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A Sequential Stochastic Assignment Problem

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  • Cyrus Derman

    (Columbia University)

  • Gerald J. Lieberman

    (Stanford University)

  • Sheldon M. Ross

    (University of California, Berkeley)

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    Abstract

    Suppose there are n men available to perform n jobs. The n jobs occur in sequential order with the value of each job being a random variable X. Associated with each man is a probability p. If a "p" man is assigned to an "X = x" job, the (expected) reward is assumed to be given by px. After a man is assigned to a job, he is unavailable for future assignments. The paper is concerned with the optimal assignment of the n men to the n jobs, so as to maximize the total expected reward. The optimal policy is characterized, and a recursive equation is presented for obtaining the necessary constants of this optimal policy. In particular, if p 1 \leqq p 2 \leqq \cdots \leqq p n the optimal choice in the initial stage of an n stage assignment problem is to use p i if x falls into an ith nonoverlapping interval comprising the real line. These intervals depend on n and the CDF of X, but are independent of the p's. The optimal policy is also presented for the generalized assignment problem, i.e., the assignment problem where the (expected) reward if a "p" man is assigned to an "x" job is given by a function r(p, x).

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    Bibliographic Info

    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 18 (1972)
    Issue (Month): 7 (March)
    Pages: 349-355

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    Handle: RePEc:inm:ormnsc:v:18:y:1972:i:7:p:349-355

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    Cited by:
    1. Gershkov, Alex & Moldovanu, Benny, 2012. "Optimal search, learning and implementation," Journal of Economic Theory, Elsevier, vol. 147(3), pages 881-909.
    2. Pancs, Romans, 2013. "Sequential negotiations with costly information acquisition," Games and Economic Behavior, Elsevier, vol. 82(C), pages 522-543.
    3. Francis Bloch & Nicolas Houy, 2009. "Optimal Assignment of Durable Objects to Successive Agents," Working Papers hal-00435385, HAL.
    4. David, Israel & Levi, Ofer, 2004. "A new algorithm for the multi-item exponentially discounted optimal selection problem," European Journal of Operational Research, Elsevier, vol. 153(3), pages 782-789, March.
    5. David, Israel & Levi, Ofer, 2001. "Asset-selling problems with holding costs," International Journal of Production Economics, Elsevier, vol. 71(1-3), pages 317-321, May.
    6. Kang, Seungmo & Ouyang, Yanfeng, 2011. "The traveling purchaser problem with stochastic prices: Exact and approximate algorithms," European Journal of Operational Research, Elsevier, vol. 209(3), pages 265-272, March.
    7. Benny Moldovanu & Alex Gershkov, 2008. "The Trade-off Between Fast Learning and Dynamic Efficiency," 2008 Meeting Papers 348, Society for Economic Dynamics.
    8. Gershkov, Alex & Moldovanu, Benny, 2013. "Non-Bayesian optimal search and dynamic implementation," Economics Letters, Elsevier, vol. 118(1), pages 121-125.
    9. Hak Chun, Young, 1996. "Selecting the best choice in the weighted secretary problem," European Journal of Operational Research, Elsevier, vol. 92(1), pages 135-147, July.

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