A matheuristic for integrated medium-term home healthcare planning

Due to staff shortages and budget restrictions, home healthcare service providers struggle to construct efficient schedules to service the growing number of people that require medical services at home. Previous research on home healthcare planning concentrates on planning periods of one to seven days, often does not focus on including real-life characteristics, and generally develops a heuristic procedure dealing with decisions sequentially or an exact approach that may not always scale very well. In this study, we propose an integrated solution approach that considers various real-life characteristics, such as service patterns, skill levels, continuity of care, and working time limits, to construct a detailed home healthcare schedule for a four-week planning horizon. The proposed approach integrates rostering, assignment, routing, and scheduling decisions, as joint optimisation of interdependent decisions enables better overall planning. The solution approach is a matheuristic based on large neighbourhood search and efficiently solves large, realistic instances. The proposed integrated algorithm approximates the optimal solutions of small instances with an average gap of merely 0.18%. It also outperforms a sequential solution method that mimics the planning procedure currently applied in practice, resulting in average cost improvements of 28.69%. A sensitivity analysis indicates that adhering to strict continuity of care constraints results in only a minimal increase in costs for service providers when decision-making is integrated. Furthermore, the efficiency of a medium-term home healthcare schedule can be significantly improved if patients are flexible concerning their availabilities and if working a small amount of overtime is allowed.