Algorithms for public healthcare facility location problems with preference constraint

Abstract

This dissertation focuses on location problems of public healthcare facilities. Among public healthcare facilities, long-term care facility, public local hospital, health center are considered. Locations of those facilities are determined to minimize or maximize the related measure. Each public healthcare facility provides different healthcare services and has different circumstances. We consider three different problems with different constraints for public healthcare facility location, and develop algorithms for the problems. First, we consider a long-term care facility location problem with the objective of minimizing the maximum load of facilities under the constraints that demands for the care are assigned to the closest facilities. We suggest a branch and bound algorithm for the facility location problem after developing dominance properties of the problem and a lower bound on the maximum load as well as a heuristic algorithm to find an initial feasible solution. Secondly, we consider a location problem of public healthcare facilities. There are two types of patients, low-income patients, who can use only public facilities, and middle- and high-income patients, who can use both public facilities and private facilities. We focus on the problem of determining locations of public healthcare facilities to be additionally established within a given budget and allocating the patients to the facilities for the objective of maximizing the number of served patients. We present an integer programming formulation for the problem and develop a heuristic algorithm based on Lagrangian relaxation and subgradient optimization methods. Finally, we consider a location problem of two-type public healthcare facilities with the objective of minimizing total constructing cost. There are two types of public healthcare facilities, public local hospital, which provide both inpatient care service and homecare service, and health center, which provide only homecare service....