Scheduling of surgeries subject to stochastic surgery and length of stay with respect to limited capacities in hospitals

手术是提高生活质量的措施。在某些情况下，这些程序甚至可以挽救生命。手术需要许多资源，包括外科医生、麻醉师、护士、工具和设备、手术室和紧接着手术后的护理病房中的一张床。如果没有可用的资源，手术必须推迟，从而降低医疗服务水平。因此，手术调度方法应该考虑有限的资源和随机性。这就缩短了手术的等待时间(通过更高的手术室利用率)，并提高了护理病房的护患比(通过更公平地利用护理病房)。目前的研究考虑的是固定的、重复的手术时间表，而不是针对不同手术需求的个别计划。因此，本研究的目的是建立一个随机手术和床位占用时间、有限的手术室和护理单元以及工作人员容量的手术调度的数学决策模型。这种模式的目标是最大限度地利用手术室，使护理单位的利用率达到平均水平，并以经济和可持续的方式利用医院资源。在项目过程中，确定了手术次数的分布和接受手术的住院时间，并调查了手术时间和住院时间之间的相关性。数学决策模型是利用从数据分析中获得的见解(即每个程序的期望值和标准差，以及手术时间和住院时间之间的相关性，如果适用)而开发的。该模型的结果是在有限资源的约束下，为给定的手术需求制定手术和床位占用计划。此外，我们将分析手术日程中的缓冲时间及其对计划健壮性的积极影响和对空闲时间的负面影响。该模型将利用真实的医院数据。提供的数据是德国汉诺威医学院三个不同学科2014-2016全年的手术次数和住院时间。手术时间的可变性因所选学科而异：眼外科的可变性很低，心脏外科的可变性中等，而意外外科的可变性很高。此外，我们有来自Vanderbilt医学中心2015-2017年的搭桥手术数据。本研究项目通过考虑持续时间的随机性和有限的床位容量来扩展主流方法的假设，以满足不同的手术需求。这样，将有助于医疗服务水平的提高。

Surgeries are measures to improve the quality of life. In some cases, the procedures are even life-saving. Surgeries require many resources, including surgeons, anesthesiologists, nurses, tools and devices, an operating room and a bed in a care unit directly following the surgery. If one resource is not available, the surgery must be postponed, reducing the health care service level. Therefore, a surgery scheduling approach should take limited resources and stochasticity into account. This leads to shorter waiting times for surgeries (by higher utilization of operating rooms) and to a better nurse-patient ratio in the care units (by more leveled utilization of the care units). Current research considers fixed, repeating surgery schedules, but not individual plans for varying demand of surgeries. Therefore, the objective of this research project is to develop a mathematical decision model for surgery scheduling subject to stochastic surgery and bed occupancy times, limited operating rooms and care units, and staff capacities. The goal of this model is to maximize the utilization of operating rooms, to level the utilization in the care units, and the economic, and therefore sustainable, use of the hospital resources. In the course of the project, the distribution of surgery times and the length of stay subject to the procedures is determined, and the correlation between the duration of the surgery and the length of stay in the wards is investigated. The mathematical decision model is developed using the insights from this data analysis (that is, the expected value and the standard deviation per procedure and, if applicable, the correlation between surgery time and length of stay). The result of the model is a surgery and bed occupancy plan for a given demand of procedures subject to the limited resources. Furthermore, we will analyze buffer times in the surgery schedule and its positive effects on robustness of the plan and its negative effects on the idle time. The model will utilize real hospital data. The provided data are surgery times and lengths of stay for the complete years 2014-2016 for three different disciplines at the Hanover Medical School in Germany. The variability of surgery times differs for the selected disciplines: eye surgery has very low variability, heart surgery has a medium variability, and accident surgery is highly variable. In addition, we have bypass surgery data from the Vanderbilt Medical Center for 2015-2017.This research project extends the assumptions of prevailing methods by the consideration of the stochasticity of durations and limited bed capacities with varying surgery demands. That way, it will contribute to the improvement of the health care service level.