Introduction to Optimization-Based Decision-Making: Chapman & Hall/CRC Series in Operations Research
Autor Joao Luis de Mirandaen Limba Engleză Paperback – 27 mai 2024
Introduction to Optimization-Based Decision-Making provides an elementary and self-contained introduction to the basic concepts involved in making decisions in an optimization-based environment. The mathematical level of the text is directed to the post-secondary reader, or university students in the initial years. The prerequisites are therefore minimal, and necessary mathematical tools are provided as needed. This lean approach is complemented with a problem-based orientation and a methodology of generalization/reduction. In this way, the book can be useful for students from STEM fields, economics and enterprise sciences, social sciences and humanities, as well as for the general reader interested in multi/trans-disciplinary approaches.
Features
- Collects and discusses the ideas underpinning decision-making through optimization tools in a simple and straightforward manner
- Suitable for an undergraduate course in optimization-based decision-making, or as a supplementary resource for courses in operations research and management science
- Self-contained coverage of traditional and more modern optimization models, while not requiring a previous background in decision theory
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Specificații
ISBN-13: 9781032119779
ISBN-10: 1032119772
Pagini: 263
Ilustrații: 98
Dimensiuni: 152 x 229 mm
Greutate: 0.45 kg
Ediția:1
Editura: CRC Press
Colecția Chapman and Hall/CRC
Seria Chapman & Hall/CRC Series in Operations Research
Locul publicării:Boca Raton, United States
ISBN-10: 1032119772
Pagini: 263
Ilustrații: 98
Dimensiuni: 152 x 229 mm
Greutate: 0.45 kg
Ediția:1
Editura: CRC Press
Colecția Chapman and Hall/CRC
Seria Chapman & Hall/CRC Series in Operations Research
Locul publicării:Boca Raton, United States
Cuprins
1. First Notes on Optimization for Decision Support. 1.1. Introduction. 1.2. First Steps. 1.3. Introducing Proportionality. 1.4. A Non-Proportional Instance. 1.5. An Enlarged and Non-Proportional Instance. 1.6. Concluding Remarks. 2. Linear Algebra. 2.1. Introduction. 2.2. Gauss Elimination on the Linear System. 2.3. Gauss Elimination with the Augmented Matrix. 2.4. Gauss-Jordan and the Inverse Matrix. 2.5. Cramer’s Rule and Determinants. 2.6. Concluding Remarks. 3. Linear Programming Basics. 3.1. Introduction. 3.2. Graphical Approach. 3.3. Algebraic Form. 3.4. Tableau Form. 3.5. Matrix Form. 3.6. Updating the Inverse Matrix. 3.7. Concluding Remarks. 4. Duality. 4.1. Introduction. 4.2. Primal-Dual Transformations. 4.3. Dual Simplex Method. 4.4. Duality Properties. 4.5. Duality and Economic Interpretation. 4.6. A First Approach to Optimality Analysis. 4.7. Concluding Remarks. 5. Calculus Optimization. 5.1. Introduction. 5.2. Constrained Optimization with Lagrange Multipliers. 5.3. Generalization of the Constrained Optimization Case. 5.4. Lagrange Multipliers for the Furniture Factory Problem. 5.5. Concluding Remarks. 6. Optimality Analysis. 6.1. Introduction. 6.2. Revising LP Simplex. 6.3. Sensitivity Analysis. 6.4. Parametric Analysis. 6.5. Concluding Remarks. 7. Integer Linear Programming. 7.1. Introduction. 7.2. Solving Integer Linear Programming Problems. 7.3. Modeling with Binary Variables. 7.4. Solving Binary Integer Programming Problems. 7.5. Concluding Remarks. 8. Game Theory. 8.1. Introduction. 8.2. Constant-Sum Game. 8.3. Zero-Sum Game. 8.4. Mixed Strategies - LP Approach. 8.5. Dominant Strategies. 8.6. Concluding Remarks. 9. Decision Making Under Uncertainty. 9.1. Introduction. 9.2. Multiple Criteria and Decision Maker Values. 9.3. Capacity Expansion for the Furniture Factory. 9.4. A Comparison Analysis. 9.5. Concluding Remarks. 10. Robust Optimization. 10.1. Introduction. 10.2. Notes on Stochastic Programming. 10.3. Robustness Promotion on Models and Solutions. 10.4. Models Generalization onto Robust Optimization. 10.5. Concluding Remarks. Selected References
Notă biografică
João Luís de Miranda is Professor at ESTG-Escola Superior de Tecnologia e Gestão (IPPortalegre) and Researcher in Optimization methods and Process Systems Engineering (PSE) at CERENA-Centro de Recursos Naturais e Ambiente (IST/ULisboa). He has been teaching for more than twenty years in the field of Mathematics (e.g., Calculus, Operations Research-OR, Management Science-MS, Numerical Methods, Quantitative Methods, Statistics) and has authored/edited several publications in Optimization, PSE, and Education subjects in Engineering and OR/MS contexts. João Luís de Miranda is addressing the research subjects through international cooperation in multidisciplinary frameworks, and is serving on several boards/committees at national and European level.
Descriere
This book provides an elementary and self-contained introduction to the basic concepts involved in making decisions in an optimization-based environment. The mathematical level of the text is directed to the post-secondary reader, or university students in the initial years.