Optimal appointment scheduling with a stochastic server: Simulation based K-steps look-ahead selection method

This paper studies the problem of scheduling a finite set of customers with stochastic service times for a single-server system. The objective is to minimize the waiting time of customers, the idle time of the server, and the lateness of the schedule. Because of the NP-hardness of the problem, the optimal schedule is notoriously hard to derive with reasonable computation times. Therefore, we develop a simulation based K-steps look-ahead selection method which can result in nearly optimal schedules within reasonable computation times. Furthermore, we study the different distributed service times, e.g., Exponential, Weibull and lognormal distribution and the results show that the proposed algorithm can obtain better results than the lag order approximation method proposed by Vink et al. (2015) [Vink, W., Kuiper, A., Kemper, B., & Bhulai, S. (2015). Optimal appointment scheduling in continuous time: The lag order approximation method. European Journal of Operational Research, 240(1), 213-219.]. Finally, a realistic appointment scheduling includes experiments to verify the good performance of the proposed method.