Stochastic Models In Operations Research

This volume of a 2-volume set explores the central facts and ideas of stochastic processes, illustrating their use in models based on applied and theoretical investigations. Explores stochastic processes, operating characteristics of stochastic systems, and stochastic optimization. Comprehensive in its scope, this graduate-level text emphasizes the practical importance, intellectual stimulation, and mathematical elegance of stochastic models.

Decision-making is an important task no matter the industry. Operations research, as a discipline, helps alleviate decision-making problems through the extraction of reliable information related to the task at hand in order to come to a viable solution. Integrating stochastic processes into operations research and management can further aid in the decision-making process for industrial and management problems. Stochastic Processes and Models in Operations Research emphasizes mathematical tools and equations relevant for solving complex problems within business and industrial settings. This research-based publication aims to assist scholars, researchers, operations managers, and graduate-level students by providing comprehensive exposure to the concepts, trends, and technologies relevant to stochastic process modeling to solve operations research problems.

This two-volume set of texts explores the central facts and ideas of stochastic processes, illustrating their use in models based on applied and theoretical investigations. They demonstrate the interdependence of three areas of study that usually receive separate treatments: stochastic processes, operating characteristics of stochastic systems, and stochastic optimization. Comprehensive in its scope, they emphasize the practical importance, intellectual stimulation, and mathematical elegance of stochastic models and are intended primarily as graduate-level texts.

Stochastic models are everywhere. In manufacturing, queuing models are used for modeling production processes, realistic inventory models are stochastic in nature. Stochastic models are considered in transportation and communication. Marketing models use stochastic descriptions of the demands and buyer's behaviors. In finance, market prices and exchange rates are assumed to be certain stochastic processes, and insurance claims appear at random times with random amounts. To each decision problem, a cost function is associated. Costs may be direct or indirect, like loss of time, quality deterioration, loss in production or dissatisfaction of customers. In decision making under uncertainty, the goal is to minimize the expected costs. However, in practically all realistic models, the calculation of the expected costs is impossible due to the model complexity. Simulation is the only practicable way of getting insight into such models. Thus, the problem of optimal decisions can be seen as getting simulation and optimization effectively combined. The field is quite new and yet the number of publications is enormous. This book does not even try to touch all work done in this area. Instead, many concepts are presented and treated with mathematical rigor and necessary conditions for the correctness of various approaches are stated. Optimization of Stochastic Models: The Interface Between Simulation and Optimization is suitable as a text for a graduate level course on Stochastic Models or as a secondary text for a graduate level course in Operations Research.

"Constructive Computation in Stochastic Models with Applications: The RG-Factorizations" provides a unified, constructive and algorithmic framework for numerical computation of many practical stochastic systems. It summarizes recent important advances in computational study of stochastic models from several crucial directions, such as stationary computation, transient solution, asymptotic analysis, reward processes, decision processes, sensitivity analysis as well as game theory. Graduate students, researchers and practicing engineers in the field of operations research, management sciences, applied probability, computer networks, manufacturing systems, transportation systems, insurance and finance, risk management and biological sciences will find this book valuable. Dr. Quan-Lin Li is an Associate Professor at the Department of Industrial Engineering of Tsinghua University, China.

Industrial engineering has expanded from its origins in manufacturing to transportation, health care, logistics, services, and more. A common denominator among all these industries, and one of the biggest challenges facing decision-makers, is the unpredictability of systems. Probability Models in Operations Research provides a comprehensive