## Geometric Programming for Design and Cost Optimization: (with Illustrative Case Study Problems and Solutions)There are numerous techniques of optimization methods such as linear programming, dynamic programming, geometric programming, queuing theory, statistical analysis, risk analysis, Monte Carlo simulation, numerous search techniques, etc. Geometric programming is one of the better tools that can be used to achieve the design requirements and minimal cost objective. Geometric programming can be used not only to provide a specific solution to a problem, but it also can in many instances give a general solution with specific design relationships. These design relationships based upon the design constants can then be used for the optimal solution without having to resolve the original problem. This fascinating characteristic appears to be unique to geometric programming. The purpose of this text is to introduce manufacturing engineers, design engineers, manufacturing technologists, cost engineers, project managers, industrial consultants and finance managers to the topic of geometric programming. |

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### Contents

Introduction | 1 |

Brief History of Geometric Programming | 3 |

Theoretical Considerations | 5 |

Trash Can Case Study | 11 |

Open Cargo Shipping Box Case Study | 15 |

Metal Casting Cylindrical Riser Case Study | 21 |

Process Furnace Design Case Study | 27 |

Gas Transmission Pipeline Case Study | 33 |

Journal Bearing Design Case Study | 37 |

Metal Casting Hemispherical Top Cylindrical Side Riser | 43 |

Summary and Future Directions | 63 |

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400 cubic yards additional equation applications arithmetic mean Beightler C2WL casting modulus CHAPTER Clarence Zener coefficients and signs constants constraint equations cooling surface area cost to machine Cost(Y Cu(var cutting speed cylindrical riser d(co degrees of difﬁculty design relationships determined diameter difficulty are equal dimensions drawing force dual equations dual expression dual formulation dual objective function dual problem formulation Engineering EVALUATIVE QUESTIONS example problem exponents ﬁnish geometric programming H terms hemispherical top JOURNAL BEARING DESIGN K1hd L terms linear programming linearity inequality equation loose constraint metal cost minimize minimum volume Modiﬁed open cargo parameters primal and dual primal equation primal objective function primal problem primal solution primal variables primal-dual relationships radius ratio reducing terms series of costs signum function signum values solidiﬁcation solution solve speciﬁc values top riser total cost transport the 400 trash values of C1 variable cost variables are found yards of gravel