Geometric programming for design and cost optimization

✍ Scribed by Creese R.

• Publisher: Morgan
• Year: 2010
• Tongue: English
• Leaves: 140
• Series: Synthesis Lectures on Engineering
• Edition: 2ed
• Category: Library

✦ Synopsis

Geometric programming is used for design and cost optimization, the development of generalized design relationships, cost ratios for specific problems, and profit maximization. The early pioneers of the process - Zener, Duffin, Peterson, Beightler, Wilde, and Phillips -- played important roles in the development of geometric programming. There are three major areas: 1) Introduction, History, and Theoretical Fundamentals, 2) Applications with Zero Degrees of Difficulty, and 3) Applications with Positive Degrees of Difficulty. The primal-dual relationships are used to illustrate how to determine the primal variables from the dual solution and how to determine additional dual equations when the degrees of difficulty are positive. A new technique for determining additional equations for the dual, Dimensional Analysis, is demonstrated. The various solution techniques of the constrained derivative approach, the condensation of terms, and dimensional analysis are illustrated with example problems. The goal of this work is to have readers develop more case studies to further the application of this exciting tool. Table of Contents: Introduction / Brief History of Geometric Programming / Theoretical Considerations / The Optimal Box Design Case Study / Trash Can Case Study / The Open Cargo Shipping Box Case Study / Metal Casting Cylindrical Riser Case Study / Inventory Model Case Study / Process Furnace Design Case Study / Gas Transmission Pipeline Case Study / Profit Maximization Case Study / Material Removal/Metal Cutting Economics Case Study / Journal Bearing Design Case Study / Metal Casting Hemispherical Top Cylindrical Side Riser\Case Study / Liquefied Petroleum Gas (LPG) Cylinders Case Study / Material Removal/Metal Cutting Economics with Two Constraints / The Open Cargo Shipping Box with Skids / Profit Maximization Considering Decreasing Cost Functions of Inventory Policy / Summary and Future Directions / Thesis and Dissertations on Geometric Programming

✦ Table of Contents

Preface......Page 11
Introduction, History, and Theoretical Fundamentals of Geometric Programming......Page 13
Geometric Programming......Page 15
References......Page 16
Pioneers of Geometric Programming......Page 17
References......Page 18
Primal and Dual Formulation......Page 19
References......Page 22
Geometric Programming Applications with Zero Degrees of Difficulty......Page 23
The Optimal Box Design Problem......Page 25
Evaluative Questions......Page 28
Example......Page 29
Evaluative Questions......Page 32
Problem Statement and General Solution......Page 33
Evaluative Questions......Page 36
References......Page 37
Introduction......Page 39
Problem Formulation and General Solution......Page 41
Example......Page 42
References......Page 43
Problem Statement and General Solution.......Page 45
Example......Page 47
References......Page 48
Problem Statement and Solution......Page 49
References......Page 53
Problem Statement and Solution......Page 55
References......Page 58
Profit Maximization using the Cobb-Douglas Production Function......Page 59
Evaluative Questions......Page 61
References......Page 62
Problem Formulation......Page 63
Evaluative Questions......Page 66
References......Page 67
Geometric Programming Applications with Positive Degrees of Difficulty......Page 69
Primal and Dual Formulation of Journal Bearing Design......Page 71
Dimensional Analysis Technique for Additional Equation......Page 75
Evaluative Questions......Page 76
References......Page 77
Problem Formulation......Page 79
Dimensional Analysis Technique for Additional Two Equations......Page 84
References......Page 87
Problem Formulation......Page 89
Dimensional Analysis Technique for Additional Equation......Page 94
Evaluative Questions......Page 95
References......Page 96
Problem Formulation......Page 97
Problem Solution......Page 99
Evaluative Questions......Page 103
References......Page 104
Primal-Dual Problem Formulation......Page 107
Constrained Derivative Approach......Page 109
Dimensional Analysis Approach for Additional Equation......Page 110
Condensation of Terms Approach......Page 112
References......Page 114
Model Formulation......Page 115
Example......Page 119
Transformed Dual Approach......Page 121
References......Page 124
Development of New Design Relationships......Page 127
Thesis and Dissertations on Geometric Programming......Page 131
Author's Biography......Page 137
Index......Page 139