Mathematical Models and Polyhedral Studies for Integral Sheet Metal Design
E. Ferreira C, Günther U, Martin A (2012)
Publication Language: English
Publication Type: Journal article
Publication year: 2012
Journal
Publisher: Society for Industrial and Applied Mathematics
Book Volume: 22
Pages Range: 1493 -- 1517
Journal Issue: 4
Abstract
We deal with the optimization of the production of branched sheet metal products. New forming techniques for sheet metal give rise to a wide variety of possible profiles and possible ways of production. In particular, we show how the problem of producing a given profile geometry can be modeled as a discrete optimization problem. We provide a theoretical analysis of the model in order to improve its solution time. In this context we give the complete convex hull description of some substructures of the underlying polyhedron. Moreover, we introduce a new class of facet-defining inequalities that represent connectivity constraints for the profile and show how these inequalities can be separated in polynomial time. Finally, we present numerical results for various test instances, both real-world and academic examples.
Moreover, we introduce a new class of facet-defining inequalities that
Read More: http://epubs.siam.org/doi/abs/10.1137/110853248
Read More: http://epubs.siam.org/doi/abs/10.1137/110853248
Moreover, we introduce a new class of facet-defining inequalities that represent connectivity constraints for the profile and show how these inequalities can be separated in polynomial time. Finally, we present numerical results for various test instances, both real-world and academic examples.
Read More: http://epubs.siam.org/doi/abs/10.1137/110853248
Read More: http://epubs.siam.org/doi/abs/10.1137/110853248
We deal with the optimization of the production of branched sheet metal products. New forming techniques for sheet metal give rise to a wide variety of possible profiles and possible ways of production. In particular, we show how the problem of producing a given profile geometry can be modeled as a discrete optimization problem. We provide a theoretical analysis of the model in order to improve its solution time. In this context we give the complete convex hull description of some substructures of the underlying polyhedron. Moreover, we introduce a new class of facet-defining inequalities that represent connectivity constraints for the profile and show how these inequalities can be separated in polynomial time. Finally, we present numerical results for various test instances, both real-world and academic examples.
Read More: http://epubs.siam.org/doi/abs/10.1137/110853248
Read More: http://epubs.siam.org/doi/abs/10.1137/110853248
Authors with CRIS profile
Involved external institutions
University of São Paulo / Universidade de São Paulo (USP)
Brazil (BR)
Technische Universität Darmstadt
Germany (DE)
Brazil (BR)
Technische Universität Darmstadt
Germany (DE)
How to cite
APA:
E. Ferreira, C., Günther, U., & Martin, A. (2012). Mathematical Models and Polyhedral Studies for Integral Sheet Metal Design. SIAM Journal on Optimization, 22(4), 1493 -- 1517.
MLA:
E. Ferreira, Carlos, Ute Günther, and Alexander Martin. "Mathematical Models and Polyhedral Studies for Integral Sheet Metal Design." SIAM Journal on Optimization 22.4 (2012): 1493 -- 1517.
BibTeX: Download