Technical Note—A Stochastic Assignment Problem with Unknown Eligibility Probabilities

Abstract

Consider [Formula: see text] initially empty boxes, numbered 1 through [Formula: see text]. Balls arrive sequentially. Each ball has a binary vector [Formula: see text] attached to it, with the interpretation that the ball is eligible to be put in box [Formula: see text] if [Formula: see text]. An arriving ball can be put in any empty box for which it is eligible. Assume that components of the vector are independent Bernoulli random variables with initially unknown probabilities [Formula: see text]. In “A Stochastic Assignment Problem with Unknown Eligible Probabilities,” Ross, Weiss, and Zhang discuss policies that aim at minimizing the number of balls needed until all boxes are filled. When full memory is allowed, the optimal policy is identified in the sense that it stochastically minimizes the number of balls taken. Two random policies are considered and compared when no memory is allowed. A reordering rule is proposed when one can only keep partial memory.