基于机会约束的单服务台就诊预约调度优化

Appointment scheduling optimization with chance constraints in a single-server consultation system

随着社会的发展,能够提高医疗服务质量的预约调度管理越来越受到医疗机构运营管理者的重视.本文研究了单服务台就诊的预约调度问题,考虑了服务台对每个患者的服务时长具有随机性;为了保证医疗服务人员的工作质量,本文利用概率约束控制服务台的超时时长,将医疗服务人员的加班时长以一定概率限制在合理范围内,建立了基于机会约束的预约调度模型.为了求解大规模场景下该类预约调度问题,本文首先对原机会约束模型进行重构,得到原问题的等价模型;随后考虑服务时长的随机向量服从Gaussian分布和不服从Gaussian分布的情形.针对随机向量服从Gaussian分布的情形,本文设计了基于梯度的方法对等价模型进行求解,并证明该方法能够获得模型的全局最优解;而对于不服从Gaussian分布的情形,本文基于条件风险价值近似等价模型,并设计了Benders分解算法求解得到近似模型的全局最优解.最后通过仿真实验展示了在大规模算例下,模型的可行性和算法的有效性,并通过分析数值结果,为医疗机构运营管理者提供预约调度决策建议.

With the development of modern society,appointment scheduling management which facilitates the improvement of healthcare service quality has been gaining increased attention from healthcare service providers.This paper considers the appointment scheduling of a healthcare consultation system in a single-server setting.In this consultation server,the service duration for patients is random and the overtime is restricted to a reasonable level with a chance constraint.Therefore,the appointment scheduling model with the chance constraint is formulated.To solve the model under large-scale scenarios,we analyze and reformulate the original model.Then the following two reformulations are proposed.The first reformulation is developed based on the assumption that the service duration follows the Gaussian distribution,and the gradient-based method is implemented to obtain the global optimal solution.In the second reformulation,an approximation is designed based on the conditional value-at-risk,and Benders decomposition is tailored to tackle the resulting model.Simulation experiments demonstrate the feasibility of the two reformulations and the effectiveness of the algorithms under large-scale scenarios.Through analysis of the numerical results,appointment scheduling decisions are provided for healthcare service providers.