Home Healthcare Staffing, Routing, and Scheduling Problem With Multiple Shifts and Emergency Considerations

ABSTRACT Effective planning of human resources is critical in designing an efficient home healthcare system. In this study, we present a novel home healthcare staffing, routing, and scheduling problem inspired by a real‐world application. The proposed problem addresses a set of patients, with varying daily visit requirements, being served by a set of caregivers with different qualification levels over a multi‐day multi‐shift planning horizon. The problem aims to minimize the number of extra shifts for caregivers, maximize the allocation of caregivers to emergencies, and minimize the sum of route durations over the planning horizon. These objectives are optimized hierarchically while considering a set of restrictions, including time windows, skill matching, synchronization, care continuity, and labor regulations. To tackle the problem, we introduce a mixed‐integer linear programming model. The model is then extended and two sets of valid inequalities are incorporated to enhance its tightness. Computational experiments are conducted on a set of 20 instances. The results highlight the efficiency of the proposed extension in increasing both the number of instances that can be solved to optimality and the number of instances for which a feasible solution is found.