不确定更新过程及其在生产计划中的应用

Uncertain process is a powerful tool for modeling the evolution of uncertain phenomenon. As an important case of uncertain process, uncertain renewal process can be used to represent the amount of production or demand evolving with respect to time. At present, the theory of uncertain renewal process has developed stably, and the models for the related problems have been introduced. To apply uncertain renewal process in production scheduling, we will further perfect the theory and algorithm, as well as improve the reliability of decision making by introducing concepts such as shortage risk index. This project is an interdisciplinary field among operations research, information science, management science and computer science. Our research consists of theory, algorithm and application. At the part of theory, we develop uncertain renewal process to the processes of production and demand. At the part of algorithm, we propose some equivalent forms of production scheduling with uncertain renewal process and optimize the accuracy for numerical computation. At the part of application, we try to help the decision makers set up the optimal production scheduling and minimize the cost of enterprise in a given risk level by the theory of uncertain renewal process. Finally, a complete theory of uncertain renewal process and its application in process scheduling will be founded.

不确定过程是研究随时间演变的不确定现象的有力工具。而作为一类重要的不确定过程，不确定更新过程可用以表示随时间变化的生产量或需求量。目前，不确定更新过程的理论得到稳定的发展，相关问题的数学模型亦得以建立。为了把不确定更新过程应用至实际的生产计划问题上，本项目组将会进一步加强其理论体系及算法基础研究。通过引入缺货风险指数等概念以提高决策的可靠性。本项目是运筹学、信息科学、管理科学及计算机科学的交叉项目，研究内容主要有理论、算法和应用三个方面。理论部分包括拓展不确定更新过程的内容至生产过程和需求过程，算法部分包括生产计划问题的等价形式以及数值计算精度的提升，应用部分包括如何在给定风险水平的限制下，通过不确定更新过程这一工具，使得决策者作出最优的生产计划，实现成本最小化，并且最终形成一套完整的不确定更新过程理论并应用到生产计划的指导体系中。

大量的实证案例都表明，即使研究者可以得到充足的数据，现实中的样本也无法满足概率论意义下的同分布假设，因此应该把研究对象刻画成不确定变量。为了解决实际生产计划中的决策问题，本项目研究了不确定更新过程及其应用。首先，本项目成功完善了不确定更新过程理论，研究了不确定随机更新过程、不确定保险模型以及不确定排队模型，进而丰富了不确定更新过程的理论框架及研究工具。其次，本项目也通过引入缺货指数和缺货时间等概念，成功建立了不确定生产模型，为生产商在实际生产计划中决策提供了有力指导。不仅如此，本项目还有广泛的拓展，包括不确定回归分析、不确定时间序列分析、不确定假设检验、不确定微分方程、不确定数据包络分析和艾尔斯伯格罐子问题等领域。文献表明，本项目的研究成果在生产、管理、工程、物流等领域中都有广泛的应用。