Managing home health-care services with dynamic arrivals during a public health emergency

Abstract

We consider a public health emergency, during which a high number of patients and their varying health conditions necessitate prioritizing patients receiving home health care. Moreover, the dynamic emergence of patients needing urgent care during the day should be handled by rescheduling these patients. In this article, we present a reoptimization framework for this dynamic problem to periodically determine which patients will be visited in which order on each day to maximize the total priority of visited patients and to minimize the overtime for the health-care provider. This optimization framework also aims to minimize total routing time. A mixed-integer programming (MIP) model is formulated and solved at predetermined reoptimization times, to assure that urgent patients are visited within the current day, while visits of others may be postponed, if overtime is not desired or limited. The effectiveness of a schedule is evaluated with respect to several performance metrics, such as the number of patients whose visits are postponed to the next day, waiting time of urgent patients, and required overtime. The MIP-based approach is compared to two practical heuristics that achieve satisfactory performance under a nervous service system by excelling in different criteria. The MIP-based reoptimization approach is demonstrated for a case during the COVID-19 pandemic. We contribute to the home health-care literature by managing dynamic/urgent patient arrivals under a multiperiod setting with prioritized patients, where we optimize different rescheduling objectives via three alternative reoptimization approaches.