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Applications of operations research and statistical modeling tools in industrial-scale settings
Greivel, G. Gustave
Greivel, G. Gustave
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2023
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This work considers the application of operations research and statistical models to two distinct industrial-scale operations. In the first instance, we add to an emerging literature on model formulation ``best practices" and present, as a case study, a reformulation of a widely-used industrial-scale linear program. The efficient mathematical expression of this linear program, used to plan capacity expansion in the energy sector across the entire United States, is agnostic to choice of modeling environment, allowing for greater transparency of model structures, as well as a more lucid interpretation of its solutions. This case study has been employed as an example of the advantages of implementing best practices for the expression of optimization models in several mathematical programming courses at the Colorado School of Mines.
In the second and third instances, we (i) present an optimization model for scheduling a two-caster, hot rolling steel mill, formulated as an integer program, and (ii) consider a large data set from the same mill to develop a novel regression model for the prediction of roll force at roll stands in the mill in order to better estimate a wear parameter in the integer programming model based on steel grade and coil geometry. The integer program requires a non-standard formulation to eliminate variables as well as several innovative cuts to improve model tractability, affording optimal, or near-optimal, solutions on small instances (containing 30 coils) and decreases in the penalties incurred for casting a schedule relative to a benchmark heuristic on larger instances (on the order of 150 coils). This work is unique to the hot rolling mill scheduling literature in that the model does not decouple the casting and rolling operations of the mill.
Within the hot rolling process, we also focus on a wear parameter that is a function of the roll force (i.e., the force that must be applied at a roll stand to achieve the desired reduction in the gauge, or thickness, of the coil). The wear parameter directly how many instances of one of our optimization model penalties will be incurred in a solution to the model. The associated regression model for roll force prediction is informed by a physics-based equation and applies variable transformations, variable selection and model comparisons; it illustrates several topics introduced throughout a regression modeling course, including data visualization, multiple linear regression, residual diagnostics and heteroscedastiscity, variable transformations, collinearity and confounding due to strong correlations between predictor variables, the false correlation paradox, variable selection, and measures of model quality for predictive use. It also adds an interesting data set and associated analysis to the publicly available resources for statistics and data science education.
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