Optimization of Jump Stochastic Systems

本研究计画探讨具有单一与多重特性之连续时间跳变随机系统之动态最佳化。 该项目的目标是：（i）开发新的理论结果，描述适用于大类工程系统的问题的最优策略的结构，并提供计算最优策略的有效算法，以及（ii）将这些结果应用于解决生产，服务，信息和其他人造系统的特定优化问题。 该项目包括两个主要部分。 第一部分发展了新的方法，跳跃随机系统的分析基础上：（a）开发新的近似的客观标准的非折扣连续时间跳跃过程，（B）开发这样的过程，描述了最优策略的结构，并提供算法计算，（c）研究多目标问题和相应的无限维线性规划的理论。 利用这些技术将导致发展新的结果的连续时间跳跃随机系统的多目标和约束的优化。 这些结果将包括描述的最优策略的结构与无界成本函数和计算算法的未贴现问题。 该项目的第二部分涉及第一部分的结果的应用，以分析和优化特定的工程和运营管理模型。 该项目的第一部分的结果将被应用到随机需求的生产，服务和库存系统，更换和预防性维护问题，能源管理，以及其他工程问题，这项研究的智力影响是，它将开发新的方法来优化广泛的跳跃随机系统。 它将有助于更好地理解最优策略的结构，并开发计算算法。 它将提高我们管理生产、服务、信息、能源和其他人造系统的能力。 该项目更广泛的影响是，它将有助于科学和工程人力资源的开发，技术进步，以及工业界和学术界之间的互利互动。

This research project investigates dynamic optimization of continuous time jump stochastic systems with single and multiple performance characteristics. The goals of this project are: (i) to develop new theoretical results that describe the structure of optimal strategies for problems that are applicable to large classes of engineering systems and provide efficient algorithms for computation of optimal policies, and (ii) to apply these results to solve particular optimization problems for production, service, information, and other man-made systems. This project consists of two major parts. The first part develops new methods for the analysis of jump stochastic systems based on: (a) developing new approximations of objective criteria for undiscounted continuous-time jump processes, (b) developing a theory of such processes that describes the structure of optimal policies and provides algorithms for their computation, (c) studying multiple-objective problems and the corresponding infinite-dimensional linear programs. The utilization of these techniques will lead to the development of new results for the optimization of continuous time jump stochastic systems with multiple objectives and constraints. These results will include the description of the structure of optimal strategies for undiscounted problems with unbounded cost functions and the algorithms for their computation. The second part of this project deals with the applications of the results of the first part to the analysis and optimization of particular engineering and operations management models. The results of the first part of this project will be applied to production, service, and inventory systems with stochastic demand, to replacement and preventive maintenance problems, to energy management, and to other engineering problems.The intellectual impact of this research is that it will develop new methods for optimization of broad classes of jump stochastic systems. It will contribute to a better understanding of the structure of optimal policies and develop algorithms for their computation. It will improve our ability to manage production, service, information, energy, and other man-made systems. The broader impact of this project is that it will contribute to the development of human resources in science and engineering, to technological progress, and to mutually beneficial interactions between industry and academia.