REU 2006 IE. 1

1. Simulation-based Optimization for Region Design in the U.S. Liver Transplantation NetworkGabriel Zayas-Cabán, Patricio Rocha, and Dr. Nan KongDepartment of Industrial and Management Systems Engineering REU 2006 IE. 1 • Mathematical Model (Graph Partitioning Problem) • Model Assumptions: • Entire nation as a complete undirected graph (I, E). • Transplantation and procurement: only at the “main” transplant center transplant center. • A hypothetical region r containing a subset of OPOs: Ir = {i1, , i2, … , i|r|}. • Introduction, Motivation, and Background • Transplantation and allocation of organs: • A contentious issue in the U.S. • Ongoing debate focuses on what degree of organ sharing should be allowed across geographic regions: • A major concern is the large amount of organ wastage due to allocation delays that results in organ viability loss. Formulation: • The Need for Simulation: • The actual allocation process is too complex to model analytically. • Using simulation, we are able to represent the process more faithfully. • Drawback: only a small number of system configurations can be evaluated within a reasonable amount of time. In our problem, estimating one feasible regional configuration is computationally prohibitive, and hence the need for optimization. As a result … Figure 2: Current Region Map Figure 1: OPO Service Areas … we have two major organ allocation preferences: (1) allocate organs to potential recipients with greatest medical needs regardless of location; (2) allocate organs to potential recipients with high priority in the same locale. Therefore, the United Network for Organ Sharing developed a three-tier hierarchical allocation system that divides the U.S. into 11 regions composed of 59 Organ Procurement Organizations (OPOs) (See Figures 1 and 2). A procured organ is first offered locally, then regionally, and finally, at the national level (See Figure 3). • The Need for Optimization: • Optimization provides efficient methods to select the best configuration among a large number of possibilities. • Optimization technique: Genetic Algorithms – metaheuristic that can be understood as the intelligent exploitation of a random search • Drawback: applicability of optimization techniques often requires a closed-form system representation. Therefore, there is a need for integrating optimization with simulation Pseudo-code of Genetic Algorithm Choose initial population Repeat Evaluate fitness of the population Select pairs of best individuals to reproduce Breed new generation through crossover and mutation Until terminating condition • Goals • Explore the tradeoff between modeling accuracy and solution difficulty in our particular problem. • Assist organ transplantation policy makers. • Enhance application of simulation-based optimization techniques in health care resource allocation problems. The proposed research will use simulation-based optimization to find the best set of regions, considering both allocation efficiency and equity. Figure 3 Allocation Hierarchy This research is supported by the USF New Research Grant “ Simulation-based Optimization for Region Design in the U.S. Organ Transplantation and Allocation Network.”