Details

Linear Programming and Resource Allocation Modeling


Linear Programming and Resource Allocation Modeling


1. Aufl.

von: Michael J. Panik

CHF 127.00

Verlag: Wiley
Format: PDF
Veröffentl.: 15.10.2018
ISBN/EAN: 9781119509455
Sprache: englisch
Anzahl Seiten: 448

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Beschreibungen

<p><b>Guides in the application of linear programming to firm decision making, with the goal of giving decision-makers a better understanding of methods at their disposal</b></p> <p>Useful as a main resource or as a supplement in an economics or management science course, this comprehensive book addresses the deficiencies of other texts when it comes to covering linear programming theory—especially where data envelopment analysis (DEA) is concerned—and provides the foundation for the development of DEA.</p> <p><i>Linear Programming and Resource Allocation Modeling</i> begins by introducing primal and dual problems via an optimum product mix problem, and reviews the rudiments of vector and matrix operations. It then goes on to cover: the canonical and standard forms of a linear programming problem; the computational aspects of linear programming; variations of the standard simplex theme; duality theory; single- and multiple- process production functions; sensitivity analysis of the optimal solution; structural changes; and parametric programming. The primal and dual problems are then reformulated and re-examined in the context of Lagrangian saddle points, and a host of duality and complementary slackness theorems are offered. The book also covers primal and dual quadratic programs, the complementary pivot method, primal and dual linear fractional functional programs, and (matrix) game theory solutions via linear programming, and data envelopment analysis (DEA). This book:</p> <ul> <li>Appeals to those wishing to solve linear optimization problems in areas such as economics, business administration and management, agriculture and energy, strategic planning, public decision making, and health care</li> <li>Fills the need for a linear programming applications component in a management science or economics course</li> <li>Provides a complete treatment of linear programming as applied to activity selection and usage</li> <li>Contains many detailed example problems as well as textual and graphical explanations</li> </ul> <p><i>Linear Programming and Resource Allocation Modeling</i> is an excellent resource for professionals looking to solve linear optimization problems, and advanced undergraduate to beginning graduate level management science or economics students.</p>
<p>Preface xi</p> <p>Symbols and Abbreviations xv</p> <p><b>1 Introduction 1</b></p> <p><b>2 Mathematical Foundations 13</b></p> <p>2.1 Matrix Algebra 13</p> <p>2.2 Vector Algebra 20</p> <p>2.3 Simultaneous Linear Equation Systems 22</p> <p>2.4 Linear Dependence 26</p> <p>2.5 Convex Sets and n-Dimensional Geometry 29</p> <p><b>3 Introduction to Linear Programming 35</b></p> <p>3.1 Canonical and Standard Forms 35</p> <p>3.2 A Graphical Solution to the Linear Programming Problem 37</p> <p>3.3 Properties of the Feasible Region 38</p> <p>3.4 Existence and Location of Optimal Solutions 38</p> <p>3.5 Basic Feasible and Extreme Point Solutions 39</p> <p>3.6 Solutions and Requirement Spaces 41</p> <p><b>4 Computational Aspects of Linear Programming 43</b></p> <p>4.1 The Simplex Method 43</p> <p>4.2 Improving a Basic Feasible Solution 48</p> <p>4.3 Degenerate Basic Feasible Solutions 66</p> <p>4.4 Summary of the Simplex Method 69</p> <p><b>5 Variations of the Standard Simplex Routine 71</b></p> <p>5.1 The M-Penalty Method 71</p> <p>5.2 Inconsistency and Redundancy 78</p> <p>5.3 Minimization of the Objective Function 85</p> <p>5.4 Unrestricted Variables 86</p> <p>5.5 The Two-Phase Method 87</p> <p><b>6 Duality Theory 95</b></p> <p>6.1 The Symmetric Dual 95</p> <p>6.2 Unsymmetric Duals 97</p> <p>6.3 Duality Theorems 100</p> <p>6.4 Constructing the Dual Solution 106</p> <p>6.5 Dual Simplex Method 113</p> <p>6.6 Computational Aspects of the Dual Simplex Method 114</p> <p>6.7 Summary of the Dual Simplex Method 121</p> <p><b>7 Linear Programming and the Theory of the Firm 123</b></p> <p>7.1 The Technology of the Firm 123</p> <p>7.2 The Single-Process Production Function 125</p> <p>7.3 The Multiactivity Production Function 129</p> <p>7.4 The Single-Activity Profit Maximization Model 139</p> <p>7.5 The Multiactivity Profit Maximization Model 143</p> <p>7.6 Profit Indifference Curves 146</p> <p>7.7 Activity Levels Interpreted as Individual Product Levels 148</p> <p>7.8 The Simplex Method as an Internal Resource Allocation Process 155</p> <p>7.9 The Dual Simplex Method as an Internalized Resource Allocation Process 157</p> <p>7.10 A Generalized Multiactivity Profit-Maximization Model 157</p> <p>7.11 Factor Learning and the Optimum Product-Mix Model 161</p> <p>7.12 Joint Production Processes 165</p> <p>7.13 The Single-Process Product Transformation Function 167</p> <p>7.14 The Multiactivity Joint-Production Model 171</p> <p>7.15 Joint Production and Cost Minimization 180</p> <p>7.16 Cost Indifference Curves 184</p> <p>7.17 Activity Levels Interpreted as Individual Resource Levels 186</p> <p><b>8 Sensitivity Analysis 195</b></p> <p>8.1 Introduction 195</p> <p>8.2 Sensitivity Analysis 195</p> <p>8.2.1 Changing an Objective Function Coefficient 196</p> <p>8.2.2 Changing a Component of the Requirements Vector 200</p> <p>8.2.3 Changing a Component of the Coefficient Matrix 202</p> <p>8.3 Summary of Sensitivity Effects 209</p> <p><b>9 Analyzing Structural Changes 217</b></p> <p>9.1 Introduction 217</p> <p>9.2 Addition of a New Variable 217</p> <p>9.3 Addition of a New Structural Constraint 219</p> <p>9.4 Deletion of a Variable 223</p> <p>9.5 Deletion of a Structural Constraint 223</p> <p><b>10 Parametric Programming 227</b></p> <p>10.1 Introduction 227</p> <p>10.2 Parametric Analysis 227</p> <p>10.2.1 Parametrizing the Objective Function 228</p> <p>10.2.2 Parametrizing the Requirements Vector 236</p> <p>10.2.3 Parametrizing an Activity Vector 245</p> <p>10.A Updating the Basis Inverse 256</p> <p><b>11 Parametric Programming and the Theory of the Firm 257</b></p> <p>11.1 The Supply Function for the Output of an Activity (or for an Individual Product) 257</p> <p>11.2 The Demand Function for a Variable Input 262</p> <p>11.3 The Marginal (Net) Revenue Productivity Function for an Input 269</p> <p>11.4 The Marginal Cost Function for an Activity (or Individual Product) 276</p> <p>11.5 Minimizing the Cost of Producing a Given Output 284</p> <p>11.6 Determination of Marginal Productivity, Average Productivity, Marginal Cost, and Average Cost Functions 286</p> <p><b>12 Duality Revisited 297</b></p> <p>12.1 Introduction 297</p> <p>12.2 A Reformulation of the Primal and Dual Problems 297</p> <p>12.3 Lagrangian Saddle Points 311</p> <p>12.4 Duality and Complementary Slackness Theorems 315</p> <p><b>13 Simplex-Based Methods of Optimization 321</b></p> <p>13.1 Introduction 321</p> <p>13.2 Quadratic Programming 321</p> <p>13.3 Dual Quadratic Programs 325</p> <p>13.4 Complementary Pivot Method 329</p> <p>13.5 Quadratic Programming and Activity Analysis 335</p> <p>13.6 Linear Fractional Functional Programming 338</p> <p>13.7 Duality in Linear Fractional Functional Programming 347</p> <p>13.8 Resource Allocation with a Fractional Objective 353</p> <p>13.9 Game Theory and Linear Programming 356</p> <p>13.9.1 Introduction 356</p> <p>13.9.2 Matrix Games 357</p> <p>13.9.3 Transformation of a Matrix Game to a Linear Program 361</p> <p>13.A Quadratic Forms 363</p> <p>13.A.1 General Structure 363</p> <p>13.A.2 Symmetric Quadratic Forms 366</p> <p>13.A.3 Classification of Quadratic Forms 367</p> <p>13.A.4 Necessary Conditions for the Definiteness and Semi-Definiteness of Quadratic Forms 368</p> <p>13.A.5 Necessary and Sufficient Conditions for the Definiteness and Semi-Definiteness of Quadratic Forms 369</p> <p><b>14 Data Envelopment Analysis (DEA) 373</b></p> <p>14.1 Introduction 373</p> <p>14.2 Set Theoretic Representation of a Production Technology 374</p> <p>14.3 Output and Input Distance Functions 377</p> <p>14.4 Technical and Allocative Efficiency 379</p> <p>14.4.1 Measuring Technical Efficiency 379</p> <p>14.4.2 Allocative, Cost, and Revenue Efficiency 382</p> <p>14.5 Data Envelopment Analysis (DEA) Modeling 385</p> <p>14.6 The Production Correspondence 386</p> <p>14.7 Input-Oriented DEA Model under CRS 387</p> <p>14.8 Input and Output Slack Variables 390</p> <p>14.9 Modeling VRS 398</p> <p>14.9.1 The Basic BCC (1984) DEA Model 398</p> <p>14.9.2 Solving the BCC (1984) Model 400</p> <p>14.9.3 BCC (1984) Returns to Scale 401</p> <p>14.10 Output-Oriented DEA Models 402</p> <p>References and Suggested Reading 405</p> <p>Index 411</p>
<p><b>Michael J. Panik, PhD,</b> is Professor Emeritus in the Department of Economics at the University of Hartford, CT. He has taught courses in economic and business statistics, quantitative decision methods, introductory and advanced quantitative methods, and econometrics. Dr. Panik is the author of several books, including <i>Stochastic Differential Equations</i> and <i>Growth Curve Modeling: Theory and Applications</i>, both published by Wiley. He is also a co-author of <i>Introduction to Quantitative Methods in Business: With Applications Using Microsoft Office Excel</i>.
<p><b>Guides in the application of linear programming to firm decision making, with the goal of giving decision-makers a better understanding of methods at their disposal</b> <p>Useful as a main resource or as a supplement in an economics or management science course, this comprehensive book addresses the deficiencies of other texts when it comes to covering linear programming theory—especially where data envelopment analysis (DEA) is concerned—and provides the foundation for the development of DEA. <p><i>Linear Programming and Resource Allocation Modeling</i> begins by introducing primal and dual problems via an optimum product mix problem, and reviews the rudiments of vector and matrix operations. It then goes on to cover: the canonical and standard forms of a linear programming problem; the computational aspects of linear programming; variations of the standard simplex theme; duality theory; single- and multiple- process production functions; sensitivity analysis of the optimal solution; structural changes; and parametric programming. The primal and dual problems are then reformulated and re-examined in the context of Lagrangian saddle points, and a host of duality and complementary slackness theorems are offered. The book also covers primal and dual quadratic programs, the complementary pivot method, primal and dual linear fractional functional programs, and (matrix) game theory solutions via linear programming, and data envelopment analysis (DEA). This book: <ul> <li>Appeals to those wishing to solve linear optimization problems in areas such as economics, business administration and management, agriculture and energy, strategic planning, public decision making, and health care</li> <li>Fills the need for a linear programming applications component in a management science or economics course</li> <li>Provides a complete treatment of linear programming as applied to activity selection and usage</li> <li>Contains many detailed example problems as well as textual and graphical explanations</li> </ul> <p><i>Linear Programming and Resource Allocation Modeling</i> is an excellent resource for professionals looking to solve linear optimization problems, and advanced undergraduate to beginning graduate level management science or economics students.

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