Summary and Future Directions
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
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
Metal Casting Cylindrical
2 Height, Diameter 1
7 Process Furnace Design
1 Dominant Equation
Negative Dual Variable
Pressure Ratio Factor
Journal Bearing Design 1
2 Journal Radius,
10 Hemispherical Riser
2 Height, Diameter
11 Liqueﬁed Petroleum
Gas (LPG) Cylinder
2 Multiple Solutions
Feed Rate, Cutting Speed 1
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
 C.S. Beightler, D.T. Phillips, and D.J. Wilde, Foundations of Optimization, 2nd Edition,
Prentice-Hall, Englewood Cliffs, New Jersey, 1979.
 C.S. Beightler, T. Lo, and H.G. Bylander, “Optimal Design by Geometric Programming,”
ASME, Journal of Engineering for Industry, 1970, pp. 191–196.
 R.C. Creese,“A Primal-Dual Solution Procedure for Geometric Programming,” ASME, Jour-
nal of Mechanical Design, 1979. (also as Paper No. 79-DET-78).
 R.C. Creese, “Optimal Riser Design by Geometric Programming,” AFS Cast Metals Research
Journal, Vol. 7, 1971, pp. 118–121.
 R.C. Creese, “Dimensioning of Risers for Long Freezing Range Alloys by Geometric Pro-
gramming,” AFS Cast Metals Research Journal, Vol. 7, 1971, pp. 182–184.
 R.C. Creese, “Generalized Riser Design by Geometric Programming,” AFS Transactions,
Vol. 87, 1979, pp. 661–664.
 R.C. Creese, “An Evaluation of Cylindrical Riser Designs with Insulating Materials,” AFS
Transactions, Vol. 87, 1979, pp. 665–669.
 R.C. Creese,“Cylindrical Top Riser Design Relationships for Evaluating Insulating Materials,”
AFS Transactions, Vol. 89, 1981, pp. 345–348.
 R.C. Creese and P. Tsai, “Generalized Solution for Constrained Metal Cutting Economics
Problem,” 1985 Annual International Industrial Conference Proceedings, Institute of Industrial
Engineers, pp. 113–117.
 R.J. Dufﬁn, E.L. Peterson, and C. Zener, Geometric Programming, John Wiley and Sons, New
 D.S. Ermer, “Optimization of the Constrained Machining Economics Problem by Geometric
Programming,” Journal of Engineering for Industry, Transactions of the ASME, November
1971, pp. 1067–1072.
 U. Passey and D.J. Wilde, “Generalized Polynomial Optimization,” Stanford Chemical Engi-
neering Report, August 1966.