An Exact Method for Balancing Efficiency and Equity in the Liver Allocation Hierarchy

We study the problem of (re)designing the regional network by which cadaveric livers are allocated. Whereas prior research focused mainly on maximizing a measure of efficiency of the network that was based on aggregate patient survival, we explicitly account for the trade-off between efficiency and a measure of geographical equity in the allocation process. To this end, we extend earlier optimization models to incorporate both objectives and develop an exact branch-and-price approach to solve this problem, generalizing a solution approach studied for the case where only efficiency is taken into account. In addition, we propose an effective solution algorithm that approximates the (generally nonconcave) frontier of Pareto-efficient solutions with respect to the two objectives by simultaneously generating and successively improving upper and lower bounds on this frontier. We implement and test our approach on observed data and show that solutions significantly dominating the current configuration in both efficiency and equity can be found. Of course, other subjective criteria are needed to choose among the different Pareto-efficient candidate solutions.