IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v23y1975i6p1120-1130.html
   My bibliography  Save this article

A Stochastic Sequential Allocation Model

Author

Listed:
  • C. Derman

    (Columbia University, New York, New York)

  • G. J. Lieberman

    (Stanford University, Stanford, California)

  • S. M. Ross

    (University of California, Berkeley, California)

Abstract

This paper considers the following model, described in terms of an investment problem. We have D units available for investment. During each of N time periods an opportunity to invest will occur with probability p . As soon as an opportunity presents itself, we must decide how much of our available resources to invest. If we invest y , then we obtain an expected profit P ( y ), where P is a nondecreasing continuous function. The amount y then becomes unavailable for future investment. The problem is to decide how much to invest at each opportunity so as to maximize total expected profit. When P ( y ) is a concave function, the structure of the optimal policy is obtained (§1). Bounds on the optimal value function and asymptotic results are presented in §2. A closed-form expression for the optimal value to invest is found in §3 for the special cases of P ( y ) = log y and P ( y ) = y α , for 0

Suggested Citation

  • C. Derman & G. J. Lieberman & S. M. Ross, 1975. "A Stochastic Sequential Allocation Model," Operations Research, INFORMS, vol. 23(6), pages 1120-1130, December.
    • Handle: RePEc:inm:oropre:v:23:y:1975:i:6:p:1120-1130
    DOI: 10.1287/opre.23.6.1120
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.23.6.1120
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.23.6.1120?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
    ---><---

    Citations

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


    Cited by:

    1. David T. Wu & Sheldon M. Ross, 2015. "A stochastic assignment problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 62(1), pages 23-31, February.
    2. Arash Khatibi & Golshid Baharian & Banafsheh Behzad & Sheldon Jacobson, 2015. "Extensions of the sequential stochastic assignment problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 82(3), pages 317-340, December.
    3. Xuhan Tian & Junmin (Jim) Shi & Xiangtong Qi, 2022. "Stochastic Sequential Allocations for Creative Crowdsourcing," Production and Operations Management, Production and Operations Management Society, vol. 31(2), pages 697-714, February.
    4. Richard Weber, 2013. "ABCs of the bomber problem and its relatives," Annals of Operations Research, Springer, vol. 208(1), pages 187-208, September.
    5. Michael Katehakis & Ingram Olkin & Sheldon Ross & Jian Yang, 2013. "On the life and work of Cyrus Derman," Annals of Operations Research, Springer, vol. 208(1), pages 5-26, September.
    6. Alexander G. Nikolaev & Sheldon H. Jacobson, 2010. "Technical Note ---Stochastic Sequential Decision-Making with a Random Number of Jobs," Operations Research, INFORMS, vol. 58(4-part-1), pages 1023-1027, August.
    7. Yuanzheng Ma & Tong Wang & Huan Zheng, 2023. "On fairness and efficiency in nonprofit operations: Dynamic resource allocations," Production and Operations Management, Production and Operations Management Society, vol. 32(6), pages 1778-1792, June.
    8. 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.
    9. Shantanu Bhattacharya & Vibha Gaba & Sameer Hasija, 2015. "A Comparison of Milestone-Based and Buyout Options Contracts for Coordinating R&D Partnerships," Management Science, INFORMS, vol. 61(5), pages 963-978, May.
    10. Batabyal, Amitrajeet A., 1998. "Land development and preservation over time and under uncertainty: a review and a research agenda," Ecological Economics, Elsevier, vol. 25(3), pages 233-238, June.

    More about this item

    Statistics

    Access and download statistics

    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:23:y:1975:i:6:p:1120-1130. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.