A geometrical approach for generalizing the production possibility set in DEA

Consider a Data Envelopment Analysis (DEA) study with n Decision Making Units (DMUs) and a model with m inputs plus outputs. The data for this study are a point set, {a¹,…,aⁿ}in ℜ^m. A DMU is efficient if its data point is located on the efficient frontier portion of the boundary of an empirical production possibility set, a polyhedral envelopment hull described by the data. From this perspective, DEA efficiency is a purely geometric concept that can be applied to general point sets to identify records with extreme properties. The generalized approach permits new applications for nonparametric frontiers. Examples of such applications are fraud detection, auditing, security, and appraisals. We extend the concept of DEA efficiency to frontier outliers in general envelopment hulls.