a new approach to measure the effects of undesirable outputs on the efficiency of production units in the presence of ratio data

The efficiency score of the decision making units (dmus) depends on the input and output values. the efficiency sore of the dmu in the presence of undesirable outputs is greater or equal to the efficiency score of this dmu in the absence of undesirable outputs. to face this problem, we present a new ratio based data envelopment analysis (dea-r) model to measure the effects of undesirable outputs on the efficiency of production units. in this regard, we first introduce the counterpart (hypothetical) units corresponding to the original dmus. these units use the same amount of input to produce the same desirable outputs as the original dmus, but produce a small amount of undesirable outputs compared to the original units. in the following, we use non-radial dea-r models based on slacks corresponding to all the ratios of input components to desirable output and the ratios of undesirable output to desirable output to measure efficiency in the presence of undesirable outputs. also, let s use the efficiency ratio of the main units to their corresponding counterpart units as a reduction factor to show the impact of undesirable outputs. to show the validity of the proposed approach, we evaluate the performance of thirty paper mills and present the results.