A bi-objective home care scheduling problem: Analyzing the trade-off between costs and client inconvenience

Organizations providing home care services are inclined to optimize their activities in order to meet the constantly increasing demand for home care. In this context, home care providers are confronted with multiple, often conflicting, objectives such as minimizing their operating costs while maximizing the service level offered to their clients by taking into account their preferences. This paper is the first to shed some light on the trade-off relationship between these two objectives by modeling the home care routing and scheduling problem as a bi-objective problem. The proposed model accounts for qualifications, working regulations and overtime costs of the nurses, travel costs depending on the mode of transportation, hard time windows, and client preferences on visit times and nurses. A distinguishing characteristic of the problem is that the scheduling problem for a single route is a bi-objective problem in itself, thereby complicating the problem considerably. A metaheuristic algorithm, embedding a large neighborhood search heuristic in a multi-directional local search framework, is proposed to solve the problem. Computational experiments on a set of benchmark instances based on real-life data are presented. A comparison with exact solutions on small instances shows that the algorithm performs well. An analysis of the results reveals that service providers face a considerable trade-off between costs and client convenience. However, starting from a minimum cost solution, the average service level offered to the clients may already be improved drastically with limited additional costs.