Enhancing Top Efficiency by Minimizing Second-Best Scores: A Novel Perspective on Super Efficiency Models in DEA

Abstract

In this paper, we reveal a new characterization of the super-efficiency model for Data Envelopment Analysis (DEA). In DEA, the efficiency of each decision making unit (DMU) is measured by the ratio the weighted sum of outputs divided by the weighted sum of inputs. In order to measure efficiency of a DMU, ${\rm DMU}_j$, say, in CCR model, the weights of inputs and outputs are determined so that the effiency of ${\rm DMU}_j$ is maximized under the constraint that the efficiency of each DMU is less than or equal to one. ${\rm DMU}_j$ is called CCR-efficient if its efficiency score is equal to one. It often happens that weights making ${\rm DMU}_j$ CCR-efficient are not unique but form continuous set. This can be problematic because the weights representing CCR-efficiencty of ${\rm DMU}_j$ play an important role in making decisions on its management strategy. In order to resolve this problem, we propose to choose weights which minimize the efficency of the second best DMU enhancing the strength of ${\rm DMU}_j$, and demonstrate that this problem is reduced to a linear programming problem identical to the renowned super-efficiency model. We conduct numerical experiments using data of Japanese commercial banks to demonstrate the advantage of the supper-efficiency model.