Kidney exchange program: An efficient compact formulation

Abstract

This study develops a new compact mathematical formulation to improve transplant planning in a kidney exchange program with a long cycle size. Our proposed integer programming model uses a new index, called timeslot, to significantly improve the model’s solution time for problems with large cycle sizes. To enhance the performance of obtaining an optimal solution, we apply two procedures. First, we define an appropriate upper bound for the defined index that reduces the number of variables and constraints as the cycle size increases. Furthermore, we develop a variable reduction procedure to eliminate the redundant variables and strengthen its performance. Finally, we assess the model performance in a systematic computational comparison and demonstrate its advantages compared to the existing formulations in the literature.