Dealing with undesirable outputs in DEA: An aggregation method for a common set of weights

The existing approaches that deal with undesirable outputs tend to either increase the efficiency scores of DMUs or keep the efficiency scores constant and do not allow undesirable outputs to achieve the opposite effect on the efficiency scores, which is inconsistent with the characteristics of undesirable outputs. To solve this problem, You and Yan proposed a new ratio model to allocate penalty coefficients for the undesirable outputs according to their economic costs, but there are differences of magnitude and dimension in various undesirable outputs under practical applications. Therefore, this study uses common weights instead of the penalty coefficients in the original method to obtain the aggregate weights of undesirable outputs. We propose two new models to calculate the aggregate weights of undesirable outputs and illustrate the methods using data given by You and Yan on China’s textile industry. The results reveal that our approaches can generally reduce the efficiency scores of DMUs after considering undesirable outputs and are more significant than other methods available.