Environmental Systems Engineering and Economics

477 Pages·2004·13.08 MB·English

by  Robert Willis, Brad A. Finney (auth.)

ENVIRONMENTAL SYSTEMS
ENGINEERING AND ECONOMICS
Library of Congress Cataloging-in-Publication Data
A c.l.P. Catalogue record for Ihis book is available
from the Library of Congress.
Title: Environmental Systems Engineering and Economics
Editor: Robert Willis and Brad A. Finney
ISBN 978-1-4613-5097-2 ISBN 978-1-4615-0479-5 (eBook)
DOI 10.1007/978-1-4615-0479-5
Copyright © 2004 by Springer Science+Business Media New York
Originally published by Kluwer Academic Publishers in 2004
Softcover reprint of the hardcover 1s i edition 2004
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ENVIRONMENTAL SYSTEMS
ENGINEERING AND ECONOMICS
by
Robert Willis
and
Brad A. Finney
Department of Environmental Resourees Engineering
Humboldt State University
A rea ta, California
SPRINGER SCIENCE+BUSINESS MEDIA, LLC
For Margaret Mary and
Michael, Jeff, Scott, Meera and Zack
R.W.
For my children;
while I gave them life,
they have given it back many times over.
B. A. F.
Contents
1. Introduction to Environmental Systems Engineering
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 1
1.2 Systems Engineering ............................................ 4
1.3 Mathematical Models ............................................ 6
1.4 The Systems Engineering Problem .............................. 9
1.5 Systems Engineering Problems ................................ 11
1.6 The Model Building Process ................................... 13
1. 7 Simulation Modeling ........................................... 17
1.8 Optimization Modeling ......................................... 18
References .......................................................... 33
Problems ............................................................ 34
2. An Introduction to Optimization Theory
2.1 Introduction .................................................... 39
2.2 Classification of Optimization Models ......................... 40
2.3 Geometry of the Mathematical Optimization Problem ........ 46
2.4 Nonlinear Optimization and Types of Maxima ................ 48
2.5 Convex Sets and Functions .................................... 50
2.6 Weierstrass Theorems ......................................... 59
2.7 The Local-Global Theorem ..................................... 60
2.8 The Kuhn-Tucker Conditions .................................. 63
2.9 The Kuhn-Tucker Theorem .................................... 73
2.10 Interpretation of the Lagrange Multipliers ................... 77
2.11 The Saddle Point Problem .................................... 78
2.12 Maximin Dual Problem ........................................ 80
References .......................................................... 83
Problems ............................................................ 84
3. Microeconomics: Theory of Production
3.1 Introduction .................................................... 91
3.2 The Competitive Economy ..................................... 92
3.3 The Production Function ....................................... 93
3.4 Theory of the Firm ............................................. 98
3.5 Maximum Output Model ...................................... 100
3.6 Production Optimization ..................................... 104
vi Contents
3.6.1 Cost Functions .......................................... 105
3.6.2 Externalities ............................................ 109
3.7 Comparative Statics of the Firm . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 111
3.8 Public Project Evaluation ..................................... 117
3.9 Case Study I-Agricultural Benefits .......................... 124
3.9.1 Introduction ............................................ 124
3.9.2 Economic Model ........................................ 125
3.9.3 Model Results and Conclusions ........................ 126
References ........................................................ 128
Problems .......................................................... 129
4. Microeconomics: Theory of the Household
4.1 Introduction ................................................... 135
4.2 Commodity Space and Preference Relations ................. 136
4.3 Theory of the Household ..................................... 138
4.4 Comparative Statics ........................................... 142
4.5 General Equilibrium ........................................... 145
4.5.1 Classical General Equilibrium .......................... 147
4.5.2 Neoclassical General Equilibrium . . . . . . . . . . . . . . . . . . . . .. 153
4.6 Market Equilibrium ........................................... 154
References ........................................................ 159
Problems .......................................................... 160
5. Engineering Economics
5.1 Introduction ................................................... 163
5.2 The Time Value of Money .................................... 164
5.3 Engineering Economic Formulas ............................. 166
5.4 Evaluation of Alternatives .................................... 178
5.5 Present Worth Method ........................................ 179
5.6 Annual Worth Method ........................................ 183
5.7 Benefit Cost Ratio ............................................. 185
5.8 Internal Rate of Return ....................................... 187
5.9 Depreciation and Income Tax Analysis ...................... 189
5.9.1 Depreciation Methods .................................. 190
5.9.2 Pre-1982 Depreciation Methods ........................ 191
5.10 Inflation ...................................................... 193
References ........................................................ 196
Problems .......................................................... 197
Contents vii
6. linear Programming
6.1 Introduction ................................................... 207
6.2 Optimality of linear Programming Problems ................ 219
6.3 Standard Form ................................................ 220
6.4 Basic and Basic Feasible Solutions ........................... 223
6.5 The Simplex Algorithm ....................................... 226
6.6 The Simplex Tableau .......................................... 234
6.7 The Two-Phase Method ....................................... 239
6.8 General Summary of the Simplex Algorithm. . . . . . . . . . . . . . . .. 244
6.9 Duality ......................................................... 249
6.10 Matrix Representation of the Simplex Method ............. 256
6.11 Economic Interpretation of th~ Dual Problem .............. 259
6.12 The Revised Simplex Method ............................... 261
6.13 Sensitivity Analysis ......................................... 263
6.13.1 Changes in the Cost Coefficients ..................... 264
6.13.2 Changes in the Coefficient Matrix .................... 266
6.13.3 Changes in the Constant Vector ...................... 267
6.14 Large-Scale linear Programming Models ................... 268
6.14.1 Commercial Codes .................................... 268
6.14.2 Matrix Generators and MPS Data ..................... 269
6.14.3 Computational Efficiency ............................. 272
6.15 Case Study 1 Groundwater Planning ........................ 279
6.15.1 Introduction ............................................ 279
6.15.2 Groundwater Optimization Model .................... 280
6.15.3 Model Application ..................................... 282
6.15.4 Conclusions ............................................ 283
References ........................................................ 285
Problems .......................................................... 286
7. Nonlinear Programming
7.1 Introduction ................................................... 297
7.2 Unconstrained Optimization Methods ....................... 302
7.2.1 Indirect Methods ....................................... 302
7.2.2 Direct Methods ......................................... 305
7.2.3 Dichotomous Search Method .......................... 306
7.2.4 Cauchy Cyclic Coordinate Ascent ..................... 308
7.2.5 Powell's Conjugate Direction Method ................. 309
7.3 Gradient-Based Methods ...................................... 314
7.3.1 Cauchy's Method ....................................... 314
viii Contents
7.3.2 Newton's Method ....................................... 317
7.3.3 Marquardt's Algorithm ................................. 318
7.4 Constrained Optimization Methods .......................... 320
7.4.1 Separable Programming ................................ 320
7.4.2 Frank·Wolfe Algorithm ................................. 326
7.4.3 Tw's Algorithm ......................................... 331
7.4.4 The Reduced Gradient Method ........................ 332
7.4.5 The Generalized Reduced Gradient Method ........... 338
7.4.6 The Convex Simplex Method .......................... 350
7.4.7 Box's Algorithm ........................................ 355
7.5 Case Study 1 North China Plain Water Management .......... 357
7.5.1 The Management Model ................................ 358
7.5.2 Production Functions .................................. 362
7.5.3 Model Application ...................................... 363
7.5.4 Model Results ........................................... 364
7.5.5 Conclusions ............................................. 369
7.6 Dynamic Programming ....................................... 370
7.7 Case Study 2 Water Quality Management .................... 378
7.7.1 Introduction ............................................ 379
7.7.2 Mathematical Model .................................... 379
7.7.3 The Management Model ................................ 381
7.7.4 Dynamic Programming Solution ....................... 381
7.7.5 Model Application and Results ........................ 384
7.7.6 Conclusions ............................................. 385
7.8 Linked Simulation-Optimization Methodology .............. 385
7.9 Case Study 3 Management of Saltwater Intrusion ........... 394
7.9.1 Introduction ............................................ 395
7.9.2 Management Model ..................................... 397
7.9.3 Optimization Analysis ................................. 399
7.9.4 Conclusions ............................................. 402
7.10 Case Study 4 Groundwater Remediation .................... 402
7.10.1 Introduction ........................................... .403
7.10.2 Groundwater Optimization Remediation Model ...... 405
7.10.3 Optimization Results .................................. 407
7.10.4 Conclusions ............................................ 409
7.11 Multiobjective Optimization ................................ 409
7.11.1 Kuhn-Tucker Conditions for Nondominated Solutions 412
7.11.2 Weighting Method ..................................... 412
7.11.3 The Constraint Method ............................... 413
Contents ix
7.11.4 Overview of Generating Techniques ................. 414
7.11.5 Goal Programming .................................... 414
7.12 Case Study 5 Equity in Water Quality Management ........ 415
7.12.1 Equity Measures ....................................... 417
7.12.2 Model Application and Results ....................... .418
7.12.3 Conclusions ............................................ 419
References ........................................................ 420
Problems .......................................................... 424
Appendix A. Review of Mathematics
A.l Introduction ................................................... 435
A.2 Analysis ....................................................... 435
A.3 Vectors and Matrices ......................................... 437
A.4 Matrix Operations ............................................ 439
A.5 Determinants and the Matrix Inverse ........................ 440
A.6 Quadratic Forms .............................................. 442
A.7 Scalar, Vector, and Matrix Derivatives ....................... 444
A.8 Directional Derivative ........................................ .446
A.9 Eigenvalues and Eigenvectors ................................ 447
A.I0 Implicit Function Theorem .................................. 448
A.ll Taylor Series ................................................. 449
A.12 Leibnitz's Rule ............................................... 449
References ........................................................ 451
Appendix B. Classical Optimization
B.l Introduction ................................................... 453
B.2 The Unconstrained Optimization Problem ................... 453
B.3 The Lagrange Multiplier Method .............................. 456
B.4 The Lagrange Multiplier ....................................... 461
References ......................................................... 463
Index ................................................................... 465
Preface
Environmental engineering problems, whether they involve planning,
design, or operational issues, are characterized by conflicting and com
peting objectives, economic and environmental constraints, and complex
physical, hydraulic, or hydrologic processes. The contention of this text is
that the analysis of these problems, and the development of optimal plan
ning or management policies or alternatives, and the concomitant economic
and environmental tradeoffs, can be determined using the techniques and
methodology of systems engineering.
The evolution of the text parallels the development of environmental
engineering. Initially, environmental engineering was simply a specializa
tion in civil engineering, and "systems analysis" was typically a course in
engineering economics-a course emphasizing the time value of money and
the evaluation of alternatives using, for example, annual cost and present
worth. In the mid 1960's, linear programming was introduced in traditional
engineering economics as a methodology for the analysis of resource al
location problems, including more traditional cost and risk minimization
engineering economics problems. For the first time, civil engineering prob
lems were recast into systems problems by introducing the concepts of
objectives, constraints, and decision or control variables.
As engineering began to address a wider range of environmental plan
ning and design problems, e.g. conjunctively managed surface and ground
water systems, new techniques and skills were necessary for analysis and
design. In the early 1980's a series of texts were published that attempted
to present systems analysis techniques for the civil and environmental engi
neer (see Haith, 1982; Ossenbruggen, 1984). Optimization methods such as
linear and dynamiC programming were used in the analysis of water qual
ity and air quality management issues. Microeconomics was recognized
as an important discipline since environmental engineering fundamentally
involves resource decisions. The theory of production, tradeoffs, external
ities, and economies of scale were briefly introduced and discussed.
This text is the offspring of these earlier books. And in this context, the
book represents a synthesis of methodologies, tools, and algorithms that
have been and, are used in environmental systems. No attempt has been
made to review the "state of the art" of environmental systems. Rather, the
intent is to give the student the necessary mathematical background and