Mathematical models to improve the current practice in a Home Healthcare Unit

This paper addresses a home healthcare routing problem in which doctors and nurses visit patients at their homes to provide services. We consider a real-world home healthcare service arising in a particular hospital in Spain. Doctors and nurses are distributed in teams and travel by taxi; taxis transport a pre-defined set of workers who travel together the whole route. The objective is to minimise the transportation costs related to the total taxi journey time, including travelling and waiting costs. The paper presents a mathematical model that considers these current policies and permits the problem to be solved optimally. The paper also explores, after reviewing the hospital’s current model, the benefits that can be obtained by changing some of the current policies of the hospital. In this way, a new model is proposed based on two sustainable strategies that can be extended to other home service fields: (1) workers can walk between houses and (2) the workers transported by a taxi may change during the route. A complex nonlinear mathematical model is presented, and a metaheuristic is designed to provide quality solutions. Computational tests on a set of instances based on real-world data estimate the gap between the solutions of both models.