IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v196y2009i2p526-533.html
   My bibliography  Save this article

Analysis of supply contracts with quantity flexibility

Author

Listed:
  • Lian, Zhaotong
  • Deshmukh, Abhijit

Abstract

This paper explores a class of supply contracts under which a buyer receives discounts for committing to purchases in advance. The further in advance the commitment is made, the larger the discount. As time rolls forward, the buyer can increase the order quantities for future periods of the rolling horizon based on updated demand forecast information and inventory status. However, the buyer pays a higher per-unit cost for the incremental units. Such contracts are used by automobile and contract manufacturers, and are quite common in fuel oil and natural gas delivery markets. We develop a finite-horizon dynamic programming model to characterize the structure of the optimal replenishment strategy for the buyer. We present heuristic approaches to calculate the order volume in each period of the rolling horizon. Finally, we numerically evaluate the heuristic approaches and draw some managerial insights based on the findings.

Suggested Citation

  • Lian, Zhaotong & Deshmukh, Abhijit, 2009. "Analysis of supply contracts with quantity flexibility," European Journal of Operational Research, Elsevier, vol. 196(2), pages 526-533, July.
    • Handle: RePEc:eee:ejores:v:196:y:2009:i:2:p:526-533
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(08)00347-0
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Andy A. Tsay, 1999. "The Quantity Flexibility Contract and Supplier-Customer Incentives," Management Science, INFORMS, vol. 45(10), pages 1339-1358, October.
    2. James Flynn & Stanley Garstka, 1990. "A Dynamic Inventory Model with Periodic Auditing," Operations Research, INFORMS, vol. 38(6), pages 1089-1103, December.
    3. Mordechai Henig & Yigal Gerchak & Ricardo Ernst & David F. Pyke, 1997. "An Inventory Model Embedded in Designing a Supply Contract," Management Science, INFORMS, vol. 43(2), pages 184-189, February.
    4. A. A. Tsay & W. S. Lovejoy, 1999. "Quantity Flexibility Contracts and Supply Chain Performance," Manufacturing & Service Operations Management, INFORMS, vol. 1(2), pages 89-111.
    5. Suresh Chand & Vernon Ning Hsu & Suresh Sethi, 2002. "Forecast, Solution, and Rolling Horizons in Operations Management Problems: A Classified Bibliography," Manufacturing & Service Operations Management, INFORMS, vol. 4(1), pages 25-43, September.
    6. Lian, Zhaotong & Deshmukh, Abhijit & Wang, Jin, 2006. "The optimal frozen period in a dynamic production model," International Journal of Production Economics, Elsevier, vol. 103(2), pages 648-655, October.
    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. Zhaotong Lian & Liming Liu & Stuart X. Zhu, 2010. "Rolling‐horizon replenishment: Policies and performance analysis," Naval Research Logistics (NRL), John Wiley & Sons, vol. 57(6), pages 489-502, September.
    2. Chifeng Dai, 2022. "Optimal risk sharing with ex post private information: Rules versus discretion," Southern Economic Journal, John Wiley & Sons, vol. 89(1), pages 160-184, July.
    3. Wang, Yulan & Zipkin, Paul, 2009. "Agents' incentives under buy-back contracts in a two-stage supply chain," International Journal of Production Economics, Elsevier, vol. 120(2), pages 525-539, August.
    4. Cai, Wenbo & Abdel-Malek, Layek & Hoseini, Babak & Rajaei Dehkordi, Sharareh, 2015. "Impact of flexible contracts on the performance of both retailer and supplier," International Journal of Production Economics, Elsevier, vol. 170(PB), pages 429-444.
    5. Bo He & Yange Yang, 2018. "Mitigating supply risk: an approach with quantity flexibility procurement," Annals of Operations Research, Springer, vol. 271(2), pages 599-617, December.
    6. Zhou, Yong-Wu, 2009. "Two-echelon supply chain coordination through the unified number of annual orders," International Journal of Production Economics, Elsevier, vol. 117(1), pages 162-173, January.
    7. Sandun C. Perera & Suresh P. Sethi, 2023. "A survey of stochastic inventory models with fixed costs: Optimality of (s, S) and (s, S)‐type policies—Discrete‐time case," Production and Operations Management, Production and Operations Management Society, vol. 32(1), pages 131-153, January.
    8. Sainathan, Arvind & Groenevelt, Harry, 2019. "Vendor managed inventory contracts – coordinating the supply chain while looking from the vendor’s perspective," European Journal of Operational Research, Elsevier, vol. 272(1), pages 249-260.
    9. Zhu, Stuart X., 2012. "Joint pricing and inventory replenishment decisions with returns and expediting," European Journal of Operational Research, Elsevier, vol. 216(1), pages 105-112.
    10. Bicer, Isik & Hagspiel, Verena, 2016. "Valuing quantity flexibility under supply chain disintermediation risk," International Journal of Production Economics, Elsevier, vol. 180(C), pages 1-15.
    11. Xiaole Wu & Panos Kouvelis & Hirofumi Matsuo, 2013. "Horizontal Capacity Coordination for Risk Management and Flexibility: Pay Ex Ante or Commit a Fraction of Ex Post Demand?," Manufacturing & Service Operations Management, INFORMS, vol. 15(3), pages 458-472, July.
    12. Frascatore, Mark R. & Mahmoodi, Farzad, 2008. "Long-term and penalty contracts in a two-stage supply chain with stochastic demand," European Journal of Operational Research, Elsevier, vol. 184(1), pages 147-156, January.
    13. Dawn Barnes-Schuster & Yehuda Bassok & Ravi Anupindi, 2002. "Coordination and Flexibility in Supply Contracts with Options," Manufacturing & Service Operations Management, INFORMS, vol. 4(3), pages 171-207, May.
    14. Cvsa, Viswanath & Gilbert, Stephen M., 2002. "Strategic commitment versus postponement in a two-tier supply chain," European Journal of Operational Research, Elsevier, vol. 141(3), pages 526-543, September.
    15. repec:dgr:rugsom:03a25 is not listed on IDEAS
    16. Giannoccaro, Ilaria & Pontrandolfo, Pierpaolo, 2004. "Supply chain coordination by revenue sharing contracts," International Journal of Production Economics, Elsevier, vol. 89(2), pages 131-139, May.
    17. Flynn, James, 2008. "An effective heuristic for the review period in an inventory model with staggered deliveries and normal demands," European Journal of Operational Research, Elsevier, vol. 186(2), pages 671-680, April.
    18. Dubey, Vivek Kumar & Chavas, Jean-Paul & Veeramani, Dharmaraj, 2018. "Analytical framework for sustainable supply-chain contract management," International Journal of Production Economics, Elsevier, vol. 200(C), pages 240-261.
    19. DeYong, Gregory D. & Cattani, Kyle D., 2012. "Well adjusted: Using expediting and cancelation to manage store replenishment inventory for a seasonal good," European Journal of Operational Research, Elsevier, vol. 220(1), pages 93-105.
    20. Zhao, Yunpeng & Song, Jinbo & Feng, Zhuo & Jin, Lulu, 2023. "Incentive contracts with demand guarantee in BOT toll road projects," Research in Transportation Economics, Elsevier, vol. 98(C).
    21. Imdahl, Christina & Hoberg, Kai & Schmidt, William, 2025. "Applying fixed order commitment contracts in a capacitated supply chain," European Journal of Operational Research, Elsevier, vol. 320(2), pages 358-374.

    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:ejores:v:196:y:2009:i:2:p:526-533. 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/locate/eor .

    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.