Bi-objective re-planning of home healthcare services with roster stability

Abstract

Staff shortages in home healthcare (HHC) require service providers to prioritise care worker satisfaction to retain existing staff and attract new care workers. In this paper, care worker satisfaction is considered by focusing on the stability of their working rosters. More specifically, this study addresses the challenge of the weekly re-planning of an initial schedule after changes in demand have occurred. Costs and the total number of rostering deviations from the updated plan compared to an original medium-term plan are minimised using a bi-objective optimisation approach. Here, the care worker rostering, care worker-patient assignment, routing and patient scheduling decisions are re-planned. The model also incorporates important real-life HHC characteristics such as service patterns, skill requirements, continuity of care, and working time regulations. To handle the complexity of this problem, a multi-directional local search heuristic algorithm with embedded large neighbourhood search is proposed. It efficiently approximates the Pareto front for realistic problem sizes within reasonable computation times. A numerical study using small instances demonstrates the effectiveness of our solution approach. The experimental results on large instances reveal critical trade-offs in home healthcare planning, showing that initial reductions in rostering deviations are cost-effective, but diminishing returns arise as fewer deviations remain. Relaxing continuity of care constraints and increasing patient flexibility have little effect on the Pareto front, whereas reduced patient flexibility significantly increases both costs and rostering deviations.