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 transplantation and allocation policy attempts to balance allocation likelihood and geographic proximity by allocating cadaveric livers hierarchically. In this paper, we consider the problem of maximizing the efficiency of intra-regional transplants through the design of liver harvesting regions. We formulate the problem as a set partitioning problem that clusters organ procurement organizations (OPOs) into regions. We define the estimate of viability-adjusted transplant quantity to capture the tradeoff 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. As the optimal solution depends on the initial 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 design and the efficacy of our solution approach. Our test instances are generated based on real clinical data. These instances can be solved within a reasonable amount of time and the resulting region designs yield an improvement equivalent of over 130 transplants a year.