Optimization of Jump Stochastic Systems

本研究项目研究具有单一和多个性能特征的连续时间跳跃随机系统的动态优化问题。这个项目的目标是：(I)发展新的理论结果，描述适用于大类工程系统的问题的最优策略的结构，并为最优策略的计算提供有效的算法；(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。这个项目由两个主要部分组成。第一部分发展了分析跳跃随机系统的新方法，其基础是：(A)发展了非折扣连续时间跳跃过程的客观准则的新近似，(B)发展了描述最优策略结构并提供其计算算法的这类过程的理论，(C)研究了多目标问题和相应的无限维线性规划。这些技术的应用将为具有多目标和约束的连续时间跳跃随机系统的优化提供新的结果。这些结果将包括对具有无界成本函数的未折扣问题的最优策略的结构和计算算法的描述。本项目的第二部分涉及第一部分的结果在特定工程和运营管理模型的分析和优化中的应用。本项目第一部分的研究成果将应用于随机需求的生产、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，它将为广义跳跃随机系统的优化开发新的方法。它将有助于更好地理解最优策略的结构，并为其计算开发算法。它将提高我们管理生产、服务、信息、能源等人造系统的能力。该项目的更广泛影响是，它将有助于科学和工程人力资源的开发，促进技术进步，并促进产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.