Brass alloy blending problem from quality and cost perspectives: A multi-objective optimization approach

Abstract

Brass alloy is a composition of copper and zinc and it also includes lead, iron, tin, aluminum, nickel, antimony if necessary. One of the basic problems in brass casting is to determine which pure and scrap materials will be mixed at what quantities; this problem is known as the blending problem. The ingredient ratios of pure materials are exactly known, however they are expensive. The scrap materials are cheaper than the pure ones with varying ingredient ratios. Stochastic mathematical models aiming to minimize blend cost have been developed in the literature. In the solutions of these models, some of the ingredient ratios exactly equal to the specification limits. Because of the variation, some of them may violate the specification limits and cause quality problems in the actual blends. There is only one study in the literature to solve the quality problem by maximizing the process capability index. However, the blend cost increases when the process capability index maximized. In this study, a multi-objective stochastic mathematical model, which aims both to minimize blend cost and to maximize process capability index, has been developed. The developed model has been converted to a deterministic non-linear counterpart by using chance-constrained programming. Then, fuzzy programming is used to transform the multi-objective model into a single objective one. A solution procedure has been proposed to use it effectively in real life applications. The developed model and solution procedure have been tested by the data supplied from a brass factory. The solution of the numerical example has shown that the developed model and solution procedure can be used successfully in real life applications.