Detecting the multi-period performance and efficiency changes of systems with undesirable outputs

Abstract

Data envelopment analysis (DEA) is a technique to evaluate the relative efficiency of a set of decision making units (DMUs) which is applicable in different systems such as engineering, ecology, and so forth. In real-world situations, there are instances in which production processes of systems must be analyzed in multiple periods while desirable and undesirable outputs are present; therefore, in the current paper, a DEA-based procedure is suggested to estimate the performance of systems with desirable and undesirable outputs over several periods of time. Actually, the overall and period efficiencies of DMUs in the presence of undesirable outputs are calculated by using the DEA technique. Different aspects of disposability, i.e., strong and weak, are considered for undesirable outputs. Moreover, the overall efficiency is indicated as a weighted average of the efficiencies of periods. Efficiency changes between two periods are also estimated. The proposed approach has been tested by a numerical example and applied to evaluate the efficiency of commercial transport industry in 17 countries. The findings show that efficiency scores and their changes between periods might alter by incorporating undesirable outputs into the multi-period system under evaluation; consequently, the proposed approach obtains more rational and accurate results when undesirable outputs are present.