Patient unpunctuality causes perturbations in healthcare operations, compromising productivity and service quality. In this paper, we propose an approach that mitigates the negative impacts of unpunctuality using both appointment scheduling and real-time sequencing taking into account patient unpunctuality, no-shows, random service durations, and multiple providers. The objective is to minimize the total cost incurred by patient waiting and provider overtime. An optimal real-time sequencing strategy is established to serve the waiting patient with the smallest “LAR” index, which is defined as the Larger of Appointment time and Real arrival time for a patient. The optimal appointment schedule is determined by a simulation optimization approach with unbiased gradient estimators. Sample path discontinuities are smoothed by smoothed perturbation analysis. Properties of the optimal real-time sequencing strategies are used for the efficient sample path gradient estimation. Extensive experiments demonstrate the effectiveness of the proposed algorithm. Using real data, numerical experiments illustrate that the optimal appointment schedule depends on the system parameters and differs significantly from those of the existing literature. Specifically, the pattern of the appointment schedule is determined by the number of providers and the real-time sequencing strategy. The length of the appointment intervals is sensitive to the degree of unpunctuality and no-shows. Compared with the schedules in the previous studies, our schedule can achieve a significant cost reduction. Further, the optimal real-time sequencing strategy outperforms the commonly-used strategies in practice (e.g., appointment order, arrival order). Managerial insights are also provided for hospital managers to schedule unpunctual patients.

患者不守时会扰乱医疗保健运营，影响生产力和服务质量。在本文中，我们提出了一种方法，考虑到患者不准时、未出现、随机服务持续时间和多个提供者，使用预约安排和实时排序来减轻不准时的负面影响。目标是将患者等待和提供者加班所产生的总成本降至最低。建立最佳实时测序策略，以最小的“LAR”指数为等待患者服务，该指数定义为预约时间和实际到达时间中的较大者对于一个病人。最佳预约时间表由具有无偏梯度估计器的模拟优化方法确定。样本路径不连续性通过平滑扰动分析进行平滑处理。最佳实时测序策略的特性用于有效的样本路径梯度估计。大量实验证明了所提出算法的有效性。使用真实数据，数值实验表明，最佳预约时间表取决于系统参数，与现有文献的参数有很大不同。具体来说，预约时间表的模式由提供者的数量和实时排序策略决定。约会间隔的长度对不准时和未出现的程度很敏感。与以往研究中的时间表相比，我们的时间表可以实现显着的成本降低。此外，最佳实时排序策略优于实践中常用的策略（例如，预约顺序、到达顺序）。还为医院管理人员提供了管理见解，以安排不准时的患者。