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A generalized coupon collecting model as a parsimonious optimal stochastic assignment model

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  • Sheldon Ross
  • David Wu

Abstract

There is a given set of n boxes, numbered 1 thru n. Coupons are collected one at a time. Each coupon has a binary vector x 1 ,…,x n attached to it, with the interpretation being that the coupon is eligible to be put in box i if x i =1,i=1…,n. After a coupon is collected, it is put in a box for which it is eligible. Assuming the successive coupon vectors are independent and identically distributed from a specified joint distribution, the initial problem of interest is to decide where to put successive coupons so as to stochastically minimize N, the number of coupons needed until all boxes have at least one coupon. When the coupon vector X 1 ,…,X n is a vector of independent random variables, we show, if P(X i =1) is nondecreasing in i, that the policy π that always puts an arriving coupon in the smallest numbered empty box for which it is eligible is optimal. Efficient simulation procedures for estimating P π (N>r) and E π [N] are presented; and analytic bounds are determined in the independent case. We also consider the problem where rearrangements are allowed. Copyright Springer Science+Business Media, LLC 2013

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  • 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.
    • Handle: RePEc:spr:annopr:v:208:y:2013:i:1:p:133-146:10.1007/s10479-012-1086-5
    DOI: 10.1007/s10479-012-1086-5
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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.
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    Cited by:

    1. 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.
    2. Sheldon M. Ross & Gideon Weiss & Zhengyu Zhang, 2021. "Technical Note—A Stochastic Assignment Problem with Unknown Eligibility Probabilities," Operations Research, INFORMS, vol. 69(1), pages 266-272, January.

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