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    Can the uncertainty in brass casting blending problem be managed? A probability/possibility transformation approach
    (Pergamon-Elsevier Science Ltd, 2011) Sakalli, Umit Sami; Baykoc, Omer Faruk
    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.
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    An optimization approach for brass casting blending problem under aletory and epistemic uncertainties
    (Elsevier Science Bv, 2011) Sakalli, Umit Sami; Baykoc, Omer Faruk
    A critical process in brass casting is the determination of the materials and their quantities to be added into the blend. The reason of being critical is the uncertainty about metal percentages in scrap raw materials. In this paper, the aleatory and epistemic uncertainties, which are modeled by using probability and possibility theory, respectively, have been handled simultaneously in a blending optimization problem for brass casting and a solution approach that transforms the possibilistic uncertainties into probabilistic ones is proposed. A numerical example is performed by the data supplied from MKE brass factory in Turkey. The results of the example have showed that the proposed approach can be effectively used for solving blending problem including aleatory and epistemic uncertainties in brass casting and other scrap based production process. (C) 2011 Elsevier B.V. All rights reserved.
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    A possibilistic aggregate production planning model for brass casting industry
    (Taylor & Francis Ltd, 2010) Sakalli, Umit Sami; Baykoc, Omer Faruk; Birgoren, Burak
    This article discusses a possibilistic aggregate production planning (APP) model for blending problem in a brass factory; the problem computing optimal amounts of raw materials for the total production of several types of brass in a planning period. The model basically has a multi-blend model formulation in which demand quantities, percentages of the ingredient in some raw materials, cost coefficients, minimum and maximum procurement amounts are all imprecise and have triangular possibility distributions. A mathematical model and a solution algorithm are proposed for solving this model. In the proposed model, the Lai and Hwang's fuzzy ranking concept is relaxed by using 'Either-or' constraints. An application of the brass casting APP model to a brass factory demonstrates that the proposed model successfully solves the multi-blend problem for brass casting and determines the optimal raw material purchasing policies.
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    Stochastic optimization for blending problem in brass casting industry
    (Springer, 2011) Sakalli, Umit Sami; Baykoc, Omer Faruk; Birgoren, Burak
    A critical process in brass casting is blending of the raw materials in a furnace so that the specified metal ratios are satisfied. The uncertainties in raw material compositions may cause violations of the specification limits and extra cost. In this study, we proposed a chance-constrained stochastic programming approach for blending problem in brass casting industry to handle the statistical variations in raw material compositions. The proposed approach is a non-linear mathematical model that is solved global optimally by using GAMS/BARON solver. An application has been performed in MKEK brass factory in KA +/- rA +/- kkale, Turkey and the solution of the application has been compared with alternative solution approaches based on cost and specification violation risk conditions. This comparison demonstrates that the proposed model is the most effective solution approach for managing stochastic uncertainties in blending problems and successfully can be used other industries such as alloy steel or secondary aluminum production.