Deriving Common Set of Weights in the Presence of the Undesirable Inputs: A DEA based Approach

Data Envelopment Analysis (DEA) as a non-parametric method for efficiency measurement allows decision making units (DMUs) to select the most advantageous weight factors in order to maximize their efficiency scores.  In most practical applications of DEA presented in the literature, the presented models assume that all inputs are fully desirable. However, in many real situations undesirable inputs are part of the production process. In order to deal with undesirable inputs, this paper changes the undesirable inputs to be desirable ones by reversing, then a compromise solution approach is proposed to generate a common set of weights under DEA framework. The DEA efficiencies obtained with the most favorable weights to each DMU are treated as the target efficiencies of DMUs. Based on the generalized measure of distance, three types of DEA-based efficiency score programming can be derived. The proposed approach is then applied to real-world data set that characterize the performance of seven types of chemical activities.