Choosing weights of extreme efficient DMUs in DEA: A comparison of some proposals with application to the Spanish Banking sector
| Main Authors: | González-Pérez, B., López-González, E., Mendaña-Cuervo, C. |
|---|---|
| Format: | Proceeding Journal |
| Bahasa: | eng |
| Terbitan: |
, 2011
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| Subjects: | |
| Online Access: |
https://zenodo.org/record/5113254 |
Daftar Isi:
- Extended abstract This paper is focused on the analysis of one limitation of the Data Envelopment Analysis (DEA) and the effects of some proposals which try to solve it. The extensive use of DEA has demonstrated that it has a lot of advantages but it also has some limitations. An important drawback is related to the Decision Making Units (DMUs) which generate the efficient frontier, the extreme efficient DMUs. They have alterative optimal sets of weights or multipliers for their variables and only one set should be chosen. Although few authors have dealt with this question, there are some proposals which try to solve it. In this sense, we analyze the problem along with some of the formulations proposed to solve it and we apply two of these proposals in order to shed light on their effects on the weights of extreme efficient DMUs and compare them. The extreme efficient DMUs are the vertices of the efficient frontier, so they have infinite supporting hyperplanes which define infinite alternative sets of weights in the multiplier formulation of DEA. However, the efficiency measurement and other utilities of DEA, like a benchmarking tool, a ranking methodology or a method for identifying groups, require choosing only one set of weights. Many authors have ignored this problem and have opted for the first solution of the DEA model, while other researchers have tried to solve the previous limitation by means of different DEA formulations. In this paper we focus on two of these proposals. On one hand, Adu (2001), who uses the cross efficiency concept and the geometrical interpretation of DEA, proposes a DEA model to choose the set of weights associated to the supporting hyperplane which differentiates the specific extreme efficient DMU as much as possible from the rest of the closest extreme efficient DMUs. She tries to select the weights by which the extreme efficient DMU is better than the other ones, i.e., she emphasizes the best different performance of each extreme efficient DMU. On the other hand, Cooper et al. (2007) also select the optimal weights set according to the geometrical interpretation of the multiplier DEA formulation. They propose a two-stage mixed integer linear programming to choose the weights which are associated with the face of the frontier of higher possible dimension to which the extreme efficient DMU belongs, i.e, they select the coefficients of the supporting hyperplane which contains the maximum number of extreme efficient DMUs. In this paper, we apply both formulations to the Spanish Banking Sector in order to know the effects of the two previous proposals but before it, we use the super efficiency DEA model (Andersen y Petersen, 1993) in order to differentiate between efficient an inefficient DMUs and get the first combination of weights of every extreme efficient DMUs. Finally, we compare the weights which have been obtained in the three formulations by means of non-parametric tests and we can observe that the differences among them are statistically significant.