Optimization of Jump Stochastic Systems

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.