A simplistic approach without epsilon to choose the most efficient unit in data envelopment analysis

Abstract

Data envelopment analysis is a very effective mathematical instrument in assessing the performance of decision-making units. In most real cases, the decision-maker need to identify a single most efficient unit. Several approaches were proposed for this necessity in the literature using data envelopment analysis. This study, based on the two steps model suggested by Toloo and Salahi (2018), proposes a new model without epsilon to choose the most efficient unit. The proposed model has fewer constraints than their model and is solved by a one-step linear programming model without epsilon. The proposed model determines exactly one DMU as the most efficient one and other decision-making units have efficiency scores strictly less than one. A simulation study was designed to test the proposed model in terms of some criteria such as correlation. In addition, the examples of real cases whose real rank is known and frequently used in literature of the most efficient unit were preferred for the validity of the proposed model. The results illustrated that the discrimination power problem was experienced in the previous models whereas no such problem was observed in the new proposed model for the same real cases.