短期维度下手术排程优化问题的数学模型研究

The Mathematical Models of Short Term Operation Scheduling Optimization Problem

在国内医院手术室的运作管理中,普遍存在护士加班时间长和资源利用不均衡的问题.短期维度下的手术排程优化关注手术时间的确定和优化配置完整手术流程中所需的各类手术资源,考虑到手术排程优化问题的复杂性和实用性,本研究中我们从基本的择期手术排程优化模型,而后引入全面的护士资源的排班约束,再进一步将单目标的数学模型扩展到多目标,较为系统、完整地研究了医院手术室的短期手术排程模型.我们通过仿真算例、文献算例和医院实际调度算例结果进行比较,验证结果发现基于所研究的系列排程数学模型的优化排程解在均衡手术室和护士工作时间、减少护士最大加班时间和总加班时间上具有较大程度的改善,多目标模型较单目标模型总体优化效果更为明显.由于医院管理水平不同,数学模型的约束条件也有不同,医院管理者可以使用对应的数学模型进行手术排程.研究成果可为医院管理形成新的优化决策手段,可以用来提升手术室各类资源的利用率,最终达成医院增加日开放手术台数,缩短平均住院日的手术室管理目标,在优化医院服务管理实践上有普遍意义.

Long nurse＇s overtime and imbalanced utilization of resources are universal prob- lems in current domestic hospital operatin room management. The short term operation scheduling focuses on the determination of the operation time and optimizing the resource allocation of all resources which are used in the whole operation process. W＇e consider the complexity and practicability of the operation scheduling optimization problem. Firstly, the initii basic operation scheduling model is proposed, then the comprehensive nurse rostering constraints are put into the basic model, finally we expand the mathematical model from single objective to multi-objective model and study the operation scheduling optimization problem systematically. W＇e find the solutions by using the improved ant colony algorithm, and compare the results of the literature, manual scheduling, optimized scheduling based on single objec- tive and multi-objective model. We find that the optimized scheduling model has a greater performance in balancing working time of operating room and nurses, reducing maximum overtime and total overtime. The multi-objective model is better than single objective model in the overall optimization performance. The results of study can develop a new optimizing determination mean in hospiti management to improve utilization of OR（s） resources. Due to different level of hospital management~ constraint conditions of the mathematical model are different. The hospital managers can use the corresponding mathematical model for operation scheduling. Finally, we can increase the number of opening operation and reduce the average hospital stay . It has universal meaning in hospital service management.