The paper is devoted to an optimization approach to a problem of statistical modeling of mechanical properties of heavy steel plates during a real industrial manufacturing process. The approach enables the manufacturer to attain a specific set of the final product properties by optimizing the alloying composition within the grade specifications. Because this composition has to stay in the agreement with earlier indicated specifications, it leads to the large system of linear constraints, and the problem itself can be expressed in the form of linear programming (LP) task. It turns out however, that certain of the constraints contain the coefficients which have to be estimated on the base of the data gathered in the production process and as such they are uncertain. Consequently, the initial optimization task should be modeled as so-called Chance Constrained Programming problem (CCP), which is a special class within the stochastic programming problems. The paper presents mathematical models of the optimization problem that result from both approaches and indicates differences which are important for the decision makers in the production practice. Some examples illustrating the differences in solutions resulting from LP and CCP models are presented as well. Although the statistical analysis presented in this paper is based on the data gathered in the ISD Czestochowa Steelworks, the proposed approach can be adopted in any other process of steel production.
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