Linear Programming and Resource Allocation Modeling

AvMichael J. Panik

Inbunden, Engelska, 2018

1 387 kr

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Beskrivning

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 disposalUseful 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.Linear Programming and Resource Allocation Modeling 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: 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 careFills the need for a linear programming applications component in a management science or economics courseProvides a complete treatment of linear programming as applied to activity selection and usageContains many detailed example problems as well as textual and graphical explanationsLinear Programming and Resource Allocation Modeling is an excellent resource for professionals looking to solve linear optimization problems, and advanced undergraduate to beginning graduate level management science or economics students.

Produktinformation

Utgivningsdatum:2018-12-14
Mått:152 x 231 x 25 mm
Vikt:839 g
Format:Inbunden
Språk:Engelska
Antal sidor:448
Förlag:John Wiley & Sons Inc
ISBN:9781119509448

Utforska kategorier

Matematik inom Naturvetenskap och teknik

Mer om författaren

Michael J. Panik, PhD, 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 Stochastic Differential Equations and Growth Curve Modeling: Theory and Applications, both published by Wiley. He is also a co-author of Introduction to Quantitative Methods in Business: With Applications Using Microsoft Office Excel.

Innehållsförteckning

Preface xiSymbols and Abbreviations xv1 Introduction 12 Mathematical Foundations 132.1 Matrix Algebra 132.2 Vector Algebra 202.3 Simultaneous Linear Equation Systems 222.4 Linear Dependence 262.5 Convex Sets and n-Dimensional Geometry 293 Introduction to Linear Programming 353.1 Canonical and Standard Forms 353.2 A Graphical Solution to the Linear Programming Problem 373.3 Properties of the Feasible Region 383.4 Existence and Location of Optimal Solutions 383.5 Basic Feasible and Extreme Point Solutions 393.6 Solutions and Requirement Spaces 414 Computational Aspects of Linear Programming 434.1 The Simplex Method 434.2 Improving a Basic Feasible Solution 484.3 Degenerate Basic Feasible Solutions 664.4 Summary of the Simplex Method 695 Variations of the Standard Simplex Routine 715.1 The M-Penalty Method 715.2 Inconsistency and Redundancy 785.3 Minimization of the Objective Function 855.4 Unrestricted Variables 865.5 The Two-Phase Method 876 Duality Theory 956.1 The Symmetric Dual 956.2 Unsymmetric Duals 976.3 Duality Theorems 1006.4 Constructing the Dual Solution 1066.5 Dual Simplex Method 1136.6 Computational Aspects of the Dual Simplex Method 1146.7 Summary of the Dual Simplex Method 1217 Linear Programming and the Theory of the Firm 1237.1 The Technology of the Firm 1237.2 The Single-Process Production Function 1257.3 The Multiactivity Production Function 1297.4 The Single-Activity Profit Maximization Model 1397.5 The Multiactivity Profit Maximization Model 1437.6 Profit Indifference Curves 1467.7 Activity Levels Interpreted as Individual Product Levels 1487.8 The Simplex Method as an Internal Resource Allocation Process 1557.9 The Dual Simplex Method as an Internalized Resource Allocation Process 1577.10 A Generalized Multiactivity Profit-Maximization Model 1577.11 Factor Learning and the Optimum Product-Mix Model 1617.12 Joint Production Processes 1657.13 The Single-Process Product Transformation Function 1677.14 The Multiactivity Joint-Production Model 1717.15 Joint Production and Cost Minimization 1807.16 Cost Indifference Curves 1847.17 Activity Levels Interpreted as Individual Resource Levels 1868 Sensitivity Analysis 1958.1 Introduction 1958.2 Sensitivity Analysis 1958.2.1 Changing an Objective Function Coefficient 1968.2.2 Changing a Component of the Requirements Vector 2008.2.3 Changing a Component of the Coefficient Matrix 2028.3 Summary of Sensitivity Effects 2099 Analyzing Structural Changes 2179.1 Introduction 2179.2 Addition of a New Variable 2179.3 Addition of a New Structural Constraint 2199.4 Deletion of a Variable 2239.5 Deletion of a Structural Constraint 22310 Parametric Programming 22710.1 Introduction 22710.2 Parametric Analysis 22710.2.1 Parametrizing the Objective Function 22810.2.2 Parametrizing the Requirements Vector 23610.2.3 Parametrizing an Activity Vector 24510.A Updating the Basis Inverse 25611 Parametric Programming and the Theory of the Firm 25711.1 The Supply Function for the Output of an Activity (or for an Individual Product) 25711.2 The Demand Function for a Variable Input 26211.3 The Marginal (Net) Revenue Productivity Function for an Input 26911.4 The Marginal Cost Function for an Activity (or Individual Product) 27611.5 Minimizing the Cost of Producing a Given Output 28411.6 Determination of Marginal Productivity, Average Productivity, Marginal Cost, and Average Cost Functions 28612 Duality Revisited 29712.1 Introduction 29712.2 A Reformulation of the Primal and Dual Problems 29712.3 Lagrangian Saddle Points 31112.4 Duality and Complementary Slackness Theorems 31513 Simplex-Based Methods of Optimization 32113.1 Introduction 32113.2 Quadratic Programming 32113.3 Dual Quadratic Programs 32513.4 Complementary Pivot Method 32913.5 Quadratic Programming and Activity Analysis 33513.6 Linear Fractional Functional Programming 33813.7 Duality in Linear Fractional Functional Programming 34713.8 Resource Allocation with a Fractional Objective 35313.9 Game Theory and Linear Programming 35613.9.1 Introduction 35613.9.2 Matrix Games 35713.9.3 Transformation of a Matrix Game to a Linear Program 36113.A Quadratic Forms 36313.A.1 General Structure 36313.A.2 Symmetric Quadratic Forms 36613.A.3 Classification of Quadratic Forms 36713.A.4 Necessary Conditions for the Definiteness and Semi-Definiteness of Quadratic Forms 36813.A.5 Necessary and Sufficient Conditions for the Definiteness and Semi-Definiteness of Quadratic Forms 36914 Data Envelopment Analysis (DEA) 37314.1 Introduction 37314.2 Set Theoretic Representation of a Production Technology 37414.3 Output and Input Distance Functions 37714.4 Technical and Allocative Efficiency 37914.4.1 Measuring Technical Efficiency 37914.4.2 Allocative, Cost, and Revenue Efficiency 38214.5 Data Envelopment Analysis (DEA) Modeling 38514.6 The Production Correspondence 38614.7 Input-Oriented DEA Model under CRS 38714.8 Input and Output Slack Variables 39014.9 Modeling VRS 39814.9.1 The Basic BCC (1984) DEA Model 39814.9.2 Solving the BCC (1984) Model 40014.9.3 BCC (1984) Returns to Scale 40114.10 Output-Oriented DEA Models 402References and Suggested Reading 405Index 411