Mathematical modelling and optimization of distributed capacitated kidney paired donation programs with transportability of kidneys after nephrectomy

Abstract

Due to the limitation in the number of deceased and compatible live kidney donors compared to end stage renal disease (ESRD) patients, kidney paired donation (KPD) exchange programs were proposed in various countries around the world. Due to logistic and resource constraints, the maximum size of each kidney exchange cycle cannot exceed a preset limit k. The decision version of the k-cycle exchange problem is of the NP-Complete time-complexity class. Various algorithms were proposed in literature to solve the vanilla k-cycle exchange problem with no regards to assigning nephrectomy and implantation operations to transplant centers given capacity constraints, and the geographical distribution of patients, donors and transplant centers around the country and therefore the access they have to each other. Moreover, it was proposed in literature that it is medically viable to transport a kidney for long distances after nephrectomy and before implantation in the patient at another center. In this thesis, a number of compact mathematical programs and associated algorithms are proposed and benchmarked for solving the capacitated k-cycle kidney exchange problem given the geographical locations of donors, patients and transplant centers, with and without transportability of kidneys after nephrectomy. Computational experiments show that 2 formulations, namely capacitated reduced extended edge assignment (CRXEA) and capacitated reduced extended edge assignment with transportability (CRXEAT), were the most computationally efficient, for the problem variants without and with kidney transportability respectively. Moreover, the standard KPD instance generator was extended and used alongside the dominant formulations to identify the extent of benefits attainable by allowing kidneys to be transported after nephrectomy in different simulation scenarios. Computational experiments validated the merit of allowing transportability of kidneys under specific, arguably realistic scenarios.