Optimal location-allocation of specialized healthcare service across public hospital networks

Abstract

In this thesis, we propose a location-allocation model for a specialized diagnostic service that requires costly diagnostic equipment such as MRI, CT, PET/CT, and Digital Mammography in a segmented public healthcare system. The aim is to determine which hospitals will provide the service and their capacity levels, the allocation of demand in each institution, and the reallocation of uncovered demand to other institutions or private providers in each period while minimizing the total equivalent annual cost of investment and operating cost required to satisfy all the demand. The capacity levels are based on the number of equipment, and different equipment types are considered. The service is segmented in levels of patient acuity, to identify the degree of severity of the illness. Two variants of the model are also presented, the first one considers levels of specialization of the service instead of urgency demand levels, and the second one is a particular case of the original model when some additional assumptions are met. The proposed mixed-integer linear programming models can be solved by conventional branch-and-bound for relatively small instances. An empirical evaluation to determine solvable instance sizes for each model is carried out. A sensitive analysis is performed to evaluate solution behavior as a function of some key parameters. To cope with large-scale instances, heuristics and metaheuristic methods are proposed and implemented. Two constructive methods are developed. These procedures are embedded into an iterated greedy algorithm that is combined with a variable neighborhood descent algorithm. A greedy randomized adaptive search procedure is additionally developed. This metaheuristic relies on some of the components already developed for the iterated greedy algorithm. In general, good quality results in moderate computation times are found for larger instances using different strategies that combine constructive methods and different neighborhood structures.