Balancing Efficiency, Patient Preference, and Operational Caregiver Burden in Dynamic Home Healthcare Scheduling: A Four-Objective NSGA-II Approach

In the home healthcare sector, patients often prefer familiar caregivers. Honoring these preferences can unbalance caregivers’ workloads, which can overload some caregivers and disrupt the day’s schedule. Patient cancellations, no-shows, emergencies, and caregiver delays and absences further disrupt schedules. This study proposes a four-objective mathematical model of the home healthcare scheduling and routing problem that jointly optimizes patient preference satisfaction, an operational caregiver burden index, travel distance, and workload balance; the index, built from duty time, patient acuity, and late visits, is a proxy, not a validated measure of burnout. The solution method combines NSGA-II with a local search procedure, and a dynamic extension re-optimizes the schedule when disruptions occur. The model is tested on 18 adapted Solomon instances spanning three scales and three distribution structures. A controlled ablation shows that optimizing the index lowers it in every instance (median change −25%, −15%, and −9% at 25, 50, and 100 patients, and −25% with seven caregivers on six 50-patient instances), but at the cost of 18%, 37%, and 39% more travel and, from 50 patients onward, worse patient preferences; it lowers the share of late visits but does not reduce overtime. NSGA-II is competitive with NSGA-III and MOEA/D. In 1080 simulated disruptions, re-optimization reduces travel, lateness, and overtime relative to keeping the plan, but it increases workload imbalance, does not lower the realized burden, and moves 9% to 11% of the patients to another caregiver (3% to 4% under keeping the plan).