A new method in data envelopment analysis to find efficient decision making units and rank both technical efficient and inefficient DMUs together

The inefficient DMUs are usually arranged after the technical efficient ones by DEA methods, however, it is possible that a technical efficient DMU neither be efficient nor be more efficient than some inefficient ones. This study distinguishes between the terms 'technical efficiency' and 'efficiency' and demonstrates that the technical efficiency is a necessary condition for being efficient and it is not an enough condition to call a DMU as efficient DMU. The study identifies the definitions of those terms and gives a new strong method to characterize efficient DMUs among the technical efficient ones. The new method, although, avoids the need for recourse to prices, weights or other assumptions between inputs and outputs of DMUs, it is also able to consider the prices and weights. A numerical example is also characterized the worth and benefits of the new proposed model in comparison with all current DEA models.