Adaptive appointment scheduling with periodic updates

The classical paradigm in appointment scheduling is to rely on 'a priori schedules', determined by minimizing the given cost function; the corresponding arrival times are then announced to the clients, and not adjusted while serving them. The idea of the present paper is to reduce the cost by periodically updating the schedule (and notifying the clients about this), based on the current state of the system. Evaluation of the objective function is done highly efficiently and accurately by approximating the service times by their phase-type counterparts. The resulting method is computationally inexpensive, thus facilitating frequent evaluation and periodic adaptation of schedules 'on the fly'. A computational study illustrates the performance of the method, including an assessment of the impact of the rescheduling frequency and the variability of the service times. The most prominent conclusion is that typically, even with relatively few updates, costs can be reduced drastically. Our experiments, however, also reveal that one can construct instances for which increasing the rescheduling frequency does not guarantee a cost reduction; we provide an in-depth analysis of the remarkable phenomenon. The work has broad application potential, e.g., in healthcare and for delivery companies.