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Doubly Stochastic Sequential Assignment Problem

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  • Arash Khatibi
  • Sheldon H. Jacobson

Abstract

This article introduces the Doubly Stochastic Sequential Assignment Problem (DSSAP), an extension of the Sequential Stochastic Assignment Problem (SSAP), where sequentially arriving tasks are assigned to workers with random success rates. A given number of tasks arrive sequentially, each with a random value coming from a known distribution. On a task arrival, it must be assigned to one of the available workers, each with a random success rate coming from a known distribution. Optimal assignment policies are proposed for DSSAP under various assumptions on the random success rates. The optimal assignment algorithm for the general case of DSSAP, where workers have distinct success rate distribution, has an exponential running time. An approximation algorithm that achieves a fraction of the maximum total expected reward in a polynomial time is proposed. The results are illustrated by several numerical experiments. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 124–137, 2016

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:63:y:2016:i:2:p:124-137
    DOI: 10.1002/nav.21682
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    References listed on IDEAS

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    1. Arash Khatibi & Golshid Baharian & Estelle R. Kone & Sheldon H. Jacobson, 2014. "The sequential stochastic assignment problem with random success rates," IISE Transactions, Taylor & Francis Journals, vol. 46(11), pages 1169-1180, November.
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    3. Adrian Lee & Sheldon Jacobson, 2011. "Sequential stochastic assignment under uncertainty: estimation and convergence," Statistical Inference for Stochastic Processes, Springer, vol. 14(1), pages 21-46, February.
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    5. 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.
    6. S. Christian Albright, 1974. "Optimal Sequential Assignments with Random Arrival Times," Management Science, INFORMS, vol. 21(1), pages 60-67, September.
    7. 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.
    8. 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.
    9. Chris Albright & Cyrus Derman, 1972. "Asymptotic Optimal Policies for the Stochastic Sequential Assignment Problem," Management Science, INFORMS, vol. 19(1), pages 46-51, September.
    10. Toru Nakai, 1986. "A Sequential Stochastic Assignment Problem in a Partially Observable Markov Chain," Mathematics of Operations Research, INFORMS, vol. 11(2), pages 230-240, May.
    11. D. P. Kennedy, 1986. "Optimal Sequential Assignment," Mathematics of Operations Research, INFORMS, vol. 11(4), pages 619-626, November.
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