Introduction to Optimization-Based Decision-Making:
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Milton
CRC Press LLC
2021
|
| Schriftenreihe: | Chapman and Hall/CRC Series in Operations Research Ser
|
| Online-Zugang: | HWR01 |
| Beschreibung: | Description based on publisher supplied metadata and other sources |
| Beschreibung: | 1 Online-Ressource (265 Seiten) |
| ISBN: | 9781351778718 |
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| 245 | 1 | 0 | |a Introduction to Optimization-Based Decision-Making |
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| 505 | 8 | |a Cover -- Half Title -- Series Page -- Title Page -- Copyright Page -- Dedication -- Table of Contents -- Foreword -- Preface -- Author -- Chapter 1 First Notes on Optimization for Decision Support -- 1.1 Introduction -- 1.2 First Steps -- 1.2.1 The Furniture Factory Problem: First Level -- 1.3 Introducing Proportionality -- 1.3.1 The Furniture Factory Problem: Second Level -- 1.4 A Non-Proportional Instance -- 1.4.1 The Furniture Factory Problem: Third Level -- 1.5 An Enlarged and Non-Proportional Instance -- 1.5.1 The Furniture Factory Problem: Fourth Level -- 1.6 Concluding Remarks -- Chapter 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 -- Chapter 3 Linear Programming Basics -- 3.1 Introduction -- 3.2 Graphical Approach -- 3.3 Algebraic Form -- 3.3.1 First Iteration -- 3.3.2 Second Iteration -- 3.3.3 Third Iteration -- 3.4 Tableau Form -- 3.4.1 Iterative Cycle: First Iteration -- 3.4.2 Second Tableau -- 3.4.3 Third Tableau -- 3.5 Matrix Form -- 3.5.1 First Iteration -- 3.5.2 Second Iteration -- 3.5.3 Third Iteration -- 3.6 Updating the Inverse Matrix -- 3.7 Concluding Remarks -- Chapter 4 Duality -- 4.1 Introduction -- 4.2 Primal-Dual Transformations -- 4.3 Dual Simplex Method -- 4.3.1 First Iteration -- 4.3.2 Second Iteration -- 4.3.3 Dual Simplex in Tableau Form -- 4.4 Duality Properties -- 4.5 Duality and Economic Interpretation -- 4.6 A First Approach to Optimality Analysis -- 4.7 Concluding Remarks -- Chapter 5 Calculus Optimization -- 5.1 Introduction -- 5.1.1 One-Variable Function: Maxima and Minima -- 5.1.2 Two-Variable Function: Maxima and Minima -- 5.1.3 Two-Variable Function: Saddle Point -- 5.1.4 The Implicit Function | |
| 505 | 8 | |a 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 -- Chapter 6 Optimality Analysis -- 6.1 Introduction -- 6.2 Revising LP Simplex -- 6.2.1 Sensitivity Analysis Procedure -- 6.3 Sensitivity Analysis -- 6.3.1 Variation in the RHS Parameters, b' -- 6.3.2 Variation in the Objective Function Coefficients, c' -- 6.3.3 Introduction of New Variables -- 6.3.4 Variation in Non-Basic Coefficients -- 6.3.5 Variation in Basic Coefficients -- 6.3.6 Introduction of New Restriction -- 6.4 Parametric Analysis -- 6.4.1 Parametric Analysis: b1 -- 6.4.2 Parametric Analysis: c1 -- 6.5 Concluding Remarks -- Chapter 7 Integer Linear Programming -- 7.1 Introduction -- 7.2 Solving Integer Linear Programming Problems -- 7.2.1 The Furniture Factory Integer Problem -- 7.3 Modeling with Binary Variables -- 7.4 Solving Binary Integer Programming Problems -- 7.4.1 BIP Solution by B& -- B -- 7.4.2 The Furniture Factory Binary Integer Problem -- 7.4.3 The Problem Solution by B& -- B -- 7.5 Concluding Remarks -- Chapter 8 Game Theory -- 8.1 Introduction -- 8.2 Constant-Sum Game -- 8.2.1 Constant-Sum Game with Stable Equilibrium -- 8.2.2 Constant-Sum Game with Cycle -- 8.3 Zero-Sum Game -- 8.3.1 Zero-Sum Game with Stable Equilibrium -- 8.3.2 Zero-Sum Game with Cycle -- 8.4 Mixed Strategies: LP Approach -- 8.4.1 Player-One: Mixed Strategies and LP -- 8.4.2 Player-Two: Mixed Strategies and LP -- 8.4.3 Primal-Dual Approaches for Zero-Sum Game with Cycle -- 8.5 Dominant Strategies -- 8.5.1 Player-One: Dominant Strategies and LP -- 8.5.2 Player-Two: Dominant Strategies and LP -- 8.6 Concluding Remarks -- Chapter 9 Decision-Making Under Uncertainty -- 9.1 Introduction -- 9.2 Multiple Criteria and Decision-Maker Values | |
| 505 | 8 | |a 9.3 Capacity Expansion for the Furniture Factory -- 9.3.1 The Furniture Factory's Capacity Expansion Problem -- 9.4 A Comparison Analysis -- 9.5 Concluding Remarks -- Chapter 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 -- 10.4.1 Analytical Insights -- 10.4.2 Graphical Analysis -- 10.4.3 Notes on the Robust Approach -- 10.5 Concluding Remarks -- Selected References -- Index | |
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| contents | Cover -- Half Title -- Series Page -- Title Page -- Copyright Page -- Dedication -- Table of Contents -- Foreword -- Preface -- Author -- Chapter 1 First Notes on Optimization for Decision Support -- 1.1 Introduction -- 1.2 First Steps -- 1.2.1 The Furniture Factory Problem: First Level -- 1.3 Introducing Proportionality -- 1.3.1 The Furniture Factory Problem: Second Level -- 1.4 A Non-Proportional Instance -- 1.4.1 The Furniture Factory Problem: Third Level -- 1.5 An Enlarged and Non-Proportional Instance -- 1.5.1 The Furniture Factory Problem: Fourth Level -- 1.6 Concluding Remarks -- Chapter 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 -- Chapter 3 Linear Programming Basics -- 3.1 Introduction -- 3.2 Graphical Approach -- 3.3 Algebraic Form -- 3.3.1 First Iteration -- 3.3.2 Second Iteration -- 3.3.3 Third Iteration -- 3.4 Tableau Form -- 3.4.1 Iterative Cycle: First Iteration -- 3.4.2 Second Tableau -- 3.4.3 Third Tableau -- 3.5 Matrix Form -- 3.5.1 First Iteration -- 3.5.2 Second Iteration -- 3.5.3 Third Iteration -- 3.6 Updating the Inverse Matrix -- 3.7 Concluding Remarks -- Chapter 4 Duality -- 4.1 Introduction -- 4.2 Primal-Dual Transformations -- 4.3 Dual Simplex Method -- 4.3.1 First Iteration -- 4.3.2 Second Iteration -- 4.3.3 Dual Simplex in Tableau Form -- 4.4 Duality Properties -- 4.5 Duality and Economic Interpretation -- 4.6 A First Approach to Optimality Analysis -- 4.7 Concluding Remarks -- Chapter 5 Calculus Optimization -- 5.1 Introduction -- 5.1.1 One-Variable Function: Maxima and Minima -- 5.1.2 Two-Variable Function: Maxima and Minima -- 5.1.3 Two-Variable Function: Saddle Point -- 5.1.4 The Implicit Function 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 -- Chapter 6 Optimality Analysis -- 6.1 Introduction -- 6.2 Revising LP Simplex -- 6.2.1 Sensitivity Analysis Procedure -- 6.3 Sensitivity Analysis -- 6.3.1 Variation in the RHS Parameters, b' -- 6.3.2 Variation in the Objective Function Coefficients, c' -- 6.3.3 Introduction of New Variables -- 6.3.4 Variation in Non-Basic Coefficients -- 6.3.5 Variation in Basic Coefficients -- 6.3.6 Introduction of New Restriction -- 6.4 Parametric Analysis -- 6.4.1 Parametric Analysis: b1 -- 6.4.2 Parametric Analysis: c1 -- 6.5 Concluding Remarks -- Chapter 7 Integer Linear Programming -- 7.1 Introduction -- 7.2 Solving Integer Linear Programming Problems -- 7.2.1 The Furniture Factory Integer Problem -- 7.3 Modeling with Binary Variables -- 7.4 Solving Binary Integer Programming Problems -- 7.4.1 BIP Solution by B& -- B -- 7.4.2 The Furniture Factory Binary Integer Problem -- 7.4.3 The Problem Solution by B& -- B -- 7.5 Concluding Remarks -- Chapter 8 Game Theory -- 8.1 Introduction -- 8.2 Constant-Sum Game -- 8.2.1 Constant-Sum Game with Stable Equilibrium -- 8.2.2 Constant-Sum Game with Cycle -- 8.3 Zero-Sum Game -- 8.3.1 Zero-Sum Game with Stable Equilibrium -- 8.3.2 Zero-Sum Game with Cycle -- 8.4 Mixed Strategies: LP Approach -- 8.4.1 Player-One: Mixed Strategies and LP -- 8.4.2 Player-Two: Mixed Strategies and LP -- 8.4.3 Primal-Dual Approaches for Zero-Sum Game with Cycle -- 8.5 Dominant Strategies -- 8.5.1 Player-One: Dominant Strategies and LP -- 8.5.2 Player-Two: Dominant Strategies and LP -- 8.6 Concluding Remarks -- Chapter 9 Decision-Making Under Uncertainty -- 9.1 Introduction -- 9.2 Multiple Criteria and Decision-Maker Values 9.3 Capacity Expansion for the Furniture Factory -- 9.3.1 The Furniture Factory's Capacity Expansion Problem -- 9.4 A Comparison Analysis -- 9.5 Concluding Remarks -- Chapter 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 -- 10.4.1 Analytical Insights -- 10.4.2 Graphical Analysis -- 10.4.3 Notes on the Robust Approach -- 10.5 Concluding Remarks -- Selected References -- Index |
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| id | DE-604.BV048226388 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T19:50:45Z |
| indexdate | 2024-07-10T09:32:31Z |
| institution | BVB |
| isbn | 9781351778718 |
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| series2 | Chapman and Hall/CRC Series in Operations Research Ser |
| spelling | de Miranda, Joao Luis Verfasser aut Introduction to Optimization-Based Decision-Making Milton CRC Press LLC 2021 ©2022 1 Online-Ressource (265 Seiten) txt rdacontent c rdamedia cr rdacarrier Chapman and Hall/CRC Series in Operations Research Ser Description based on publisher supplied metadata and other sources Cover -- Half Title -- Series Page -- Title Page -- Copyright Page -- Dedication -- Table of Contents -- Foreword -- Preface -- Author -- Chapter 1 First Notes on Optimization for Decision Support -- 1.1 Introduction -- 1.2 First Steps -- 1.2.1 The Furniture Factory Problem: First Level -- 1.3 Introducing Proportionality -- 1.3.1 The Furniture Factory Problem: Second Level -- 1.4 A Non-Proportional Instance -- 1.4.1 The Furniture Factory Problem: Third Level -- 1.5 An Enlarged and Non-Proportional Instance -- 1.5.1 The Furniture Factory Problem: Fourth Level -- 1.6 Concluding Remarks -- Chapter 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 -- Chapter 3 Linear Programming Basics -- 3.1 Introduction -- 3.2 Graphical Approach -- 3.3 Algebraic Form -- 3.3.1 First Iteration -- 3.3.2 Second Iteration -- 3.3.3 Third Iteration -- 3.4 Tableau Form -- 3.4.1 Iterative Cycle: First Iteration -- 3.4.2 Second Tableau -- 3.4.3 Third Tableau -- 3.5 Matrix Form -- 3.5.1 First Iteration -- 3.5.2 Second Iteration -- 3.5.3 Third Iteration -- 3.6 Updating the Inverse Matrix -- 3.7 Concluding Remarks -- Chapter 4 Duality -- 4.1 Introduction -- 4.2 Primal-Dual Transformations -- 4.3 Dual Simplex Method -- 4.3.1 First Iteration -- 4.3.2 Second Iteration -- 4.3.3 Dual Simplex in Tableau Form -- 4.4 Duality Properties -- 4.5 Duality and Economic Interpretation -- 4.6 A First Approach to Optimality Analysis -- 4.7 Concluding Remarks -- Chapter 5 Calculus Optimization -- 5.1 Introduction -- 5.1.1 One-Variable Function: Maxima and Minima -- 5.1.2 Two-Variable Function: Maxima and Minima -- 5.1.3 Two-Variable Function: Saddle Point -- 5.1.4 The Implicit Function 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 -- Chapter 6 Optimality Analysis -- 6.1 Introduction -- 6.2 Revising LP Simplex -- 6.2.1 Sensitivity Analysis Procedure -- 6.3 Sensitivity Analysis -- 6.3.1 Variation in the RHS Parameters, b' -- 6.3.2 Variation in the Objective Function Coefficients, c' -- 6.3.3 Introduction of New Variables -- 6.3.4 Variation in Non-Basic Coefficients -- 6.3.5 Variation in Basic Coefficients -- 6.3.6 Introduction of New Restriction -- 6.4 Parametric Analysis -- 6.4.1 Parametric Analysis: b1 -- 6.4.2 Parametric Analysis: c1 -- 6.5 Concluding Remarks -- Chapter 7 Integer Linear Programming -- 7.1 Introduction -- 7.2 Solving Integer Linear Programming Problems -- 7.2.1 The Furniture Factory Integer Problem -- 7.3 Modeling with Binary Variables -- 7.4 Solving Binary Integer Programming Problems -- 7.4.1 BIP Solution by B& -- B -- 7.4.2 The Furniture Factory Binary Integer Problem -- 7.4.3 The Problem Solution by B& -- B -- 7.5 Concluding Remarks -- Chapter 8 Game Theory -- 8.1 Introduction -- 8.2 Constant-Sum Game -- 8.2.1 Constant-Sum Game with Stable Equilibrium -- 8.2.2 Constant-Sum Game with Cycle -- 8.3 Zero-Sum Game -- 8.3.1 Zero-Sum Game with Stable Equilibrium -- 8.3.2 Zero-Sum Game with Cycle -- 8.4 Mixed Strategies: LP Approach -- 8.4.1 Player-One: Mixed Strategies and LP -- 8.4.2 Player-Two: Mixed Strategies and LP -- 8.4.3 Primal-Dual Approaches for Zero-Sum Game with Cycle -- 8.5 Dominant Strategies -- 8.5.1 Player-One: Dominant Strategies and LP -- 8.5.2 Player-Two: Dominant Strategies and LP -- 8.6 Concluding Remarks -- Chapter 9 Decision-Making Under Uncertainty -- 9.1 Introduction -- 9.2 Multiple Criteria and Decision-Maker Values 9.3 Capacity Expansion for the Furniture Factory -- 9.3.1 The Furniture Factory's Capacity Expansion Problem -- 9.4 A Comparison Analysis -- 9.5 Concluding Remarks -- Chapter 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 -- 10.4.1 Analytical Insights -- 10.4.2 Graphical Analysis -- 10.4.3 Notes on the Robust Approach -- 10.5 Concluding Remarks -- Selected References -- Index Erscheint auch als Druck-Ausgabe de Miranda, Joao Luis Introduction to Optimization-Based Decision-Making Milton : CRC Press LLC,c2021 9781138712164 |
| spellingShingle | de Miranda, Joao Luis Introduction to Optimization-Based Decision-Making Cover -- Half Title -- Series Page -- Title Page -- Copyright Page -- Dedication -- Table of Contents -- Foreword -- Preface -- Author -- Chapter 1 First Notes on Optimization for Decision Support -- 1.1 Introduction -- 1.2 First Steps -- 1.2.1 The Furniture Factory Problem: First Level -- 1.3 Introducing Proportionality -- 1.3.1 The Furniture Factory Problem: Second Level -- 1.4 A Non-Proportional Instance -- 1.4.1 The Furniture Factory Problem: Third Level -- 1.5 An Enlarged and Non-Proportional Instance -- 1.5.1 The Furniture Factory Problem: Fourth Level -- 1.6 Concluding Remarks -- Chapter 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 -- Chapter 3 Linear Programming Basics -- 3.1 Introduction -- 3.2 Graphical Approach -- 3.3 Algebraic Form -- 3.3.1 First Iteration -- 3.3.2 Second Iteration -- 3.3.3 Third Iteration -- 3.4 Tableau Form -- 3.4.1 Iterative Cycle: First Iteration -- 3.4.2 Second Tableau -- 3.4.3 Third Tableau -- 3.5 Matrix Form -- 3.5.1 First Iteration -- 3.5.2 Second Iteration -- 3.5.3 Third Iteration -- 3.6 Updating the Inverse Matrix -- 3.7 Concluding Remarks -- Chapter 4 Duality -- 4.1 Introduction -- 4.2 Primal-Dual Transformations -- 4.3 Dual Simplex Method -- 4.3.1 First Iteration -- 4.3.2 Second Iteration -- 4.3.3 Dual Simplex in Tableau Form -- 4.4 Duality Properties -- 4.5 Duality and Economic Interpretation -- 4.6 A First Approach to Optimality Analysis -- 4.7 Concluding Remarks -- Chapter 5 Calculus Optimization -- 5.1 Introduction -- 5.1.1 One-Variable Function: Maxima and Minima -- 5.1.2 Two-Variable Function: Maxima and Minima -- 5.1.3 Two-Variable Function: Saddle Point -- 5.1.4 The Implicit Function 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 -- Chapter 6 Optimality Analysis -- 6.1 Introduction -- 6.2 Revising LP Simplex -- 6.2.1 Sensitivity Analysis Procedure -- 6.3 Sensitivity Analysis -- 6.3.1 Variation in the RHS Parameters, b' -- 6.3.2 Variation in the Objective Function Coefficients, c' -- 6.3.3 Introduction of New Variables -- 6.3.4 Variation in Non-Basic Coefficients -- 6.3.5 Variation in Basic Coefficients -- 6.3.6 Introduction of New Restriction -- 6.4 Parametric Analysis -- 6.4.1 Parametric Analysis: b1 -- 6.4.2 Parametric Analysis: c1 -- 6.5 Concluding Remarks -- Chapter 7 Integer Linear Programming -- 7.1 Introduction -- 7.2 Solving Integer Linear Programming Problems -- 7.2.1 The Furniture Factory Integer Problem -- 7.3 Modeling with Binary Variables -- 7.4 Solving Binary Integer Programming Problems -- 7.4.1 BIP Solution by B& -- B -- 7.4.2 The Furniture Factory Binary Integer Problem -- 7.4.3 The Problem Solution by B& -- B -- 7.5 Concluding Remarks -- Chapter 8 Game Theory -- 8.1 Introduction -- 8.2 Constant-Sum Game -- 8.2.1 Constant-Sum Game with Stable Equilibrium -- 8.2.2 Constant-Sum Game with Cycle -- 8.3 Zero-Sum Game -- 8.3.1 Zero-Sum Game with Stable Equilibrium -- 8.3.2 Zero-Sum Game with Cycle -- 8.4 Mixed Strategies: LP Approach -- 8.4.1 Player-One: Mixed Strategies and LP -- 8.4.2 Player-Two: Mixed Strategies and LP -- 8.4.3 Primal-Dual Approaches for Zero-Sum Game with Cycle -- 8.5 Dominant Strategies -- 8.5.1 Player-One: Dominant Strategies and LP -- 8.5.2 Player-Two: Dominant Strategies and LP -- 8.6 Concluding Remarks -- Chapter 9 Decision-Making Under Uncertainty -- 9.1 Introduction -- 9.2 Multiple Criteria and Decision-Maker Values 9.3 Capacity Expansion for the Furniture Factory -- 9.3.1 The Furniture Factory's Capacity Expansion Problem -- 9.4 A Comparison Analysis -- 9.5 Concluding Remarks -- Chapter 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 -- 10.4.1 Analytical Insights -- 10.4.2 Graphical Analysis -- 10.4.3 Notes on the Robust Approach -- 10.5 Concluding Remarks -- Selected References -- Index |
| title | Introduction to Optimization-Based Decision-Making |
| title_auth | Introduction to Optimization-Based Decision-Making |
| title_exact_search | Introduction to Optimization-Based Decision-Making |
| title_exact_search_txtP | Introduction to Optimization-Based Decision-Making |
| title_full | Introduction to Optimization-Based Decision-Making |
| title_fullStr | Introduction to Optimization-Based Decision-Making |
| title_full_unstemmed | Introduction to Optimization-Based Decision-Making |
| title_short | Introduction to Optimization-Based Decision-Making |
| title_sort | introduction to optimization based decision making |
| work_keys_str_mv | AT demirandajoaoluis introductiontooptimizationbaseddecisionmaking |