 346-363, March.
    9. Jian Yang & Zhaoqiong Qin, 2007. "Capacitated Production Control with Virtual Lateral Transshipments," Operations Research, INFORMS, vol. 55(6), pages 1104-1119, December.
    10. Wang, Xun & Disney, Stephen M. & Ponte, Borja, 2023. "On the stationary stochastic response of an order-constrained inventory system," European Journal of Operational Research, Elsevier, vol. 304(2), pages 543-557.
    11. Shi Chen & Hau Lee & Kamran Moinzadeh, 2016. "Supply Chain Coordination with Multiple Shipments: The Optimal Inventory Subsidizing Contracts," Operations Research, INFORMS, vol. 64(6), pages 1320-1337, December.
    12. Woonghee Tim Huh & Ganesh Janakiraman & Mahesh Nagarajan, 2010. "Technical Note ---Capacitated Serial Inventory Systems: Sample Path and Stability Properties Under Base-Stock Policies," Operations Research, INFORMS, vol. 58(4-part-1), pages 1017-1022, August.
    13. Leng, Mingming & Zhu, An, 2009. "Side-payment contracts in two-person nonzero-sum supply chain games: Review, discussion and applications," European Journal of Operational Research, Elsevier, vol. 196(2), pages 600-618, July.
    14. Saif Benjaafar & David Chen & Rowan Wang, 2017. "Managing Production-Inventory Systems with Scarce Resources," Manufacturing & Service Operations Management, INFORMS, vol. 19(2), pages 216-229, May.
    15. Fernando Bernstein & Gregory A. DeCroix, 2006. "Inventory Policies in a Decentralized Assembly System," Operations Research, INFORMS, vol. 54(2), pages 324-336, April.
    16. Felipe Caro & Victor Martínez-de-Albéniz, 2010. "The Impact of Quick Response in Inventory-Based Competition," Manufacturing & Service Operations Management, INFORMS, vol. 12(3), pages 409-429, January.
    17. Kevin H. Shang & Jing-Sheng Song & Paul H. Zipkin, 2009. "Coordination Mechanisms in Decentralized Serial Inventory Systems with Batch Ordering," Management Science, INFORMS, vol. 55(4), pages 685-695, April.
    18. Gérard P. Cachon & Paul H. Zipkin, 1999. "Competitive and Cooperative Inventory Policies in a Two-Stage Supply Chain," Management Science, INFORMS, vol. 45(7), pages 936-953, July.
    19. Xinxin Hu & Izak Duenyas & Roman Kapuscinski, 2008. "Optimal Joint Inventory and Transshipment Control Under Uncertain Capacity," Operations Research, INFORMS, vol. 56(4), pages 881-897, August.
    20. Han Zhu, 2022. "A simple heuristic policy for stochastic inventory systems with both minimum and maximum order quantity requirements," Annals of Operations Research, Springer, vol. 309(1), pages 347-363, 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:inm:oropre:v:59:y:2011:i:4:p:866-881. 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.