Scheduling healthcare services in a home healthcare system

We consider a scheduling problem in a home healthcare system in which nurses visit patients regularly for relatively minor healthcare services. Intervals between the visits may differ for different patients. On each day in the planning horizon, a nurse must visit the patients assigned to her/him on that day, and then return to the hospital. For the problem of determining the visiting schedule with the objective of minimizing total travel time of the nurse over the planning horizon, we develop a two-phase heuristic algorithm. To evaluate performance of the proposed algorithm, a series of computational tests is performed on a number of randomly generated problem instances and a real instance. Results of the tests show that the heuristic algorithm gives near optimal solutions for problems of practical sizes in a reasonable time.