IDEAS home Printed from
   My bibliography  Save this article

Adjustment Strategies for a Fixed Delivery Contract


  • Kamran Moinzadeh

    () (University of Washington, Seattle, Washington 98195)

  • Steven Nahmias

    () (Santa Clara University, Santa Clara, California 95053)


We consider a long term contractual agreement between buyer and seller in which Q units are delivered to the buyer at regular time intervals. It must be true that the delivery quantity, Q , is less than the mean demand per period. In order to manage the inventory, the buyer has the option of adjusting the delivery quantity upwards just prior to a delivery, but must pay a premium to do so. Demand is assumed random, and we model the system in a continuous review setting. We show that the equations one must solve to find optimal adjustment strategies are intractable. A diffusion approximation is developed which when coupled with the solution to an even simpler deterministic version of the problem yields very simple but effective approximations. Extensive computations are included to compare the performance of the optimal and approximate policies. We also empirically derive a formula for computing Q whose accuracy is established computationally. We prove that the fixed delivery contract results in lower variance of orders to the seller. We also include a computational study to find the unit cost discount that equalizes the expected costs for the fixed delivery contract and the base stock contract for a large parameter set.

Suggested Citation

  • Kamran Moinzadeh & Steven Nahmias, 2000. "Adjustment Strategies for a Fixed Delivery Contract," Operations Research, INFORMS, vol. 48(3), pages 408-423, June.
  • Handle: RePEc:inm:oropre:v:48:y:2000:i:3:p:408-423
    DOI: 10.1287/opre.48.3.408.12435

    Download full text from publisher

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. Kamran Moinzadeh & Steven Nahmias, 1988. "A Continuous Review Model for an Inventory System with Two Supply Modes," Management Science, INFORMS, vol. 34(6), pages 761-773, June.
    2. Yigal Gerchak & Mahmut Parlar, 1990. "Yield randomness, cost tradeoffs, and diversification in the EOQ model," Naval Research Logistics (NRL), John Wiley & Sons, vol. 37(3), pages 341-354, June.
    3. Kamran Moinzadeh & Hau L. Lee, 1989. "Approximate Order Quantities and Reorder Points for Inventory Systems Where Orders Arrive in Two Shipments," Operations Research, INFORMS, vol. 37(2), pages 277-287, April.
    4. Ravi Anupindi & Ram Akella, 1993. "Diversification Under Supply Uncertainty," Management Science, INFORMS, vol. 39(8), pages 944-963, August.
    5. Hau L. Lee & V. Padmanabhan & Seungjin Whang, 1997. "Information Distortion in a Supply Chain: The Bullwhip Effect," Management Science, INFORMS, vol. 43(4), pages 546-558, April.
    6. Andy A. Tsay, 1999. "The Quantity Flexibility Contract and Supplier-Customer Incentives," Management Science, INFORMS, vol. 45(10), pages 1339-1358, October.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Jong Soo Kim & K Y Shin & S E Ahn, 2003. "A multiple replenishment contract with ARIMA demand processes," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(11), pages 1189-1197, November.
    2. Xavier Brusset, 2005. "Comparison between minimum purchase, quantity flexibility contracts and spot procurement in a supply chain," Econometrics 0512007, University Library of Munich, Germany.
    3. Han, Xiaoya & Yu, Yugang & Hu, Guiping, 2019. "A dynamic newsvendor problem with goodwill-dependent demands and minimum commitment," Omega, Elsevier, vol. 89(C), pages 242-256.
    4. J S Kim & T C Kwak, 2007. "Game theoretic analysis of the bargaining process over a long-term replenishment contract," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(6), pages 769-778, June.
    5. Katia C. Frank & Rachel Q. Zhang & Izak Duenyas, 2003. "Optimal Policies for Inventory Systems with Priority Demand Classes," Operations Research, INFORMS, vol. 51(6), pages 993-1002, December.
    6. Zhao, Yingxue & Choi, Tsan-Ming & Cheng, T.C.E. & Wang, Shouyang, 2018. "Supply option contracts with spot market and demand information updating," European Journal of Operational Research, Elsevier, vol. 266(3), pages 1062-1071.
    7. Konstantaras, I. & Skouri, K. & Lagodimos, A.G., 2019. "EOQ with independent endogenous supply disruptions," Omega, Elsevier, vol. 83(C), pages 96-106.
    8. Xavier Brusset, 2005. "How information influences the cost of transport in a supply chain, a monte carlo simulation," Econometrics 0512008, University Library of Munich, Germany.
    9. Chen, Xu & Wan, Nana & Wang, Xiaojun, 2017. "Flexibility and coordination in a supply chain with bidirectional option contracts and service requirement," International Journal of Production Economics, Elsevier, vol. 193(C), pages 183-192.


    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:48:y:2000:i:3:p:408-423. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Matthew Walls). General contact details of provider: .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.