This paper attempts to compare the performance between a single-stage appointment scheduling system and two-stage appointment scheduling system. For this purpose, a queuing model is firstly formulated with the objective of maximizing the weighted hospitals benefit minus the cost of patient waiting and doctor overtime, for a two-stage appointment scheduling system considering no-shows. To facilitate the comparison, we can alter the number of diagnosis stages by adjusting the probabilities that patients need to do further examinations, e.g., X-rays or blood tests. The single-stage queuing model assumes that all patients will finish their treatment after their first diagnosis, and other assumptions are the same as that in a two-stage appointment scheduling system. The performances of two-stage appointment scheduling systems varying with no-show probabilities and probabilities that patients have a second-stage diagnosis are presented. Experimental results indicate that the optimal number of patients needs to be more than the capacity of doctors in the first few slots, and less than those in the last few slots. We need to weigh the probability of no-shows and the probability of doing further examinations (second-stage) when determining the total number of patients to be scheduled. Under a higher no-show probability, arranging more patients than the workload reduces the waste of doctors capacity; and on the contrary, under a higher probability of doing examinations, arranging fewer patients than the workload can reduce system congestion.

中文翻译：

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门诊两阶段诊断的预约调度优化

本文试图比较单阶段约会调度系统和两阶段约会调度系统的性能。为此，首先建立了一个排队模型，其目的是在考虑到缺席的两阶段约会调度系统的情况下，最大化加权医院收益减去患者等待和医生加班的成本。为了便于进行比较，我们可以通过调整患者需要进行进一步检查（例如X射线或血液检查）的概率来更改诊断阶段的数量。单阶段排队模型假设所有患者都将在首次诊断后完成治疗，其他假设与两阶段约会计划系统中的假设相同。介绍了两阶段约会调度系统的性能，这些系统随未出现概率和患者进行第二阶段诊断的概率而变化。实验结果表明，最佳患者人数应大于前几个时段的医生人数，而小于最后几个时段的医生人数。在确定要安排的患者总数时，我们需要权衡未出现的可能性和进行进一步检查（第二阶段）的可能性。在没有出现的可能性更高的情况下，安排比工作量更多的患者可以减少医生的工作量；相反，在进行检查的可能性较高的情况下，安排比工作量少的患者可以减少系统拥塞。