Design Equations Developed by Geometric Programming

Robert Creese

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Conference: 2022 ASEE Annual Conference & Exposition
Location: Minneapolis, MN
Publication Date: August 23, 2022
Start Date: June 26, 2022
End Date: June 29, 2022
Conference Session: DEED Technical Session 8 - Design Methodologies
Page Count: 10
DOI: 10.18260/1-2--41224
Permanent URL: https://strategy.asee.org/41224
Download Count: 221

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Paper Authors

biography

Robert Creese West Virginia University

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He was born and raised in Pittsburgh, PA, Graduated from Penn State in Industrial Engineering in 1963, Graduated from Berkeley in 1964 with a MS in IEOR, worked for US Steel from 1964-66, returned as a full time Instructor in the Department of Industrial Engineering and was a PhD Student in Metallurgy and graduated in1972. He taught Metallurgy at Grove City College and started a Management Engineering Program from 1972-1976 and returned to Penn State in IE from 1976 to 1979. He went to West Virginia University in1979 and taught in Industrial Engineering until retirement in 2014. He has published books on Manufacturing Processes, Geometric Programming and Strategic Cost Fundamentals. He has been a member of ASEE since 1968.

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Abstract

Geometric Programming(GP) is based on the arithmetic-geometric inequality where the arithmetic mean is always greater than the geometric mean. Geometric programming is similar to linear programming in that it has a primal and dual solution, but the relationships in linear programming must be linear whereas in geometric programming they are non-linear. Geometric programming started in the 1960’s and focused on problems which had non-linear terms in its primal format. The dual format has a linear form which makes it easier to solve. The individual dual terms of the dual objective function represent the portion that term contributes to the total cost. The primal variables can then often be solved by using the primal-dual relationships for each term. Design equations for the primal variables can be developed from the primal and dual solutions and the primal-dual relationships. These relationships can be used to evaluate the output variables without reworking the problem to obtain the solution by using the design equations developed. Two examples are presented in detail to illustrate the unique design equations developed for the primal variables. The first example is the Metal Casting Riser Design Problem which was published in 1971 and illustrates the primal format, the dual format, and the design equations for the two variables - riser height and riser diameter as well as the objective function which is the minimum riser volume. The second example is a Cobb-Douglas Cost Minimization Model for the Civil Engineering Construction Sector of Turkey which was first published in 2012 and the initial design equations were first published 2015. The Cobb-Douglas equation is more complex than the riser solidification time requirement and the equations for the variables were also more complex. The model was tested over a wide range of the input values to evaluate the primal and dual objective functions and the primal variables. The testing results indicated that the exponents of the Cobb-Douglas constraint must be positive and sum to unity for this specific problem, which was not indicated in the initial paper. This led to a better final set of design equations for the problem.

Citation
Format

Creese, R. (2022, August), Design Equations Developed by Geometric Programming Paper presented at 2022 ASEE Annual Conference & Exposition, Minneapolis, MN. 10.18260/1-2--41224

TY - CPAPER
AB - Geometric Programming(GP) is based on the arithmetic-geometric inequality where the arithmetic mean is always greater than the geometric mean. Geometric programming is similar to linear programming in that it has a primal and dual solution, but the relationships in linear programming must be linear whereas in geometric programming they are non-linear. Geometric programming started in the 1960’s and focused on problems which had non-linear terms in its primal format. The dual format has a linear form which makes it easier to solve. The individual dual terms of the dual objective function represent the portion that term contributes to the total cost. The primal variables can then often be solved by using the primal-dual relationships for each term. Design equations for the primal variables can be developed from the primal and dual solutions and the primal-dual relationships. These relationships can be used to evaluate the output variables without reworking the problem to obtain the solution by using the design equations developed. Two examples are presented in detail to illustrate the unique design equations developed for the primal variables. The first example is the Metal Casting Riser Design Problem which was published in 1971 and illustrates the primal format, the dual format, and the design equations for the two variables - riser height and riser diameter as well as the objective function which is the minimum riser volume. The second example is a Cobb-Douglas Cost Minimization Model for the Civil Engineering Construction Sector of Turkey which was first published in 2012 and the initial design equations were first published 2015. The Cobb-Douglas equation is more complex than the riser solidification time requirement and the equations for the variables were also more complex. The model was tested over a wide range of the input values to evaluate the primal and dual objective functions and the primal variables. The testing results indicated that the exponents of the Cobb-Douglas constraint must be positive and sum to unity for this specific problem, which was not indicated in the initial paper. This led to a better final set of design equations for the problem.

AU - Robert Creese
CY - Minneapolis, MN
DA - 2022/08/23
PB - ASEE Conferences
TI - Design Equations Developed by Geometric Programming
UR - https://strategy.asee.org/41224
DO - 10.18260/1-2--41224
ER -