Appointment scheduling for multi-stage sequential service systems with limited distributional information

Abstract

We study a multi-stage appointment scheduling problem with limited distributional information of stochastic service times, and formulate the distributionally robust (DR) model. In our studied problem, only the means and supports of service times are known to the planner, and the planner has to determine a job allowance for each appointment in the first stage. The objective is to minimize the maximum total expected weighted costs of customers’ waiting times and service providers’ idle times and overtimes over multiple stages under the worst-case distribution of service times. For the DR multi-stage appointment scheduling model, we first establish linear relationships among performance indicators (i.e., waiting times, idle times and overtimes), and then develop a cutting-plane approach to solve it. To overcome the difficulty of implementing the cutting-plane approach, we reformulate the inner maximization problem in the DR model as a mixed-integer linear program. Finally, computational experiments are conducted to evaluate the computational and simulational performance of the DR model, investigate the structure of the optimal schedule and examine the efficiency of some potential sequencing heuristics.