A note on some of DEA models and finding efficiency and complete ranking using common set of weights

Efficiency evaluation in Data Envelopment Analysis (DEA) depends on different factors. The most important factors arc the values of input and output. In this paper, we present an alternative proof that, if one component of output or input vectors of a DMU dominates the corresponding component of other DMUs whatever the value of other components of this DMU may be, then that DMU is efficient in some of the DEA models. An important outcome of such an analysis is a set of virtual multipliers or weights accorded to each factor taken into account. These sets of weights are, typically, different for each of the participating DMUs. In this paper, by means of solving only one problem, we can determine common set of weights (CSW) for all DMUs and their efficiencies. Finally, a method for ranking DMUs, is presented. In this method by solving only two problems, efficient DMUs are ranked.