Environmental Systems Engineering and Economics emphasizes the application of optimization, economics, and systems engineering to problems in environmental resources management. This senior level/graduate textbook introduces optimization theory and algorithms that have been successful in resolving water quality and groundwater management problems. Both linear programming and nonlinear optimization are presented. Multiobjective optimization and the linked simulation-optimization (LSO) methodology are also introduced. The basic principles of economics and engineering economics are also…mehr
Environmental Systems Engineering and Economics emphasizes the application of optimization, economics, and systems engineering to problems in environmental resources management. This senior level/graduate textbook introduces optimization theory and algorithms that have been successful in resolving water quality and groundwater management problems. Both linear programming and nonlinear optimization are presented. Multiobjective optimization and the linked simulation-optimization (LSO) methodology are also introduced. The basic principles of economics and engineering economics are also discussed to provide a framework for economic decision making. This text contains numerous example problems. Case studies are presented that address water resources management issues in the north China plain, the control of saltwater intrusion in Jakarta, Indonesia, and groundwater resources management in the Yun Lin basin, Taiwan.
1. Introduction to Environmental Systems Engineering.- 1.1 Introduction.- 1.2 Systems Engineering.- 1.3 Mathematical Models.- 1.4 The Systems Engineering Problem.- 1.5 Systems Engineering Problems.- 1.6 The Model Building Process.- 1.7 Simulation Modeling.- 1.8 Optimization Modeling.- References.- Problems.- 2. An Introduction to Optimization Theory.- 2.1 Introduction.- 2.2 Classification of Optimization Models.- 2.3 Geometry of the Mathematical Optimization Problem.- 2.4 Nonlinear Optimization and Types of Maxima.- 2.5 Convex Sets and Functions.- 2.6 Weierstrass Theorems.- 2.7 The Local-Global Theorem.- 2.8 The Kuhn-Tucker Conditions.- 2.9 The Kuhn-Tucker Theorem.- 2.10 Interpretation of the Lagrange Multipliers.- 2.11 The Saddle Point Problem.- 2.12 Maximin Dual Problem.- References.- Problems.- 3. Microeconomics: Theory of Production.- 3.1 Introduction.- 3.2 The Competitive Economy.- 3.3 The Production Function.- 3.4 Theory of the Firm.- 3.5 Maximum Output Model.- 3.6 Production Optimization.- 3.6.1 Cost Functions.- 3.6.2 Externalities.- 3.7 Comparative Statics of the Firm.- 3.8 Public Project Evaluation.- 3.9 Case Study 1- Agricultural Benefits.- 3.9.1 Introduction.- 3.9.2 Economic Model.- 3.9.3 Model Results and Conclusions.- References.- Problems.- 4. Microeconomics: Theory of the Household.- 4.1 Introduction.- 4.2 Commodity Space and Preference Relations.- 4.3 Theory of the Household.- 4.4 Comparative Statics.- 4.5 General Equilibrium.- 4.5.1 Classical General Equilibrium.- 4.5.2 Neoclassical General Equilibrium.- 4.6 Market Equilibrium.- References.- Problems.- 5. Engineering Economics.- 5.1 Introduction.- 5.2 The Time Value of Money.- 5.3 Engineering Economic Formulas.- 5.4 Evaluation of Alternatives.- 5.5 Present Worth Method.- 5.6 Annual Worth Method.- 5.7 Benefit Cost Ratio.- 5.8 Internal Rate of Return.- 5.9 Depreciation and Income Tax Analysis.- 5.9.1 Depreciation Methods.- 5.9.2 Pre-1982 Depreciation Methods.- 5.10 Inflation.- References.- Problems.- 6. Linear Programming.- 6.1 Introduction.- 6.2 Optimality of Linear Programming Problems.- 6.3 Standard Form.- 6.4 Basic and Basic Feasible Solutions.- 6.5 The Simplex Algorithm.- 6.6 The Simplex Tableau.- 6.7 The Two-Phase Method.- 6.8 General Summary of the Simplex Algorithm.- 6.9 Duality.- 6.10 Matrix Representation of the Simplex Method.- 6.11 Economic Interpretation of the Dual Problem.- 6.12 The Revised Simplex Method.- 6.13 Sensitivity Analysis.- 6.13.1 Changes in the Cost Coefficients.- 6.13.2 Changes in the Coefficient Matr.- 6.13.3 Changes in the Constant Vector.- 6.14 Large-Scale Linear Programming Models.- 6.14.1 Commercial Codes.- 6.14.2 Matrix Generators and MPS Data.- 6.14.3 Computational Efficiency.- 6.15 Case Study 1 Groundwater Planning.- 6.15.1 Introduction.- 6.15.2 Groundwater Optimization Model.- 6.15.3 Model Application.- 6.15.4 Conclusions.- References.- Problems.- 7. Nonlinear Programming.- 7.1 Introduction.- 7.2 Unconstrained Optimization Methods.- 7.2.1 Indirect Methods.- 7.2.2 Direct Methods.- 7.2.3 Dichotomous Search Method.- 7.2.4 Cauchy Cyclic Coordinate Ascent.- 7.2.5 Powell's Conjugate Direction Method.- 7.3 Gradient-Based Methods.- 7.3.1 Cauchy's Method.- 7.3.2 Newton's Method.- 7.3.3 Marquardt's Algorithm.- 7.4 Constrained Optimization Methods.- 7.4.1 Separable Programming.- 7.4.2 Frank-Wolfe Algorithm.- 7.4.3 Tin's Algorithm.- 7.4.4 The Reduced Gradient Method.- 7.4.5 The Generalized Reduced Gradient Method.- 7.4.6 The Convex Simplex Method.- 7.4.7 Box's Algorithm.- 7.5 Case Study 1 North China Plain Water Management.- 7.5.1 The Management Model.- 7.5.2 Production Functions.- 7.5.3 Model Application.- 7.5.4 Model Results.- 7.5.5 Conclusions.- 7.6 Dynamic Programming.- 7.7 Case Study 2 Water Quality Management.- 7.7.1 Introduction.- 7.7.2 Mathematical Model.- 7.7.3 The Management Model.- 7.7.4 Dynamic Programming Solution.- 7.7.5 Model Application and Results.- 7.7.6 Conclusions.- 7.8 linked Simulation-Optimization Methodology.- 7.9 Case Study 3 Management of Saltwater Intrusion.- 7.9.1 Introduction.- 7.9.2 Management Model.- 7.9.3 Optimization Analysis.- 7.9.4 Conclusions.- 7.10 Case Study 4 Groundwater Remediation.- 7.10.1 Introduction.- 7.10.2 Groundwater Optimization Remediation Model.- 7.10.3 Optimization Results.- 7.10.4 Conclusions.- 7.11 Multiobjective Optimization.- 7.11.1 Kuhn-Tucker Conditions for Nondominated Solutions.- 7.11.2 Weighting Method.- 7.11.3 The Constraint Method.- 7.11.4 Overview of Generating Techniques.- 7.11.5 Goal Programming.- 7.12 Case Study 5 Equity in Water Quality Management.- 7.12.1 Equity Measures.- 7.12.2 Model Application and Results.- 7.12.3 Conclusions.- References.- Problems.- Appendix A. Review of Mathematics.- A.1 Introduction.- A.2 Analysis.- A.3 Vectors and Matrices.- A.4 Matrix Operations.- A.5 Determinants and the Matrix Inverse.- A.6 Quadratic Forms.- A.7 Scalar, Vector, and Matrix Derivatives.- A.8 Directional Derivative.- A.9 Eigenvalues and Eigenvectors.- A.10 Implicit Function Theorem.- A.ll Taylor Series.- A.12 Leibnitz's Rule.- References.- Appendix B. Classical Optimization.- B.1 Introduction.- B.2 The Unconstrained Optimization Problem.- B.3 The Lagrange Multiplier Method.- B.4 The Lagrange Multiplier.- References.
1. Introduction to Environmental Systems Engineering.- 1.1 Introduction.- 1.2 Systems Engineering.- 1.3 Mathematical Models.- 1.4 The Systems Engineering Problem.- 1.5 Systems Engineering Problems.- 1.6 The Model Building Process.- 1.7 Simulation Modeling.- 1.8 Optimization Modeling.- References.- Problems.- 2. An Introduction to Optimization Theory.- 2.1 Introduction.- 2.2 Classification of Optimization Models.- 2.3 Geometry of the Mathematical Optimization Problem.- 2.4 Nonlinear Optimization and Types of Maxima.- 2.5 Convex Sets and Functions.- 2.6 Weierstrass Theorems.- 2.7 The Local-Global Theorem.- 2.8 The Kuhn-Tucker Conditions.- 2.9 The Kuhn-Tucker Theorem.- 2.10 Interpretation of the Lagrange Multipliers.- 2.11 The Saddle Point Problem.- 2.12 Maximin Dual Problem.- References.- Problems.- 3. Microeconomics: Theory of Production.- 3.1 Introduction.- 3.2 The Competitive Economy.- 3.3 The Production Function.- 3.4 Theory of the Firm.- 3.5 Maximum Output Model.- 3.6 Production Optimization.- 3.6.1 Cost Functions.- 3.6.2 Externalities.- 3.7 Comparative Statics of the Firm.- 3.8 Public Project Evaluation.- 3.9 Case Study 1- Agricultural Benefits.- 3.9.1 Introduction.- 3.9.2 Economic Model.- 3.9.3 Model Results and Conclusions.- References.- Problems.- 4. Microeconomics: Theory of the Household.- 4.1 Introduction.- 4.2 Commodity Space and Preference Relations.- 4.3 Theory of the Household.- 4.4 Comparative Statics.- 4.5 General Equilibrium.- 4.5.1 Classical General Equilibrium.- 4.5.2 Neoclassical General Equilibrium.- 4.6 Market Equilibrium.- References.- Problems.- 5. Engineering Economics.- 5.1 Introduction.- 5.2 The Time Value of Money.- 5.3 Engineering Economic Formulas.- 5.4 Evaluation of Alternatives.- 5.5 Present Worth Method.- 5.6 Annual Worth Method.- 5.7 Benefit Cost Ratio.- 5.8 Internal Rate of Return.- 5.9 Depreciation and Income Tax Analysis.- 5.9.1 Depreciation Methods.- 5.9.2 Pre-1982 Depreciation Methods.- 5.10 Inflation.- References.- Problems.- 6. Linear Programming.- 6.1 Introduction.- 6.2 Optimality of Linear Programming Problems.- 6.3 Standard Form.- 6.4 Basic and Basic Feasible Solutions.- 6.5 The Simplex Algorithm.- 6.6 The Simplex Tableau.- 6.7 The Two-Phase Method.- 6.8 General Summary of the Simplex Algorithm.- 6.9 Duality.- 6.10 Matrix Representation of the Simplex Method.- 6.11 Economic Interpretation of the Dual Problem.- 6.12 The Revised Simplex Method.- 6.13 Sensitivity Analysis.- 6.13.1 Changes in the Cost Coefficients.- 6.13.2 Changes in the Coefficient Matr.- 6.13.3 Changes in the Constant Vector.- 6.14 Large-Scale Linear Programming Models.- 6.14.1 Commercial Codes.- 6.14.2 Matrix Generators and MPS Data.- 6.14.3 Computational Efficiency.- 6.15 Case Study 1 Groundwater Planning.- 6.15.1 Introduction.- 6.15.2 Groundwater Optimization Model.- 6.15.3 Model Application.- 6.15.4 Conclusions.- References.- Problems.- 7. Nonlinear Programming.- 7.1 Introduction.- 7.2 Unconstrained Optimization Methods.- 7.2.1 Indirect Methods.- 7.2.2 Direct Methods.- 7.2.3 Dichotomous Search Method.- 7.2.4 Cauchy Cyclic Coordinate Ascent.- 7.2.5 Powell's Conjugate Direction Method.- 7.3 Gradient-Based Methods.- 7.3.1 Cauchy's Method.- 7.3.2 Newton's Method.- 7.3.3 Marquardt's Algorithm.- 7.4 Constrained Optimization Methods.- 7.4.1 Separable Programming.- 7.4.2 Frank-Wolfe Algorithm.- 7.4.3 Tin's Algorithm.- 7.4.4 The Reduced Gradient Method.- 7.4.5 The Generalized Reduced Gradient Method.- 7.4.6 The Convex Simplex Method.- 7.4.7 Box's Algorithm.- 7.5 Case Study 1 North China Plain Water Management.- 7.5.1 The Management Model.- 7.5.2 Production Functions.- 7.5.3 Model Application.- 7.5.4 Model Results.- 7.5.5 Conclusions.- 7.6 Dynamic Programming.- 7.7 Case Study 2 Water Quality Management.- 7.7.1 Introduction.- 7.7.2 Mathematical Model.- 7.7.3 The Management Model.- 7.7.4 Dynamic Programming Solution.- 7.7.5 Model Application and Results.- 7.7.6 Conclusions.- 7.8 linked Simulation-Optimization Methodology.- 7.9 Case Study 3 Management of Saltwater Intrusion.- 7.9.1 Introduction.- 7.9.2 Management Model.- 7.9.3 Optimization Analysis.- 7.9.4 Conclusions.- 7.10 Case Study 4 Groundwater Remediation.- 7.10.1 Introduction.- 7.10.2 Groundwater Optimization Remediation Model.- 7.10.3 Optimization Results.- 7.10.4 Conclusions.- 7.11 Multiobjective Optimization.- 7.11.1 Kuhn-Tucker Conditions for Nondominated Solutions.- 7.11.2 Weighting Method.- 7.11.3 The Constraint Method.- 7.11.4 Overview of Generating Techniques.- 7.11.5 Goal Programming.- 7.12 Case Study 5 Equity in Water Quality Management.- 7.12.1 Equity Measures.- 7.12.2 Model Application and Results.- 7.12.3 Conclusions.- References.- Problems.- Appendix A. Review of Mathematics.- A.1 Introduction.- A.2 Analysis.- A.3 Vectors and Matrices.- A.4 Matrix Operations.- A.5 Determinants and the Matrix Inverse.- A.6 Quadratic Forms.- A.7 Scalar, Vector, and Matrix Derivatives.- A.8 Directional Derivative.- A.9 Eigenvalues and Eigenvectors.- A.10 Implicit Function Theorem.- A.ll Taylor Series.- A.12 Leibnitz's Rule.- References.- Appendix B. Classical Optimization.- B.1 Introduction.- B.2 The Unconstrained Optimization Problem.- B.3 The Lagrange Multiplier Method.- B.4 The Lagrange Multiplier.- References.
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