医疗服务能力和质量直接影响人民健康水平，面对日益增加的医疗服务需求，合理的医疗资源配置与调度优化有助于提高人民健康水平和医疗服务效率，同时降低医疗系统运营成本，具有重要的现实意义。然而医疗服务流程中多种不确定性因素成为决策者面临的挑战。本研究基于实际医疗服务运作管理问题，选取家庭医疗服务、疾病诊断和住院治疗三个典型场景为研究对象，考虑不确定的患者需求、服务时间和服务能力，使用数据驱动的分布鲁棒优化方法建模并求解问题，为医疗资源配置与调度优化提供兼具可靠性和成本效益的决策支持。首先，本文研究了考虑需求和服务时间不确定性的家庭医疗服务人员配备与能力规划问题。研究考虑一个家庭护医疗服务机构需要决策未来规划周期内需雇用的服务人员数量并将服务人员的能力分配到不同类型的服务，目标是最小化与人员配备、能力分配、人员配备过剩和人员配备不足相关的总成本。针对提前规划型和灵活调整型决策者，研究提出基于mean-support和1-Wasserstain模糊集的分布鲁棒优化模型，设计列与约束生成算法和多种有效不等式求解灵活调整型决策者的模型，依托青松康护的实际服务数据进行了案例分析。其次，本文研究了考虑患者到达和服务能力不确定性的医技部门患者预约调度问题。研究提出了三种块调度策略，并使用基于1-Wasserstain模糊集的分布鲁棒优化模型优化多类患者的到达时间，目标是最小化与延迟服务预约型患者、患者现场等待时间、服务器空闲和加班相关的成本之和。根据问题结构，研究将min-max-min问题转化为min-max-min-max问题，设计嵌套的列与约束生成算法进行求解，并使用国内某三甲医院B超室真实服务数据进行了案例分析。最后，本文研究了考虑患者住院时长不确定性的择期入院患者入院调度问题。从住院中心角度，考虑决策现有等待患者在下一个规划周期内的入院日期，目标是最小化与治疗延期和床位溢出相关的总成本。研究使用回归模型对患者住院时长进行预测，针对不确定的回归残差，使用基于mean absolute deviation模糊集的分布鲁棒优化方法来建模和求解问题，提出列与约束生成算法对其进行求解，并使用纽约市患者住院公开数据集进行了案例分析。综合上述研究内容，本文对主要研究成果和创新点进行了总结，并结合研究趋势从研究问题和建模方法等多个角度对未来研究进行了展望。
The provision of high-quality healthcare services is vital for effective health management. The planning and scheduling optimization for healthcare resources can achieve high-quality care at a reduced cost. However, the existence of uncertainties in the healthcare service process presents significant challenges. In this study, we focus on the optimization of home health care, disease diagnosis, and hospitalization services under uncertainty. Specifically, we consider uncertainties related to demand, service duration, and service capacity. To address these challenges, we use data-driven distributionally robust optimization approaches to model and solve these problems. Our study aims to provide reliable and cost-effective decision support for healthcare resource planning and scheduling optimization.First, we address a home health care service staffing and capacity planning problem under uncertain demand and service duration. Specifically, given sets of providers, service types, and days in the planning horizon, we aim to determine the number of providers to hire and the allocation of hired providers to different types of services. The objective is to minimize the total cost associated with staffing, capacity allocation, over-staffing, and under-staffing. We propose two-stage data-driven distributionally robust optimization (DRO) approaches considering two types of decision-makers, namely an everything-in-advance decision-maker (EA) and a flexible adjustment decision-maker (FA). We propose a computationally efficient column-and-constraint generation algorithm with valid inequalities to solve the proposed DRO models for the FA decision-maker. Numerical experiments based on data from a home services provider in Beijing are used to compare the proposed approaches and illustrate the potential for impact in practice.Second, we study the patient appointment scheduling problem in medical diagnosis departments while considering uncertainties in patient arrival and service capacity. Specifically, we propose three block scheduling strategies and use data-driven distributionally robust optimization approach based on a 1-Wasserstein ambiguity set to optimize the arrival time of multiple types of patient. The objective is to minimize the sum of costs associated with delayed service of appointed patients, patient on-site waiting time, server idleness, and overtime. To solve the problem, we reformulate the original min-max-min problem into a min-max-min-max problem and design a nested column and constraint generation algorithm to solve it. We construct a case study using real service data from the ultrasound room in our collaborated institution to compare the proposed approaches and illustrate the potential for impact in practice.Finally, we address an elective patient admission scheduling problem under uncertain patients‘ length of stay (LOS). Specifically, we consider that decision makers have to decide the admission time for the waiting elective patients in a fixed planning horizon. The objective is to minimize total cost associated with service postponement and daily bed over-utilization. We first predict patients‘ LOS using elaborate clusterwise regression methods. Considering the distribution ambiguity of the regression residuals, we propose a DRO approach to model and solve the elective patient admission scheduling problem. To efficiently solve the problem, we reformulate the proposed DRO model and construct a column-and-constraint generation algorithm. In addition, we conduct a case study using real-world data to demonstrate the effectiveness of our proposed approach.In the light of the above research, we present a summary of the main research results and innovations, and provide an outlook on future research from multiple perspectives including research questions and modeling methods.
