ABSTRACT
Geometric programming is used for design and cost optimization and the development of generalized
design relationships and cost rations for specific problems. The early pioneers of the process, Zener,
Duffin, Peterson, Beightler, and Wilde, played important roles in the development of geometric
programming. The theory of geometric programming is presented and 10 examples are presented
and solved in detail. The examples illustrate some of the difficulties encountered in typical problems
and techniques for overcoming these difficulties. The primal-dual relationships are used to illustrate
how to determine the primal variables from the dual solution. These primal-dual relationships can
be used to determine additional dual equations when the degrees of difficulty are positive. The goal
of this work is to have readers develop more case studies to further the application of this exciting
mathematical tool.
KEYWORDS
cost optimization, design optimization, general solutions, posynominials, primal, dual,
pioneers, casting design, metal cutting economics, LPG cylinder design
vii
Contents
Preface ..........................................................................xi
1
Introduction ......................................................................1
1.1 Optimization and Geometric Programming ...................................1
1.1.1 Optimization 1
1.1.2 Geometric Programming 1
1.2 Evaluative Questions ........................................................2
2
Brief History of Geometric Programming ...........................................3
2.1 Pioneers of Geometric Programming .........................................3
2.2 Evaluative Questions ........................................................3
3
Theoretical Considerations ........................................................5
3.1 Primal and Dual Formulation ...............................................5
3.2 The Optimal Box Design Problem ...........................................7
3.3 Evaluative Questions ......................................................10
4
Trash Can Case Study ............................................................11
4.1 Introduction ..............................................................11
4.2 Problem Statement and General Solution ....................................11
4.3 Evaluative Questions ......................................................14
5
Open Cargo Shipping Box Case Study .............................................15
5.1 Problem Statement and General Solution ....................................15
5.2 Evaluative Questions ......................................................18
6
Metal Casting Cylindrical Riser Case Study ........................................21
6.1 Introduction ..............................................................21
viii CONTENTS
6.2 Problem Formulation and General Solution ..................................23
6.3 Example Problem .........................................................24
6.4 Evaluative Questions ......................................................25
7
Process Furnace Design Case Study ...............................................27
7.1 Problem Statement and Solution ............................................27
7.2 Evaluative Questions ......................................................30
8
Gas Transmission Pipeline Case Study .............................................33
8.1 Problem Statement and Solution ............................................33
8.2 Evaluative Questions ......................................................36
9
Journal Bearing Design Case Study ................................................37
9.1 Introduction ..............................................................37
9.2 Primal and Dual Formulation of Journal Bearing Design ......................37
9.3 Evaluative Questions ......................................................41
10
Metal Casting Hemispherical Top Cylindrical Side Riser Case Study .................43
10.1 Introduction ..............................................................43
10.2 Problem Formulation ......................................................43
10.3 Evaluative Questions ......................................................48
11
Liquefied Petroleum Gas(LPG) Cylinders Case Study...............................49
11.1 Introduction ..............................................................49
11.2 Problem Formulation ......................................................49
11.3 Evaluative Questions ......................................................54
12
Material Removal/Metal Cutting Economics Case Study ............................57
12.1 Introduction ..............................................................57
12.2 Problem Formulation ......................................................57
12.3 Evaluative Questions ......................................................60
13
Summary and Future Directions ..................................................63
CONTENTS ix
13.1 Summary .................................................................63
13.2 Future Directions ..........................................................63
13.3 Development of New Design Relationships ..................................63
Bibliography ....................................................................67
Index ...........................................................................69

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