Abstract
Cross-efficiency evaluation is an effective methodology for discriminating among a set of decision-making units (DMUs) through both self- and peer-evaluation methods. This evaluation technique is usually used for data envelopment analysis (DEA) models with constant returns to scale due to the fact that negative efficiencies never happen in this case. For cases of variable returns to scale (VRSs), the evaluation may generate negative cross-efficiencies. However, when the production technology is known to be VRS, a VRS model must be used. In this case, negative efficiencies may occur. Negative efficiencies are unreasonable and cause difficulties in calculating the final cross-efficiency. In this paper, we propose a cross-efficiency evaluation method, with the technology of VRS. The cross-efficiency intervals of DMUs were derived from the associated aggressive and benevolent formulations. More importantly, the proposed approach does not produce negative efficiencies. For comparison of DMUs with their cross-efficiency intervals, a numerical index is required. Since the concept of entropy is an effective tool to measure the uncertainty, this concept was employed to build an index for ranking DMUs with cross efficiency intervals. A real-case example was used to illustrate the approach proposed in this paper.
Highlights
Data envelopment analysis (DEA) is a non-parametric method for efficiency evaluation of a group of homogeneous decision-making units (DMUs) that consume multiple inputs to produce multiple outputs
One of the main shortfalls of the traditional DEA models is their inability to discriminate among DMUs that are all deemed efficient [1]
Cross efficiency is an aggregate efficiency measured from the viewpoints of all DMUs
Summary
Data envelopment analysis (DEA) is a non-parametric method for efficiency evaluation of a group of homogeneous decision-making units (DMUs) that consume multiple inputs to produce multiple outputs. Entropy 2019, 21, 1205 aggregating its self-evaluated efficiency and its efficiencies peer-evaluated by the others In this case, every DMU has n efficiency scores calculated from n sets of weights selected by all n DMUs, including itself. Under constant returns to scale (CRS), Liang et al [5] proposed a game cross-efficiency model to generate a set of cross efficiencies that constitutes a Nash equilibrium point for the DMUs. Jahanshahloo et al [6] incorporated a symmetric technique into the cross-efficiency evaluation that could choose symmetric weights for DMUs. There are some methods that select suitable weights from alternative solutions to avoid large differences among the weights. Existing approaches for cross-efficiency evaluations are often averaging the entries of the crossefficiency matrix column-wise, that is, the average cross-efficiency, to further discriminate among the DEA efficient units In this case, the problem of choosing the aggressive (lower bound efficiency) or benevolent formulation (upper bound efficiency) for decision-making might still remain.
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