Application Of Geometric Programming Research Articles

Investments in energy efficiency with government environmental sensitiveness: An application of geometric programming and game theory

Investments in energy efficiency with government environmental sensitiveness: An application of geometric programming and game theory

Geometric Programming for Design Equation Development and Cost/Profit Optimization (with illustrative case study problems and solutions), Third Edition

Geometric Programming is used for cost minimization, profit maximization, obtaining cost ratios, and the development of generalized design equations for the primal variables. The early pioneers of geometric programming—Zener, Duffin, Peterson, Beightler, Wilde, and Phillips—played important roles in its development. Five new case studies have been added to the third edition. There are five major sections: (1) Introduction, History and Theoretical Fundamentals; (2) Cost Minimization Applications with Zero Degrees of Difficulty; (3) Profit Maximization Applications with Zero Degrees of Difficulty; (4) Applications with Positive Degrees of Difficulty; and (5) Summary, Future Directions, and Geometric Programming Theses & Dissertations Titles. The various solution techniques presented are the constrained derivative approach, condensation of terms approach, dimensional analysis approach, and transformed dual approach. A primary goal of this work is to have readers develop more case studies and new solution techniques to further the application of geometric programming.

The application of geometric programming for solving various technical and economic problems

This article describes the solution of two technical and economic problems by methods of geometric programming. It is shown that due to their relative simplicity and clarity this method is best for the solution of such specific tasks as the project evaluation and the definition of expediency of obtaining investment on capital costs.

Profit maximization with quantity discount: An application of geometric programming

Profit maximization is an important issue to the firms that pursue the largest economic profit possible. Traditionally, profit maximization problem is solved by differentiating with respect to input prices. The total differentiation of the first-order conditions might give complicated equations difficult to handle. Different from traditional studies, this paper considers input quantity discount and employs geometric programming technique to derive the objective value for the profit-maximization problem. The geometric programming approach not only gives the global optimum solution but also provides the information that is able to discover the relationship between profit maximization and returns to scale in the solution process. No differentiation is required. Moreover, geometric programming can provide a computationally attractive view of sensitivity analysis for the changes in parameters. Examples are given to illustrate the idea proposed in this paper.

Optimal allocation of stratified samples with several variance constraints and equal workloads over time by geometric programming

We apply geometric programming, developed by Duffin, Peterson and Zener (1967), to the optimal allocation of stratified samples with several variance constraints arising from several estimates of deficiency rates in the quality control of administrative decisions. We develop also a method for imposing constraints on sample sizes to equalize workloads over time, as required by the practicalities of clerical work for quality control. We allocate samples by an extension of the work of Neyman (1934), following the exposition of Cochran (1977). Davis and Schwartz (1987) developed methods for multiconstraint Neyman allocation by geometric programming for integrated sampling. They also applied geometric programming to Neyman allocation of a sample for estimating college enrollments by Cornell (1947) and Cochran (1977). This paper continues the application of geometric programming to Neyman allocation with multiple constraints on variances and workloads and minimpal sampling costs.

Synthesis of 4-bar function-generators using geometric programming

Application of Geometric Programming (G.P.) to linkage synthesis has not been reported so far. In this paper this technique is applied to the synthesis of a planar 4-bar function generating mechanism and a spherical mechanism with minimum structural error. The programming adapted here deviates from the present concept of G P. in the sense that the negative “integer” “weights” are used though the coefficients of the corresponding terms in the objective function are not negative. Example problems are solved. The synthesis with the transmission angle constraint is dealt with in the Appendix.

Application of Geometric Programming for Spring Design

The present paper discusses the design of conical helical springs and torsional helical springs using geometric programming technique. It is shown that the present method provides a saving about 20 per cent of material by weight a particular case which is substantial.

An application of geometric programming to regional economics

An application of geometric programming to regional economics

OPTIMUM LIMIT STATE DESIGN OF HIGHWAY BRIDGE SUPERSTRUCTURES USING GEOMETRIC PROGRAMMING

Abstract A number of studies, by the author and others, have shown that the Limit State Design method can, when applied to the design of bridge superstructures, produce more rational and economic designs than conventional methods. Most studies have been made on the assumption that the basic structural layout, proportioning, and material characteristics would be determined by the rules used for conventional design. The authors have pointed out that these rules are possibly no longer applicable and that greater economies could be obtained by some form of optimization procedure. This paper describes the application of Geometric Programming to the solution of such a problem. It is shown that excellent results can be obtained with a simplified version of the technique in which the “degree of difficulty” is reduced to zero. The superiority of Geometric Programming as an optimum design technique is demonstrated by comparing the results for the example chosen with those obtained by alternative methods.

Optimal capacities of production facilities. an application of geometric programming

Optimal capacities of production facilities. an application of geometric programming