© 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.The success of businesses today is largely dependent on their ability to find solutions to complex problems they encounter. Vehicle selection, which requires considering many objective and subjective criteria, is at the top of these problems. The tramway selection problem of a company operating in the public transport sector in Turkey is discussed in this study. The company wants to increase passenger carrying capacity and renew its vehicle fleet. For this purpose, it has to choose from eight alternative vehicles with different superior features. Considering the high costs that may arise from wrong selection, it becomes clear how important it is to use the right method to solve the problem. In this study, the evaluation criteria were determined by taking the opinions of experts first. Then, weights were assigned to the criteria using the Analytical Hierarchy Process (AHP). In the last stage, the best alternative has been tried to be determined by using grey relationship analysis (GRA). It is common to use more than one method to test the reliability of the results in solving multi-criteria decision-making (MCDM) problems. In this study, multi-objective optimization, based on ratio analysis (MOORA), which is one of the most preferred methods to solve MCDM problems, was used to test the accuracy of the results. Although various MCDM methods are used in the literature to solve similar problems, the use of grey relationship analysis has not been encountered. With this aspect, this study has expanded the application of grey theory and made an important contribution to the literature. Another important contribution of the study is that the evaluation criteria for the tramway selection problem have been determined with the help of experts. Finally, this study presents a scientific approach to the solution of a complex real-life problem.