Measurement of Returns to Scale and Damages to Scale for DEA-based operational and environmental assessment: How to manage desirable (good) and undesirable (bad) outputs?

Environmental assessment is increasingly important in preventing various types of pollutions. Data Envelopment Analysis (DEA) has been long used as an operational performance measure, but we have insufficiently explored the use of DEA for environmental assessment. This study explores a new use of DEA for the environmental assessment in which outputs are classified into desirable (good) and undesirable (bad) outputs. Such an output separation is important in the DEA-based environmental assessment. This study extends the use of DEA to the measurement of both Returns to Scale (RTS) for desirable outputs and Damages to Scale (DTS) for undesirable outputs. A Range-Adjusted Measure (RAM) is used as a DEA model for this study because the non-radial model can easily combine the two types of outputs in a unified treatment. All the mathematical features regarding the RAM-based RTS/DTS measurement are first discussed from the operational and environmental performance in a separate treatment. Then, this study combines the two performance measures as a unified measure. The RAM-based RTS/DTS is mathematically explored from the unified measure for operational and environmental performance.