基于分布式鲁棒优化的门诊预约调度

The increasing mismatch between supply and demand in healthcare service can be improved properly by optimally allocating healthcare resources, in which outpatient scheduling has great impacts on the efficiency of successive services and even the overall hospital operations. This research, based on abundant healthcare data, takes the uncertainties of service time, patient demand and behavioral characteristics into account, and intends to design optimal outpatient appointment scheduling rules to minimize the cost of patients’ waiting time, doctors’ idle time and overtime. Based on the idea of distributionally robust optimization, we take full use of the moments and moment intervals information of random variables, and employ mathematical optimization methods combined with graph theory, queuing theory, Markov decision process and so on, so as to design heuristic algorithms to solve the optimal appointment scheduling rules under uncertainties. Using the moments or moment intervals information of uncertain service time, we formulate distributionally robust outpatient appointment scheduling models as a set of non-linear programming, in which the uncertainties of patient behaviors will also be taken into consideration. These models will be improved by introducing the concept of min-max regret value. Additionally, by virtue of CVaR theory, we propose an appointment scheduling rule to incorporate risk preference of decision makers. Furthermore, besides static robust scheduling of routine patients, demand uncertainty of same-day patients and sequential scheduling will also be studied in this research, and online algorithms will be proposed under the assumption that patients are heterogeneous. Results of this research can provide decision support for outpatient appointment scheduling to improve patients’ satisfaction, and maximize hospital operations efficiency and utilization of healthcare resources.

医疗资源优化配置是解决我国当前医疗供需矛盾的可行手段，而门诊资源优化调度是否高效会对后续服务及整个医院的运营效率产生直接影响。本项目拟以医疗数据为基础，针对门诊预约调度中存在的服务时间、患者需求和行为特征等不确定信息，以最小化患者等待时间和医生空闲及加班时间为目标，利用随机变量的矩信息或矩区间信息，基于分布式鲁棒优化的思想，综合运用最优化方法、图论、排队论、马尔科夫决策过程等，设计算法求解不确定信息下的最优门诊预约调度规则。具体包括：基于服务时间不确定的门诊预约调度模型，考虑患者行为及其不确定性的门诊预约机制，并基于最小化最大后悔值思想对模型进行改进；决策者存在行为偏好时基于CVaR测度的门诊预约调度模型；考虑患者需求不确定的门诊预约调度优化以及序贯调度下基于鲁棒优化思想的预约调度在线优化。研究成果可为门诊预约调度提供决策支持，提高患者满意度，实现医疗服务运营效率和资源利用率的最大化。

门诊资源优化调度对于优化我国医疗资源配置有着重要的意义。本项目以实践调研中的数据为基础，考虑门诊预约调度问题中的多种不确定因素，以最小化患者等待时间、医生空闲时间和加班时间为目标，基于分布式鲁棒优化的思想，综合运用混合整数规划、随机规划、动态规划、排队论、马尔可夫决策过程等优化方法，充分利用随机变量的矩信息或矩区间信息，建立一系列优化模型并设计算法进行求解。本项目首先研究了服务时间不确定的门诊预约调度问题，进而考虑患者爽约、不守时、当天到达等行为特征对模型的影响，对模型进行改进，进一步地，采用CVaR测度对模型的期望目标进行修正，最后，考虑在患者需求不确定的情况下的序贯调度以及在线优化。针对上述研究内容，项目组发表相关学术论文17篇，培养与项目研究内容相关的博士研究生15名（其中4名围绕项目撰写了毕业论文），硕士研究生5名。本项目的研究成果为门诊预约调度问题提供理论与方法指导，丰富了医疗运营管理研究体系，同时也为我国门诊预约调度问题提供决策支持，对提高我国医疗服务运营效率具有重要的实践意义。