In order to adapt to ever-changing customer needs and satisfy them, good Business Process Management (BPM) in Small and Medium-sized Enterprises (SMEs) is crucial. The target group of this research is production SMEs whose BPM can be monitored respecting the values of key performance indicators (KPIs). This paper shows how improving the performance of the observed business processes can improve the level of customer satisfaction. This improvement should lead to the sustainability of SMEs in the market. In this paper, evaluation of business processes performance is defined as a multi-criteria decision problem. The relative importance of considered KPIs and their imprecise values are described by linguistic expressions, which are then modeled by triangular intuitionistic fuzzy numbers (TIFNs). Calculation of KPI weights is done by using the fuzzy analytic hierarchy process (FAHP). Evaluation of BPM success is conducted respecting the obtained KPI weights and KPI values. An optimal solution for BPM success improvement, respecting customer satisfaction indicators, is calculated using the Artificial Neural Network (ANN) and Genetic Algorithm (GA) approaches. By applying the proposed model, managers of production SMEs can determine the management initiatives that will improve their business and the sustainability of their companies.