The subject of this study is the optimization of the paper production process in one of Poland’s leading paper mills. In addition to its primary objective of paper production, the company generates heat and electricity for internal consumption and external clients, including the local municipality. Surplus energy may be sold on the power exchange; however, this requires forecasting the quantity of energy to be sold 24 h in advance, which introduces an element of uncertainty. Production stoppages, often caused by random events such as paper breakage, force a power decrease in the CHP system, further complicating energy forecasting. To minimize the occurrence of such events, numerical taxonomy methods were employed to determine the optimal screen speed (Vs) and winding speed (Vn) for two paper machines, based on the type and weight of the paper produced. This analysis utilized detailed daily data collected by the company over the period 2015–2020. The findings contribute to minimizing the occurrence of paper roll tearing, thereby reducing the risk of inaccurate forecasts of the energy and heat produced by the CHP system. Furthermore, the methodology employed in this study may be effectively applied to other optimization problems in industrial processes.