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

TL;DR

This paper addresses the challenge of multiple supporting hyperplanes in DEA when measuring returns to scale with weight restrictions, proposing a new two-stage linear programming method to effectively handle the issue.

Contribution

It introduces a novel two-stage linear programming procedure to manage simultaneous occurrences of multiple hyperplanes in DEA with weight restrictions, extending existing methodologies.

Findings

The method effectively circumvents multiple hyperplane issues.

It is computationally efficient and applicable to real-world data.

Demonstrated on data from 80 Iranian secondary schools.

Abstract

While measuring returns to scale in data envelopment analysis (DEA), the occurrence of multiple supporting hyperplanes has been perceived as a crucial issue. To deal effectively with this in weigh restrictions (WR) framework, we first precisely identify the two potential sources of its origin in the non-radial DEA setting. If the firm under evaluation P is WR-efficient, the non-full-dimensionality of its corresponding P-face-a face of minimum dimension that contains P-is the unique source of origin (problem Type I). Otherwise, the occurrence of multiple WR-projections or, correspondingly, multiple P-faces becomes the other additional source of origin (problem Type II). To the best of our knowledge, while problem Type I has been correctly addressed in the literature, the simultaneous occurrences of problems Types I and II have not effectively been coped with. Motivated by this, we first show that problem Type II can be circumvented by using a P-face containing all the P-faces. Based on this finding, we then devise a two-stage linear programming based procedure by extending a recently developed methodology by [Mehdiloozad, M., Mirdehghan, S. M., Sahoo, B. K., & Roshdi, I. (2015). On the identification of the global reference set in data envelopment analysis. European Journal of Operational Research, 245, 779-788]. Our proposed method inherits all the advantages of the recently developed method and is computationally efficient. The practical applicability of our proposed method is demonstrated through a real-world data set of 80 Iranian secondary schools.