Software selection process for many organizations is a challenging task to conduct their business activities and sustain competitiveness. This paper develops a new hybrid multi-criteria decision-making (MCDM) method to select the most efficient vendor-supplied software package which is used in all business activities for planning or designing, organizing, and supervising functions by operations management of a fuel oil company operated in Turkey. The proposed method is a hybridization of two well-known MCDM approaches, namely TODIM (an acronym in Portuguese for interactive and multi-criteria decision making) and TOPSIS (technique for order preference by similarity to an ideal solution) using Pythagorean cubic fuzzy sets to manage uncertainty, subjectivity and bias of decision makers. To prove the efficiency and applicability of the proposed method, a real-life application to select best software package for fuel oil company is conducted. Finally, sensitivity and comparison analyses are carried out to verify validity and stability of the results obtained by the proposed approach.