Dynamic periodic fixed appointment scheduling for home health

This paper defines the Home Health Nurse Routing and Scheduling (HHNRS) problem and presents a rolling horizon approach for its solution. The HHNRS is a dynamic periodic fixed appointment time routing problem with visit time consistency constraints. A set of patients, revealed dynamically, must be visited according to a prescribed weekly frequency over a prescribed number of weeks, where each visit must be assigned a precise appointment time chosen from a fixed menu of allowable appointments. Furthermore, weekly visits must repeat on the same days and times throughout a patient's service duration, and should occur according to an allowable visit day combination for the patient. The objective is to maximize the number of patients served per nurse per unit time. We develop a rolling horizon myopic planning approach for the single nurse HHNRS variant that uses a new capacity-based insertion heuristic to explicitly consider remaining available time in the nurse's schedule when inserting current patient requests. A computational study reveals that the heuristic produces schedules which accept 4% more patients and perform 4% more visits per day than a traditional distance-based insertion heuristic, while requiring an average of 8.7% additional minutes of travel per visit.