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Limiting behavior of the stochastic sequential assignment problem

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  • Golshid Baharian
  • Sheldon H. Jacobson

Abstract

The stochastic sequential assignment problem (SSAP) considers how to allocate available distinct workers to sequentially arriving tasks with stochastic parameters such that the expected total reward obtained from the sequential assignments is maximized. Implementing the optimal assignment policy for the SSAP involves calculating a new set of breakpoints upon the arrival of each task (i.e., for every time period), which is impractical for large‐scale problems. This article studies two problems that are concerned with obtaining stationary policies, which achieve the optimal expected reward per task as the number of tasks approaches infinity. The first problem considers independent and identically distributed (IID) tasks with a known distribution function, whereas in the second problem tasks are derived from r different unobservable distributions governed by an ergodic Markov chain. The convergence rate of the expected reward per task to the optimal value is also obtained for both problems. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013

Suggested Citation

  • Golshid Baharian & Sheldon H. Jacobson, 2013. "Limiting behavior of the stochastic sequential assignment problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 60(4), pages 321-330, June.
    • Handle: RePEc:wly:navres:v:60:y:2013:i:4:p:321-330
    DOI: 10.1002/nav.21536
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    References listed on IDEAS

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    1. Cyrus Derman & Gerald J. Lieberman & Sheldon M. Ross, 1972. "A Sequential Stochastic Assignment Problem," Management Science, INFORMS, vol. 18(7), pages 349-355, March.
    2. Alexander G. Nikolaev & Sheldon H. Jacobson & Laura A. McLay, 2007. "A Sequential Stochastic Security System Design Problem for Aviation Security," Transportation Science, INFORMS, vol. 41(2), pages 182-194, May.
    3. S. Christian Albright, 1977. "A Bayesian Approach to a Generalized House Selling Problem," Management Science, INFORMS, vol. 24(4), pages 432-440, December.
    4. Xuanming Su & Stefanos A. Zenios, 2005. "Patient Choice in Kidney Allocation: A Sequential Stochastic Assignment Model," Operations Research, INFORMS, vol. 53(3), pages 443-455, June.
    5. S. Christian Albright, 1976. "A markov chain version of the secretary problem," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 23(1), pages 151-159, March.
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    Cited by:

    1. Arash Khatibi & Sheldon H. Jacobson, 2016. "Doubly Stochastic Sequential Assignment Problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(2), pages 124-137, March.

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