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Sequential Assignment Match Processes with Arrivals of Candidates and Offers

Published online by Cambridge University Press:  27 July 2009

Israel David  and
Uri Yechiali
Israel David
Affiliation:
Department of Mathematics and Computer ScienceBen-Gurion University of the Negev, Beer-Sheva 84105, Israel
Uri Yechiali
Affiliation:
Department of Statistics The Raymond and Beverley Sackler Faculty of Exact SciencesTel Aviv University, Tel Aviv 69978, Israel
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Abstract

An infinite random stream of ordered pairs arrives sequentially in discrete time. A pair consists of a “candidate” and an “offer,” each of which is either of type I (with probability p) or of type II (with probability q = 1 – p). Offers are to be assigned to candidates, yielding a reward R > 0 if they match in type, or a smaller reward 0 ≤ r ≤ R if not. An arriving candidate resides in the system until it is assigned, whereas an arriving offer is either assigned immediately to one of the waiting candidates or lost forever. We show that the optimal long-term average reward is R, independent of the population proportion p and the “second prize” r, and that the optimal average reward policy is to assign only a match. Optimal policies for discounted and finite horizon models are also derived.

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 4 , Issue 4 , October 1990 , pp. 413 - 430
Copyright
Copyright © Cambridge University Press 1990

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References

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