系统管理学报

系统管理学报 ›› 2023, Vol. 32 ›› Issue (3): 476-487.DOI: 10.3969/j.issn.1005-2542.2023.03.004

• 工业工程与工程管理 • 上一篇    下一篇

结合Benders分解和列生成的发热门诊排班数学建模和优化算法

王铖恺1，范晓宇1，徐捷1，刘冉1，杨之涛2   

  1. 1.上海交通大学工业工程与管理系，上海 200240；2. 上海交通大学医学院附属瑞金医院急诊科，上海 200025
  • 收稿日期:2022-05-13 修回日期:2022-09-23 出版日期:2023-05-28 发布日期:2023-06-01
  • 作者简介:王铖恺（1998-），男，博士生。研究方向为服务系统建模和优化。
  • 基金资助:

    国家自然科学基金资助项目（71972133，71672112）

Mathematical Modeling and Optimization Algorithm for Fever Clinics Scheduling Combining Benders Decomposition and  Column Generation

WANG Chengkai1，FAN Xiaoyu1，XU Jie1，LIU Ran1，YANG Zhitao2   

  1. 1. Department of Industrial Engineering and Management，Shanghai Jiao Tong University，Shanghai 200240， China；2. Department of Emergency，Ruijin Hospita，Shanghai Jiao Tong University School of Medicine，Shanghai 200025，China
  • Received:2022-05-13 Revised:2022-09-23 Online:2023-05-28 Published:2023-06-01

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摘要：

发热门诊是抗击疫情最前线，发热门诊中的医生排班对于系统运行效率和医疗服务质量都非常重要，需要科学的排班优化算法。针对发热门诊医生排班调度问题，首先采用逐点稳态流近似方法对系统建模，定量评估系统中等待服务的患者数目，基于此建立了考虑患者排队队长限制的医生排班数学优化模型。进一步，为求解该模型设计了结合Benders分解与列生成的高效算法，对此复杂优化问题加以高效求解。最后，利用上海大型医院发热门诊的实际数据加以数值实验分析，验证了所提出算法的排班结果，显示了其在控制患者队长和医生总工作时间上具有优势。数值结果进一步验证所提出方法能适应疫情严重情况下的医生排班优化要求。研究得到的模型和算法对完善疫情中发热门诊的运作管理具有实际意义。

关键词: 新冠疫情, 时变排队系统, 医生周排班, benders分解, 列生成算法

Abstract:

Fever clinics are critical sectors as the front lines of fighting against the Covid-19 outbreak. Physician scheduling in fever clinics is essential for both the efficiency of system operation and the quality of medical services, which requires scientific scheduling optimization algorithms. This paper, focusing on the physician scheduling problem in fever clinics, proposed a pointwise stationary fluid flow approximation method to quantitatively evaluate the queue length of patients. Based on this method, it developed a mathematical optimization model for physician scheduling considering patient queue length constraint. In addition, it designed an efficient algorithm combining benders decomposition and column generation to solve the model. Further, it conducted numerical experiments based on real data from fever clinics in a large hospital in Shanghai, which verified the superiority of the flexible scheduling plan obtained by the proposed algorithm. The numerical results validate that the algorithm can also be adapted to physician scheduling requirements in severe pandemics. The model and the algorithm have a significant practical value for improving the operational management of fever clinics.

Key words: Covid-19 pandemic, time-varying queueing, physician scheduling problem, benders decomposition, column generation

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