Some comments on Russell graph efficiency measures in data envelopment analysis: The multiplicative approach

Abstract

In a recently published paper, Alcaraz, J., Anton-Sanchez, L., Aparicio, J., Monge, J. F., & Ramón, N., 2021. Russell graph efficiency measures in Data Envelopment Analysis: The multiplicative approach. European Journal of Operational Research, 292(2), 663–674, propose multiplicative versions of Russell-type graph efficiency measures based on geometric aggregations of input and output efficiency measures. Within the data envelopment analysis framework, they devise an iterative algorithm to solve the multiplicative models via a second order conic programming approach. In this paper, we demonstrate that the proposed models are not convex and reformulate them as two equivalent well-known types of nonconvex optimisation problems. By providing a numerical counterexample, we illustrate that their proposed algorithm may stop at a local optimum rather than converging to a global optimal solution. Some computational remarks are further suggested in regard to solving the proposed models.