Identification of Strong and Weak Hyperplanes in Data Envelopment Analysis

Finding of the strong and weak) defining hyperplanes of the production possibility set (PPS) is an important subject in data envelopment analysis (DEA). The concept of strong defining hyperplanes is useful in dealing with the status of returns to scale (RTS), sensitivity and stability analysis and so on. Clearly, if the optimal solutions of the envelopment form for extreme efficient DMUs are degenerate, the multiplier form may have alternative optimal solutions which yield various supporting hyperplanes at the PPS. In this study, it is shown that the strong (weak) defining hyperplane is supporting and there exists, at least, one affine independent set with m + s elements of extreme efficient DMUs (extreme efficient and weak efficient virtual DMUs) where m and s are the number of inputs and outputs, respectively. This paper aims at obtaining all the defining hyperplanes of the PPS. Moreover, the characterization of the stability region preserving the RTS classification and efficiency classification is an arguable issue which is easily obtained by strong defining hyperplanes.