Title Details: | |
Stochastic Models in Operations Research |
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Authors: |
Burnetas, Apostolos Economou, Antonis |
Subject: | MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > PROBABILITY THEORY AND STOCHASTIC PROCESSES > STOCHASTIC PROCESSES MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > PROBABILITY THEORY AND STOCHASTIC PROCESSES > MARKOV PROCESSES MATHEMATICS AND COMPUTER SCIENCE > MATHEMATICS > OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING > OPERATIONS RESEARCH AND MANAGEMENT SCIENCE |
Keywords: |
Stochastic Processes
Renewal Processes Markov Processes Markovian Decision Processes Dynamic Programming Queueing Theory Inventory Theory |
Description: | |
Abstract: |
In this book we present an introduction to Stochastic Operations Research, a discipline focused on creating mathematical techniques for assessing performance and optimizing systems and processes that operate under uncertainty. Our primary aim is to provide the reader with a thorough understanding of how to apply the fundamental methods of Stochastic Operations Research with precision, as well as to analyze numerous applications, without overwhelming complexity. To achieve this objective, we present the theoretical framework in an exact and concise manner, including assumptions and mathematical results, along with simplified proofs and explanations, without excessive technical details. From a mathematical perspective, the book focuses on two essential methodological tools: Stochastic Processes with Cost Structure and Stochastic Dynamic Programming. Within the first category we analyze some fundamental models, such as renewal processes and Markovian processes with associated costs. We then extend this framework by introducing decision-making aspects, resulting in the exploration of Stochastic Dynamic Programming and Markov Decision Processes under different optimization criteria. In terms of practical applications, we present an introduction to two core areas: Queueing Theory and Inventory Management. We formulate and analyze problems in these areas utilizing the methods developed in first part. We include an introduction to Queueing Theory, with references to various problem types and an emphasis on modeling and performance assessment. We also consider problems related to the optimal design and dynamic control of service systems. Lastly, we present an introduction to Inventory Management Theory, covering essential concepts and highlighting stochastic models dealing with demand uncertainty.
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Linguistic Editors: |
Kalliaras, Dimitrios |
Technical Editors: |
Burnetas, Apostolos Economou, Antonis |
Type: |
Undergraduate textbook |
Creation Date: | 25-02-2024 |
Item Details: | |
License: |
Attribution - NonCommercial - ShareAlike 4.0 International (CC BY-NC-SA 4.0) |
DOI | http://dx.doi.org/10.57713/kallipos-497 |
Handle | http://hdl.handle.net/11419/12645 |
Bibliographic Reference: | Burnetas, A., & Economou, A. (2024). Stochastic Models in Operations Research [Undergraduate textbook]. Kallipos, Open Academic Editions. https://dx.doi.org/10.57713/kallipos-497 |
Language: |
Greek |
Consists of: |
1. Renewal processes with costs: Basic theory 2. Renewal processes with costs: Applications 3. Markov chains with costs: Basic theory 4. Markov chains with costs: Applications 5. Dynamic Programming and finite-horizon Markov Decision Processes 6. Infinite-horizon Markov Decision Processes: Discounted cost criterion 7. Infinite-horizon Markov Decision Processes: Average cost criterion 8. Basic elements of queueing theory 9. Queueing theory: performance evaluation 10. Queueing control 11. Basic models of Inventory Theory 12. Multi-period inventory control under uncertainty |
Number of pages |
266 |
Publication Origin: |
Kallipos, Open Academic Editions |
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