A biobjective Home Care Scheduling Problem with dynamic breaks

This paper presents a multiobjective Home Care Scheduling Problem (from now on multiobjective HCSP) related to a home care company for elderly and dependent people located in the North of Spain. In particular, a biobjective problem is considered, with the following two conflicting objectives: the welfare of users and the cost of schedules. To tackle the problem, a custom metaheuristic algorithm based on the Multi-Directional Local Search (MDLS) was designed, obtaining good approximations of the Pareto frontier in efficient computational times. This biobjective algorithm can be divided into three steps: initializing the set of non dominated solutions, generating solutions composed by different routes and obtaining non dominated solutions. The performance of the biobjective algorithm was analyzed by implementing two other well known methods in the literature: the exact method AUGMECON2, which is just an improved version of the Epsilon Constraint approach, and an NSGA-II-based algorithm. Finally, an extensive computational study was developed to compare the three methods over a set of instances from the literature, where the biobjective algorithm exhibited a superior behaviour. Furthermore, the algorithm was also applied to real instances providing solutions to the company with a good trade-off between the two objectives.