This study aims to evaluate critical success factors (CSFs), considering the perspectives of various stakeholders who are involved in enterprise resource planning (ERP) implementation in agricultural processing companies in Central Macedonia (Greece). This evaluation—combined with aspects from the literature—may show how a digital production system can be managed and redesigned to become sustainable for a company. Research was conducted through the use of a specially designed questionnaire that was addressed to various stakeholders in the ERP implementation in agricultural processing companies. Descriptive statistics, Grey Relational Analysis (GRA), and Friedman test methods were used in order for relevant information to be identified and valid conclusions to be drawn. Given the results of the grey relational analysis (GRA), respondents consider 33 out of 37 critical success factors to be “very important”. Friedman test results seem to differ from GRA results in 19 out of 37 factors with regard to their ranking. Based on this, and using two different methods, the most important ERP critical success factors are highlighted. For the objective aim of this paper to be fulfilled, there is a contribution giving insights into stakeholders’ perspectives regarding the management of a digital production system in the field of agricultural processing companies. It also contributes to the literature, as it highlights methods that refer to the evaluation of critical success factors for ERP implementation.