Can the uncertainty in brass casting blending problem be managed? A probability/possibility transformation approach

Abstract

Problems about the uncertainty in raw material compositions are a critical issue for the blending problems. It is feared that uncertainty in raw material compositions would often cause percent values of the actual blend to go out of specification limits. In this paper, the aleatory and epistemic uncertainties have been handled simultaneously in a blending optimization problem for brass casting. The aleatory and epistemic uncertainties are modeled by using probability and possibility theories respectively. However, the probabilistic and the possibilistic uncertainties are different from the each other. Therefore to solve the mathematical model, including these uncertainties, a transformation of any type of uncertainty to the other is needed. In this study, probabilistic uncertainties are transformed to the possibilistic uncertainties by considering Rong and Landelma's (2008) and the Dubois, Prade, and Sandri (1993) and Dubois, Foulloy, Mauris, and Prade (2004) transformation approaches. This transformation process converts the former model to a possibilistic model. Then the possibilistic models, obtained from each transformation, are solved by using a cuts approach. The solutions of the two possibilistic models have shown that the model, which uses Dubois's transformation, prepares blends with lower cost than the other model, which uses Rong and Landelma's transformation. (C) 2011 Elsevier Ltd. All rights reserved.