Simulation-based Optimization for Region Design in the U.S. Liver Transplantation Network

Gabriel Zayas-Cabán, Patricio Rocha, and Dr. Nan KongDepartment of Industrial and Management Systems Engineering

REU 2006IE. 1

Introduction, Motivation, and BackgroundTransplantation 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.

As a result …

… 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).

Figure 1: OPO Service Areas Figure 2: Current

Region Map

Figure 3 Allocation Hierarchy

The proposed research will use simulation-based optimization to find the best set of regions, considering both allocation efficiency and equity.

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|}.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.

Formulation:

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 simulationPseudo-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.

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.”