Semi-disposability of undesirable outputs in data envelopment analysis for environmental assessments

The assumptions of strong and weak disposability for undesirable outputs have long dominated studies of data envelopment analysis for environmental assessments. Unfortunately, these assumptions cannot describe the diverse technical features of different undesirable outputs during the actual production process. Thus, we introduce a non-disposal degree to develop a new semi-disposability assumption, which can replace the assumptions of strong and weak disposability in environmental assessments. This assumption ensures that decision makers can address undesirable outputs freely within the scope of current production technology; otherwise, they have to reduce desirable outputs in the same proportion to decrease undesirable outputs. A reference point comparison method is proposed for determining the non-disposal degree from an objective perspective. The assumption of semi-disposability is extended to uncertain circumstances by using the interval non-disposal degree. Finally, two empirical examples are provided to illustrate the effectiveness of the semi-disposability assumption.