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While measuring returns to scale in data envelopment analysis (DEA), theoccurrence of multiple supporting hyperplanes has been perceived as a crucialissue. To deal effectively with this in weigh restrictions (WR) framework, wefirst precisely identify the two potential sources of its origin in thenon-radial DEA setting. If the firm under evaluation P is WR-efficient, thenon-full-dimensionality of its corresponding P-face-a face of minimum dimensionthat contains P-is the unique source of origin (problem Type I). Otherwise, theoccurrence of multiple WR-projections or, correspondingly, multiple P-facesbecomes the other additional source of origin (problem Type II). To the best ofour knowledge, while problem Type I has been correctly addressed in theliterature, the simultaneous occurrences of problems Types I and II have noteffectively been coped with. Motivated by this, we first show that problem TypeII can be circumvented by using a P-face containing all the P-faces. Based onthis finding, we then devise a two-stage linear programming based procedure byextending a recently developed methodology by [Mehdiloozad, M., Mirdehghan, S.M., Sahoo, B. K., & Roshdi, I. (2015). On the identification of the globalreference set in data envelopment analysis. European Journal of OperationalResearch, 245, 779-788]. Our proposed method inherits all the advantages of therecently developed method and is computationally efficient. The practicalapplicability of our proposed method is demonstrated through a real-world dataset of 80 Iranian secondary schools.

Measurement of returns to scale with weight restrictions: How to deal with the occurrence of multiple supporting hyperplanes?