Decision-making is a ubiquitous and paramount issue in the modern business world. Inappropriate decisions may lead to severe consequences for companies. Considering that the evaluation of alternatives is generally affected by several criteria, decision-making should be considered a very challenging task. From the 1945s to the present day, various multi-criteria decision-making (MCDM) methods have evolved, supporting people in the decision-making process. The main aim of this paper is to propose an original MCDM method and to demonstrate its applicability in an empirical case study that relates to the Electric Vehicle (EV) selection problem. To solve the electric vehicle selection problem for the last-mile delivery, we developed and applied a new MCDM method - the AROMAN (Alternative Ranking Order Method Accounting for Two-Step Normalization) method. The main contribution of the AROMAN method is coupling the linear and vector normalization techniques to obtain precise data structures used in further calculation. In addition, the original final ranking equation is developed. To demonstrate the robustness of the proposed method, a comparative analysis with other state-of-the-art MCDM methods is conducted. The results indicate a high level of confidence in the AROMAN method in the decision-making field. In addition, the sensitivity analysis is performed, and the results indicate a high level of stability. Nevertheless, based on the confident results, the managerial implications have also been indicated.