Emergency department (ED) crowding has become a common phenomenon worldwide. A number of interventions have been proposed to improve operations in EDs, such as scheduling physicians to manage varying patient demands. Motivated by a collaboration with a large ED, we study physician scheduling in the ED. The ED is modeled as a time-varying case managers system where the number of patients simultaneously assigned to a single physician is limited by maximum caseloads. To match real-life scenarios, we consider time-varying patient arrivals, temporary ED overloading, and patient-physician assignments. We first analyze patient flow and service procedures using real data to capture the features of the ED. Next, a mathematical model of physician scheduling is constructed. To effectively solve this complex problem, two machine learning-based solution approaches are designed. The first approach integrates an extreme gradient boosting model with Gurobi. The second involves a variable neighborhood search algorithm, in which a long short-term memory network is incorporated to evaluate the solution to the problem. Numerical experiments indicate that the proposed approaches can yield high-quality solutions within reasonable time frames. The physician schedules generated by the second approach outperform those generated by the first approach and are also superior to the actual schedules used by our partner ED. For the data from the stable period, our solutions reduce the average patient waiting time and total physician working time by 10.32 % and 14.79 %, respectively, compared to the actual ED schedules. During the COVID-19 outbreak, these two metrics are respectively reduced by 8.06 % and 12.9 %.

中文翻译：

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案例经理风格的急诊科医生调度：机器学习辅助解决方案方法

急诊科 （ED） 拥挤已成为全球普遍现象。已经提出了许多干预措施来改善急诊室的运营，例如安排医生来管理不同的患者需求。在与大型急诊室合作的推动下，我们研究了急诊室的医生排班。急诊科被建模为一个时变病例管理系统，其中同时分配给单个医生的患者数量受最大病例量的限制。为了匹配现实生活场景，我们考虑了随时间变化的患者到达、临时 ED 超负荷和患者-医生分配。我们首先使用真实数据分析患者流程和服务程序，以捕捉 ED 的特征。接下来，构建医生调度的数学模型。为了有效解决这个复杂的问题，设计了两种基于机器学习的解决方案方法。第一种方法将极端梯度提升模型与 Gurobi 集成在一起。第二个涉及可变邻域搜索算法，其中包含一个长短期记忆网络来评估问题的解决方案。数值实验表明，所提出的方法可以在合理的时间范围内产生高质量的解。第二种方法生成的医生时间表优于第一种方法生成的医生时间表，也优于我们的合作伙伴 ED 使用的实际时间表。对于稳定期的数据，与实际急诊计划相比，我们的解决方案将患者平均等待时间和医生总工作时间分别减少了 10.32% 和 14.79%。在 COVID-19 爆发期间，这两个指标分别减少了 8.06% 和 12.9%。