A Home Health Care multi-objective approach for personnel scheduling and routing problem under an uncertain environment

Abstract

Home health care services have improved medical care allowing greater coverage of patients in their homes. In order to meet the demands of the service, monthly planning of caregiver’s shifts and daily routing of caregivers are addressed. Two optimization problems have mostly been discussed individually related with HHC: Nurse Scheduling problem (NSP) and Vehicle Routing. This study integrates the two problems in a program that seeks to address in a preventive way the absenteeism of the caregivers at work and in a reactive manner, the new visits that are scheduled after generating the routes in the planning horizon. First a multi-objective mathematical model is developed for NSP using epsilon constraint and then a mono-objective model is integrated as a preventive strategy, which assigns backup caregivers in case of absenteeism throughout the month. For VRP initially a mathematical model is modeled, then the Tabu Search metaheuristic is implemented to find a greater solution to the deterministic problem. Afterwards a simheuristic is implemented with the purpose of including the uncertainty generated by time variability in the problem. Finally, a reactive strategy is designed to include new patients in the routing after having found the best solution for the planning horizon. The result after the implementation of different methods for both, NSP and VRP, is a desktop application, with a user-friendly interface that drastically reduces the time it takes a person to make the monthly shift planning for a staff and create the routes for all the visits in a planning horizon. The impact of the designed desktop application is demonstrated through simulations, were each method modeled for the problem was compared with the current decision making in the hospital in this study. Simulations demonstrated that the program has a greater approximation to the mathematical models results (optimal values found by the mathematical models). The graphical user interface´s efficiency, user satisfaction and usefulness was evaluated with a survey conducted with the hospital´s administrative nurse, to validate that the interface is user-friendly and meets the needs of the hospital in study.