The Supplier Selection Problem (SSP) plays a significant role in Supply Chain Management (SCM) in today’s competitive world. With respect to this, the literature reveals that incorporating the viability concept in the SSP for the Oil and Gas (O&G) industry has not been adequately addressed in prior studies. Hence, the current study focuses on the SSP for the energy sector by considering the viability pillars. To do so, a data-driven decision-making model is developed that calculates the weights of indicators executing the Fuzzy Best-Worst Method (FBWM) and then evaluates the performance of the supplier by integrating Data Envelopment Analysis (DEA), Support Vector Machine (SVM), and Random Forest (RF) techniques. Overall, the main contribution of this research is to develop an effective data-driven model to examine the viable SSP for the O&G industry. According to the results obtained, among the potential indicators, cost, quality, responsiveness, manufacturing flexibility, robustness, restorative capacity, pollution control, Waste Management (WM), technical capability, and smart factory are selected as the most significant indicators in their corresponding aspects. Moreover, the comparison results against the classic methods demonstrate the robustness, applicability, and validity of the developed data-driven decision framework. Finally, theoretical and managerial implications are presented.