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.

我们研究了随机服务时间的有限分布信息的多阶段约会调度问题，并提出了分布鲁棒（DR）模型。在我们研究的问题中，计划者只知道服务时间的手段和支持，因此计划者必须在第一阶段确定每次任命的工作津贴。目的是在最坏情况下分配服务时间的情况下，最大程度地减少客户等待时间和服务提供商的空闲时间以及多个阶段的加班的最大预期加权总成本。对于DR多阶段约会调度模型，我们首先建立绩效指标之间的线性关系（即等待时间，空闲时间和加班时间），然后开发一种切平面方法来解决它。为了克服实施切割平面方法的困难，我们将DR模型中的内部最大化问题重新制定为混合整数线性程序。最后，进行了计算实验，以评估DR模型的计算和仿真性能，研究最佳调度的结构，并检验某些潜在的排序启发式算法的效率。