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A stochastic assignment problem

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  • David T. Wu
  • Sheldon M. Ross

Abstract

There are n boxes with box i having a quota value m i , i = 1 … n . Balls arrive sequentially, with each ball having a binary vector X = ( X 1 , X 2 , … , X n ) attached to it, with the interpretation being that if Xi = 1 then that ball is eligible to be put in box i. A ball's vector is revealed when it arrives and the ball can be put in any alive box for which it is eligible, where a box is said to be alive if it has not yet met its quota. Assuming that the components of a vector are independent, we are interested in the policy that minimizes, either stochastically or in expectation, the number of balls that need arrive until all boxes have met their quotas. © 2014 Wiley Periodicals, Inc. 62:23–31, 2015

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:62:y:2015:i:1:p:23-31
    DOI: 10.1002/nav.21611
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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. Stefanos A. Zenios & Glenn M. Chertow & Lawrence M. Wein, 2000. "Dynamic Allocation of Kidneys to Candidates on the Transplant Waiting List," Operations Research, INFORMS, vol. 48(4), pages 549-569, August.
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    4. Sheldon Ross & David Wu, 2013. "A generalized coupon collecting model as a parsimonious optimal stochastic assignment model," Annals of Operations Research, Springer, vol. 208(1), pages 133-146, September.
    5. 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.
    6. 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.
    7. Chris Albright & Cyrus Derman, 1972. "Asymptotic Optimal Policies for the Stochastic Sequential Assignment Problem," Management Science, INFORMS, vol. 19(1), pages 46-51, September.
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    11. Anton J. Kleywegt & Jason D. Papastavrou, 2001. "The Dynamic and Stochastic Knapsack Problem with Random Sized Items," Operations Research, INFORMS, vol. 49(1), pages 26-41, February.
    12. 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.
    13. D. P. Kennedy, 1986. "Optimal Sequential Assignment," Mathematics of Operations Research, INFORMS, vol. 11(4), pages 619-626, November.
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