实际调度运作中，作业等待时间和设备空闲都是浪费；并且很多问题参数难以事先精确确定，迫切需要鲁棒优化研究。因此，本项目拟研究显式结合等待时间的鲁棒式并行机调度问题。具体地：（1）研究结合紧急作业最大等待时间承诺约束的并行机调度问题，解析计算复杂度等问题特性，从约束条件角度探究系统对紧急作业的耐受程度；（2）从目标角度显式体现等待时间最小化，建立以作业等待时间方差和等为目标的调度模型，并基于模型等价转换，开发分支定价算法精确求解；（3）研究结合区间不确定性参数和等待时间的鲁棒式并行机调度问题，利用问题特性开发精确分解算法，并就作业可接受与否决策进行拓展研究。最后，通过实例数据检验和完善模型，并对算法性能进行测试分析。本项目的研究有助于建立结合等待时间的鲁棒式调度问题的建模、优化理论和方法体系，对调度管理理论和方法的深化和拓展应用具有一定的贡献，对提高资源运营效率和减少无效等待也具有积极意义。

In practical scheduling and operations, both waiting times of jobs and idles times of devices are wastes; in addition, many parameters of scheduling problems cannot be determined accurately beforehand, which desperately needs the study of robust optimization for production scheduling. Therefore, this project is to study the robust optimization of production scheduling problem in parallel-machine environment with the explicit consideration of waiting times. The core research contents include: (1) the project is to study the parallel-machine scheduling problem integrated with the constraints of maximum waiting time for an emergency job, which may be arrived at any time in the planning horizon. The analytical analysis of the problem including the computational complexity will be conducted. From the perspective of constraints, the study of this kind of problem is to explore how the system response to the emergency job arriving at any time and how to analyze the effect of the emergency job on the scheduling system. (2) From the perspective of objective functions, the project is to formulate the scheduling problem with the objectives related to waiting time variances, such as the sum of waiting time variances. Based on the equivalent reformulations, exact branch and price algorithms will be developed for the problem. (3) The project is to exploit the robust parallel-machine scheduling problem with the constraint of waiting times and the interval data like processing times and due dates. Effective decomposition based algorithms will be developed based on the analytical analysis of the problem. Moreover, the problem will be extended with the additional decisions about the job acceptance or not. Finally, based on data from practical applications, the models will be checked and improved, and the performance of algorithms can be tested and evaluated. .The study of the project is quite helpful for model building, the theory of optimization and systematic solutions to the robust optimization problem of production scheduling with the explicit consideration of waiting times. It is, to some extent, can also deepen the theory of production scheduling and can also guide potential practical applications. Meanwhile, the study of the project is supposed to improve the utilization of the resources and also to reduce the unnecessary waiting times.