Technical Note—A Stochastic Assignment Problem with Unknown Eligibility Probabilities

Sheldon M. Ross (), Gideon Weiss () and Zhengyu Zhang ()
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Sheldon M. Ross: Department of Industrial and Systems Engineering, Viterbi School of Engineering, University of Southern California, Los Angeles, California 90007
Gideon Weiss: Department of Statistics, University of Haifa, Haifa 3498838, Israel
Zhengyu Zhang: Department of Industrial and Systems Engineering, Viterbi School of Engineering, University of Southern California, Los Angeles, California 90007

Operations Research, 2021, vol. 69, issue 1, 266-272

Abstract: Consider n initially empty boxes, numbered 1 through n . Balls arrive sequentially. Each ball has a binary n -vector attached to it, with the interpretation that the ball is eligible to be put in box i if component i of its vector is equal to 1. An arriving ball can be put in any empty box for which it is eligible. Assuming that components of the vector are independent Bernoulli random variables with initially unknown probabilities, our primary interest is to compare several policies to determine which leads to a stochastically smaller number of observed balls until all boxes are filled.

Keywords: sequential assignment problem; probability; stochastic model application (search for similar items in EconPapers)
Date: 2021
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