A new Monte Carlo based procedure for complete ranking efficient units in DEA models

Abstract

Traditional data envelopment analysis (DEA) models split DMUs into two classes – namely efficient and inefficient. Due to the identical maximum efficiency scores of the efficient units, they cannot be ranked directly. That is why various models allowing the complete ranking of DMUs have been proposed in the past. Those models are based on different principles and have various advantages and disadvantages (infeasibility, alternative optimum, computational aspects, etc.). The method proposed in this paper uses the magnitude of the area under the efficient curve. In order to estimate this magnitude we suggest to use Monte Carlo simulation for the complete ranking originally efficient DMUs so as to overcome the problems arisen from other ranking methods and it is very simple, computationally. This method generates random weights for the inputs and outputs in the feasible region and finally derives probability the DMUs are efficient. The procedure proposed is illustrated by a numerical example and its results are compared with three of most important and popular methods for ranking efficient units (i.e. cross-efficiency evaluation, Andersen and Petersen super-efficiency model, and common set of weights method).