Ute Günther

Optimization of Sheet Metal Products

Linear flow splitting enables the forming of branched sheet metal products in integral style. To optimize those products design parameters have to be based on market requirements. We show that methods that are also used in Operations Research can, in principle, be applied to solve these optimization problems. For this, engineers provide constructive parameters that describe the demands of customers in a mathematical way. Based on these descriptions, we develop a two-stage model. First, a topology and shape optimization of branched sheet metal products is carried out, where the best-possible product is automatically designed by solving some OR models. Then, in stage two, we deal with the problem of how to incorporate manufacturing constraints for sheet metal products. The solution to this model corresponds to a construction plan. The entire approach is demonstrated in the design and construction of a cable conduit.

Mathematical Models and Polyhedral Studies for Integral Sheet Metal Design

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.