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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
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    Cited by:

    1. 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.
    2. 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.
    3. Richard Weber, 2013. "ABCs of the bomber problem and its relatives," Annals of Operations Research, Springer, vol. 208(1), pages 187-208, September.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    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.

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