63

CHAPTER 13

Summary and Future Directions

13.1 SUMMARY

The object of this text is to generate interest in geometric programming amongst manufacturing

engineers,design engineers,manufacturing technologists,cost engineers,project managers,industrial

consultants and ﬁnance managers by illustrating the procedure for solving certain industrial and

practical problems. The various case studies were selected to illustrate a variety of applications as

well as a set of different types of problems from diverse ﬁelds. Table 13.1 is a summary of the case

studies presented in this text, giving the type of problem, degrees of difﬁculty, and other details.

The metal removal economics example also had variable exponents in the general solution.

The problems were worked in detail so general solutions could be obtained and also to show that

the dual and primal solutions were identical. The problems were selected to illustrate a variety of

types and also to show the use of the primal-dual relationships to determine the equations for the

primal variables. It is by showing the various types of applications in detailed examples that others

can follow the procedure and develop new applications.

13.2 FUTURE DIRECTIONS

The author is hopeful that others will communicate with him additional examples to illustrate new

applications that can be included in future editions. New applications will attract new practition-

ers to this fascinating area of geometric programming. It is believed that the scope of geometric

programming will expand with new applications.

The author would like to include some software for different applications in the future and

would welcome contributions.

13.3 DEVELOPMENT OF NEW DESIGN RELATIONSHIPS

There are many different types of problems that can be solved by geometric programming, and one

of the signiﬁcant advantages of the method is that it is possible in many applications to develop

general design relationships. The general design relationships can save considerable time and effort

in instances where the constants are changed.

Although, geometric programming was ﬁrst presented nearly 50 years ago, the applications

have been rather sparse compared to that of linear programming. One goal is that as researchers

take advantage of the potential to develop design relationships where new applications will rapidly

occur. The development of new design relationships can signiﬁcantly reduce the development time

64 CHAPTER 13. SUMMARY AND FUTURE DIRECTIONS

Table 13.1: Summary of Case Study Problems

Chapter

Case Study

Degrees

Number

Variable Description

Number

Special

of of

of

Characteristics for

Difﬁculty Variables

Solutions

Chapters 7 and 8

3 Optimal Box Design 0 3 Length, Width, Height 1

4 Trash Can Design 0 2 Height, Diameter 1

5 Open Cargo Shipping Box 0 3 Length, Width, Height 1 Classic Problem

6

Metal Casting Cylindrical

Riser Design

0

2 Height, Diameter 1

7 Process Furnace Design

0 3

Temperature, Length,

Height

1 Dominant Equation

Negative Dual Variable

8

Gas Transmission

Pipe Line

0

4

Length, Diameter,

Flow Length,

Pressure Ratio Factor

1

Fractional Exponents

Four Variables

9

Journal Bearing Design 1

2 Journal Radius,

Bearing Half-length

1

10 Hemispherical Riser

Design

1

2 Height, Diameter

1

11 Liqueﬁed Petroleum

Gas (LPG) Cylinder

1 2

Height, Diameter

2 Multiple Solutions

12

Material Removal/Metal

Cutting Economics

0 2

Feed Rate, Cutting Speed 1

Fractional Exponents

13.3. DEVELOPMENT OF NEW DESIGN RELATIONSHIPS 65

and cost for new products, and this is essential for companies to remain competitive in the global

economy.

67

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[10] R.J. Dufﬁn, E.L. Peterson, and C. Zener, Geometric Programming, John Wiley and Sons, New

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