Cadaveric liver transplantation is the only viable therapeutic option for end-stage liver disease patients who have no living donors. However, this type of transplantation is hindered in the United States by donor scarcity and organ 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 talk, we mainly consider the problem of maximizing the intra-regional transplant efficiency through the design of organ distribution regions. We formulate the problem as a partitioning problem that clusters organ procurement organizations (OPOs) into regions. We propose an estimate of viability-adjusted transplant quantity to capture the tradeoff between large and small regions. Our partitioning formulation includes too many potential regions to handle explicitly, which leads us to a branch-and-price approach. The pricing problem is a nonlinear 0-1 program for which we provide a linear reformulation and design a decomposition heuristic to generate promising columns quickly. We present computational studies that show the benefit of region design and the efficacy of our branch-and-price approach. Our test instances are generated based on recent clinical data. Almost all instances can be solved within a reasonable amount of time and the resulting optimal designs indicate an average viability-adjusted increase of nearly 9% over the current regional configuration.  

In the reminder of the talk, I present issues and challenges in network configuration and policy design for the U.S. organ transplantation and allocation system. I will discuss some current work using simulation optimization and agent-based modeling and simulation.