A Time-dependent Stopping Problem with Application to Live Organ Transplants

Israel David and Uri Yechiali
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Israel David: Tel Aviv University, Tel Aviv, Israel
Uri Yechiali: Tel Aviv University, Tel Aviv, Israel

Operations Research, 1985, vol. 33, issue 3, 491-504

Abstract: We consider a time-dependent stopping problem and its application to the decision-making process associated with transplanting a live organ. “Offers” (e.g., kidneys for transplant) become available from time to time. The values of the offers constitute a sequence of independent identically distributed positive random variables. When an offer arrives, a decision is made whether to accept it. If it is accepted, the process terminates. Otherwise, the offer is lost and the process continues until the next arrival, or until a moment when the process terminates by itself. Self-termination depends on an underlying lifetime distribution (which in the application corresponds to that of the candidate for a transplant). When the underlying process has an increasing failure rate, and the arrivals form a renewal process, we show that the control-limit type policy that maximizes the expected reward is a nonincreasing function of time. For non-homogeneous Poisson arrivals, we derive a first-order differential equation for the control-limit function. This equation is explicitly solved for the case of discrete-valued offers, homogeneous Poisson arrivals, and Gamma distributed lifetime. We use the solution to analyze a detailed numerical example based on actual kidney transplant data.

Keywords: 271 decision analysis related to live organ transplants; 570 time-dependent optimal stopping (search for similar items in EconPapers)
Date: 1985
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