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We demonstrate that this equation is statistically precise by conducting a study with a database in which machine learning techniques were applied to assess the predictive accuracy of CO<jats:sub>2<\/jats:sub> emissions. The comparison between the explicit equation and machine learning models proves its efficacy as a suitable approximation for practical applications. Then, we propose an augmented <jats:italic>\u025b<\/jats:italic>-constrained method to find the efficient Pareto frontier using a branch-and-cut method. Computational experiments were conducted on 285 instances, of which 125 were adapted from the literature, solving the augmented <jats:italic>\u025b<\/jats:italic>-constrained optimally. Result analysis indicates the ability of the approach to trade off between economy and sustainability, where, on average, lexicographic solutions show a 58% reduction in emissions and a 36% increase in costs. 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