Maximizing the Efficiency of the U.S. Liver Allocation System Through Region Design

Cadaveric liver transplantation is the only viable therapy for end-stage liver disease patients without a living donor. However, this type of transplantation is hindered in the United States by donor scarcity and rapid viability decay. Given these difficulties, the current U.S. liver allocation policy balances allocation likelihood and geographic proximity by allocating cadaveric livers hierarchically. We consider the problem of maximizing the efficiency of intraregional transplants through the redesign of liver allocation regions. We formulate the problem as a set partitioning problem that clusters organ procurement organizations into regions. We develop an estimate of viability-adjusted intraregional transplants to capture the trade-off between large and small regions. We utilize branch and price because the set partitioning formulation includes too many potential regions to handle explicitly. We formulate the pricing problem as a mixed-integer program and design a geographic-decomposition heuristic to generate promising columns quickly. Because the optimal solution depends on the design of geographic decomposition, we develop an iterative procedure that integrates branch and price with local search to alleviate this dependency. Finally, we present computational studies that show the benefit of region redesign and the efficacy of our solution approach. Our carefully calibrated test instances can be solved within a reasonable amount of time, and the resulting region designs yield a noticeable improvement over the current configuration.