Linear Programming and Resource Allocation Modeling

Name: Linear Programming and Resource Allocation Modeling
Brand: Wiley
Price: 101.99 EUR
Availability: OnlineOnly

Michael J. Panik(Autor*in)

Wiley (Verlag)

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Erschienen am 15. Oktober 2018

448 Seiten

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Beschreibung

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

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.

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 care

* Fills the need for a linear programming applications component in a management science or economics course

* Provides a complete treatment of linear programming as applied to activity selection and usage

* Contains many detailed example problems as well as textual and graphical explanations

Linear 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.

Weitere Details

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Inhalt

Intro
Title Page
Copyright Page
Contents
Preface
Symbols and Abbreviations
Chapter 1 Introduction
Chapter 2 Mathematical Foundations
2.1 Matrix Algebra
2.2 Vector Algebra
2.3 Simultaneous Linear Equation Systems
2.4 Linear Dependence
2.5 Convex Sets and n-Dimensional Geometry
Chapter 3 Introduction to Linear Programming
3.1 Canonical and Standard Forms
3.2 A Graphical Solution to the Linear Programming Problem
3.3 Properties of the Feasible Region
3.4 Existence and Location of Optimal Solutions
3.5 Basic Feasible and Extreme Point Solutions
3.6 Solutions and Requirement Spaces
Chapter 4 Computational Aspects of Linear Programming
4.1 The Simplex Method
4.2 Improving a Basic Feasible Solution
4.3 Degenerate Basic Feasible Solutions
4.4 Summary of the Simplex Method
Chapter 5 Variations of the Standard Simplex Routine
5.1 The M-Penalty Method
5.2 Inconsistency and Redundancy
5.3 Minimization of the Objective Function
5.4 Unrestricted Variables
5.5 The Two-Phase Method
Chapter 6 Duality Theory
6.1 The Symmetric Dual
6.2 Unsymmetric Duals
6.3 Duality Theorems
6.4 Constructing the Dual Solution
6.5 Dual Simplex Method (Lemke 1954)
6.6 Computational Aspects of the Dual Simplex Method
6.7 Summary of the Dual Simplex Method
Chapter 7 Linear Programming and the Theory of the Firm
7.1 The Technology of the Firm
7.2 The Single-Process Production Function
7.3 The Multiactivity Production Function
7.4 The Single-Activity Profit Maximization Model (Dano 1966
Hadar 1971
and Ferguson 1971)
7.5 The Multiactivity Profit Maximization Model (Dano 1966
Hadar 1971
and Ferguson 1971)
7.6 Profit Indifference Curves (Baumol 1977)
7.7 Activity Levels Interpreted as Individual Product Levels
7.8 The Simplex Method as an Internal Resource Allocation Process
7.9 The Dual Simplex Method as an Internalized Resource Allocation Process
7.10 A Generalized Multiactivity Profit-Maximization Model
7.11 Factor Learning and the Optimum Product-Mix Model
7.12 Joint Production Processes
7.13 The Single-Process Product Transformation Function
7.14 The Multiactivity Joint-Production Model
7.15 Joint Production and Cost Minimization
7.16 Cost Indifference Curves
7.17 Activity Levels Interpreted as Individual Resource Levels
Chapter 8 Sensitivity Analysis
8.1 Introduction
8.2 Sensitivity Analysis
8.2.1 Changing an Objective Function Coefficient
8.2.2 Changing a Component of the Requirements Vector
8.2.3 Changing a Component of the Coefficient Matrix
8.3 Summary of Sensitivity Effects
Chapter 9 Analyzing Structural Changes
9.1 Introduction
9.2 Addition of a New Variable
9.3 Addition of a New Structural Constraint
9.4 Deletion of a Variable
9.5 Deletion of a Structural Constraint
Chapter 10 Parametric Programming
10.1 Introduction
10.2 Parametric Analysis
10.2.1 Parametrizing the Objective Function
10.2.2 Parametrizing the Requirements Vector
10.2.3 Parametrizing an Activity Vector
Chapter 11 Parametric Programming and the Theory of the Firm
11.1 The Supply Function for the Output of an Activity (or for an Individual Product)
11.2 The Demand Function for a Variable Input
11.3 The Marginal (Net) Revenue Productivity Function for an Input
11.4 The Marginal Cost Function for an Activity (or Individual Product)
11.5 Minimizing the Cost of Producing a Given Output
11.6 Determination of Marginal Productivity, Average Productivity, Marginal Cost, and Average Cost Functions
Chapter 12 Duality Revisited
12.1 Introduction
12.2 A Reformulation of the Primal and Dual Problems
12.3 Lagrangian Saddle Points (Belinski and Baumol 1968
Williams 1963)
12.4 Duality and Complementary Slackness Theorems (Dreyfus and Freimer 1962)
Chapter 13 Simplex-Based Methods of Optimization
13.1 Introduction
13.2 Quadratic Programming
13.3 Dual Quadratic Programs
13.4 Complementary Pivot Method (Lemke 1965)
13.5 Quadratic Programming and Activity Analysis
13.6 Linear Fractional Functional Programming (Charnes and Cooper 1962
Lasdon 1970
Martos 1964
Craven 1978)
13.7 Duality in Linear Fractional Functional Programming (Craven and Mond 1973, 1976
Schnaible 1976
Wagner and Yuan 1968
Chadha 1971
Kydland 1962
and Kornbluth and Salkin 1972)
13.8 Resource Allocation with a Fractional Objective
13.9 Game Theory and Linear Programming
13.9.1 Introduction
13.9.2 Matrix Games
13.9.3 Transformation of a Matrix Game to a Linear Program
13.A Quadratic Forms
13.A.1 General Structure
13.A.2 Symmetric Quadratic Forms
13.A.3 Classification of Quadratic Forms
13.A.4 Necessary Conditions for the Definiteness and Semi-Definiteness of Quadratic Forms
13.A.5 Necessary and Sufficient Conditions for the Definiteness and Semi-Definiteness of Quadratic Forms
Chapter 14 Data Envelopment Analysis (DEA)
14.1 Introduction (Charnes et al. 1978
Banker et al. 1984
Seiford and Thrall 1990
and Banker and Thrall 1992)
14.2 Set Theoretic Representation of a Production Technology (Färe et al. 2008
Lovell 1994
Färe and Lovell 1978
and Fried et al. 2008)
14.3 Output and Input Distance Functions (Färe and Lovell 1978
Fried et al. 2008
Coelli et al. 2005
and Shephard 1953, 1970)
14.4 Technical and Allocative Efficiency
14.4.1 Measuring Technical Efficiency (Debreu 1951
Farrell 1957)
14.4.2 Allocative, Cost, and Revenue Efficiency (Lovell 1994
Coelli et al. 2005)
14.5 Data Envelopment Analysis (DEA) Modeling (Charnes et al. 1978
Cooper et al. 2007
Lovell 1994
Banker et al. 1984
Banker and Thrall 1992)
14.6 The Production Correspondence
14.7 Input-Oriented DEA Model under CRS (Charnes et al. 1978)
14.8 Input and Output Slack Variables
14.9 Modeling VRS (BCC 1984
Cooper et al. 2007
Banker and Thrall 1992 and Banker et al. 1996)
14.9.1 The Basic BCC (1984) DEA Model
14.9.2 Solving the BCC (1984) Model
14.9.3 BCC (1984) Returns to Scale
14.10 Output-Oriented DEA Models
References and Suggested Reading
Index
EULA

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