Abstract
Geometric Programming is extended to include convex quadratic functions. Generalized Geometric Programming is applied to this class of programs to obtain a convex dual program. Machining economics problems fall into this class. Such problems are studied by applying this duality to a nested set of three problems. One problem is zero degree of difficulty and the solution is obtained by solving a simple system of equations. The inclusion of a constraint restricting the force on the tool to be less than or equal to the breaking force provides a more realistic solution. This model is solved as a program with one degree of difficulty. Finally the behavior of the machining cost per part is studied parametrically as a function of axial depth.
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This research was supported by the Air Force Office of Scientific Research Grant AFOSR-83-0234
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Jefferson, T.R., Scott, C.H. Quadratic geometric programming with application to machining economics. Mathematical Programming 31, 137–152 (1985). https://doi.org/10.1007/BF02591746
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DOI: https://doi.org/10.1007/BF02591746