Finding the most efficient decision making unit in data envelopment Analysis

Although discriminating between all efficient decision making units (DMUs) with identical efficiency is a very important subject in data envelopment analysis (DEA), it may not be an easy task, particularly when the decision maker wants to select one and only one efficient DMU among all. There are some papers that have proposed methods for finding an efficient DMU as the most efficient one but have some difficulties when used in practice. This paper points out the difficulties of the methods presented in two articles [Amin, G. R., (2009).  Comments on finding the most efficient DMUs in DEA: An improved integrated model. Computers and Industrial Engineering 56, 1701-1702; Toloo, M., Nalchigar, S., (2009). A new integrated DEA model for finding most BCC-efficient DMU. Applied Mathematical Modelling, 33, 597-604]. In fact, in the present paper, it is proved by some examples that although some methods have principally been proposed in order to determine a single efficient DMU as the most efficient one, they may be unable to detect these DMUs.