Ranking efficient DMUs based on single virtual inefficient DMU in DEA

This paper describes an approach to rank the efficient DMUs (Decision Making Units) based on a single DMU, referred as virtual DMU. The virtual DMU is created in such a way that its inputs and outputs are the averages of the corresponding inputs and outputs of all the DMUs. It is shown that this DMU is always inefficient compared to the efficient DMUs in the set if there exists at least one inefficient DMU. The work in this paper proposes to rank efficient DMUs based on the influence of efficient DMUs on the efficiency of the virtual DMU. This paper also establishes some of the properties of the virtual DMU. Our proposed method of ranking is compared with the existing methods. This approach of ranking produces stable efficient DMUs in the higher order of the ranks. This method is simple and robust compared to existing methods.