DEA radial and non-radial models for unified efficiency under natural and managerial disposability: Theoretical extension by strong complementary slackness conditions

This study proposes a use of Data Envelopment Analysis (DEA) for environmental assessment. All radial and non-radial models are discussed under natural and managerial disposability. The natural disposability implies corporate strategy by which a firm attempts to decrease an input vector to decrease a vector of undesirable outputs. Given the decreased input vector, a firm attempts to increase a vector of desirable outputs as much as possible. This type of strategy, supported by economists, indicates negative adaptation to a regulation change on undesirable outputs. In contrast, the managerial disposability indicates opposite strategy by increasing the input vector. This disposability expresses corporate strategy by which a firm considers the regulation change as a new business opportunity. A firm attempts to improve its performance by utilizing new environmental technology and/or new management. This type of strategy, supported by corporate strategists in U.S. business schools, indicates positive adaptation to the regulation change on undesirable outputs. Using the proposed DEA assessment, this study examines the relationship among energy consumption, economic development and environmental protection in Japanese prefectures. To theoretically extend the use of DEA for environmental assessment, this study incorporates Strong Complementary Slackness Conditions (SCSCs) into the proposed radial models. The incorporation of SCSCs has three methodological strengths. First, DEA/SCSCs can handle an occurrence of multiple reference sets and multiple projections. Second, the incorporation of SCSCs makes it possible to restrict dual variables (multiples) in a specific range without any prior information. Finally, DEA/SCSCs can bypass the conventional procedure (i.e., a radial model combined with an additive model) used for DEA radial measurement.