Evaluating radial efficiency considering environmental factors: A generalization of classical DEA

Environmental issues are becoming a significant and serious worldwide problem. Undesirable outputs like waste and pollution are by-products of desirable outputs in a production system. To motivate environment friendly production, undesirable outputs should be included in the performance assessment of firms, organizations and countries. Data Envelopment Analysis (DEA) is one of the most successful methods of efficiency evaluation. Unfortunately, there is no reliable radial efficiency measure for environmental assessment in DEA. In this paper, the conventional modeling in DEA is extended to develop a new radial model for efficiency assessment in the presence of undesirable outputs. This method enables more accurate modeling of the problem. It opens a new door to the issue, and shows more reliabilities than the existing methods. The new efficiency measure is more rigorous, and provides higher discriminating power. Evaluating divisional efficiency is another advantage of the model. It also provides credible targets with greater practical accessibility for each inefficient decision making unit. The model is studied by an axiomatic approach and employed to evaluate the performance of 28 countries in economic, social and environmental dimensions. The results show that only one country achieves efficiency, and the average environmental efficiency is considerably lower than the operational efficiency among the studied countries.