In this paper, we consider the supplier selection problem, which deals with comparing two one-sided processes and selecting a better one that has a higher capability. We first review two existing approximation approaches, and an exact approach proposed which we refer to as the division method. We then develop a new exact approach called the inftraction method. We compare the two exact methods on the selection power. The results show that the proposed inftraction method is indeed more powerful than the division method. A two-phase selecting procedure is then developed based on the inftraction method for practical applications. Some computational results are tabulated for practitioners' convenience.