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 uctuating 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.