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In energy-oriented lot-sizing and scheduling research, it is often assumed that minimizing energy costs automatically leads to an improvement of the ecological footprint of a company, i.e., lower carbon dioxide emissions. More precisely, a close to one (positive) correlation between energy costs and carbon dioxide emissions is often supposed. In this contribution, we show that this conjecture does not always hold true due to fluctuating carbon dioxide emissions over the whole day. Therefore, we present a real-world business case study, combining lot-sizing and machine scheduling under time-varying electric energy costs and carbon dioxide emissions in a mixed integer optimization model; in this context, we also consider on-site power generation. The interplay between all these aspects is demonstrated via a numerical analysis.

Data envelopment analysis (DEA) is a linear programming method for measuring the performance and efficiency of units called decision-making units (DMUs). In many real-world performance measurement problems, the input and output data are not precisely known. Furthermore, the data may include dual-role factors that can be considered an input and output factor simultaneously. We propose a novel DEA model in the presence of imprecise data and imprecise dual-role factors by developing a new pair of mixed binary linear epsilon-based DEA models. The proposed models estimate the lower and upper bound efficiency scores in the presence of interval input, output, and dual-role factors by considering a fixed and unified production frontier for all DMUs. We then extend our models by including the weak ordinal dual-role factors. In contrast to the existing methods that exclude the dual-role factors, we include the dual-role factors and find a strictly positive value for the lower bound of the weights of inputs, outputs, and dual-role factors. We present a case study to demonstrate the applicability and exhibit the superiority of our approach over the existing methods.