5. Conclusions
The methodology proposed in this paper for ranking efficient and inefficient DMUs based on dominance measures derived from social network analysis has several advantages. First, the network that is built represents graphically the relationships between an inefficient DMU and its reference set. This simplifies the interpretation of the role played by each DMU within the set. Furthermore, allows managers to visualize the network relations between DMUs. Second, the modified bidimensional hubs and authorities measure provides a basis for ranking efficient and inefficient units. The values of hubs and authorities reflect the following desirable properties for ranking methods: Property
1. Efficient DMU’s are always ranked above inefficient units. (Since the set of authorities coincides with the set of efficient units) Property
2. The ranking of an efficient unit is higher when an inefficient unit that contains the efficient DMU in its reference set represents a good benchmark (the ranking of an efficiency unit is larger when the inefficient units that contain the efficient DMU in their reference sets represent “good” hubs, i.e., their reference sets contains efficient DMUs that are also good examples of management practices for the other DMUs). Property
3. An efficient DMU that is not a reference for any inefficient DMU must be ranked after the remaining efficient DMUs. In this situation, as noted by Charnes et al. (1978), the efficient unit does not act as a benchmark for any inefficient DMU except itself, which is the case of a self-evaluator. (The efficient DMUs that are not references for any inefficient DMU have an authority weight equal to zero.) Property
4. The ranking method can be used independently of the DEA model assumption (CRS, VRS, super-efficiency, etc.)
