Efficiency decomposition and aggregation in network data envelopment analysis

Network data envelopment analysis (DEA) is extended from conventional DEA to explore the internal structure of network production systems so that the efficiencies are measured more appropriately. There are two approaches for discussing the relationships between the system and division efficiencies, efficiency decomposition and efficiency aggregation. This paper develops a relational model from the viewpoint of efficiency decomposition to derive the relationships between the system and division efficiencies for network systems. The system efficiency can be decomposed into a weighted average of the division efficiencies adjusted by a factor, and the efficiency of the system is less than the weighted average of those of the divisions. The Major League Baseball example that has been discussed in the literature is used to illustrate the idea presented in this paper. The results of the efficiency decomposition model are compared to those obtained from an efficiency aggregation model that defines the aggregate efficiency of the divisions to be the system efficiency. This system efficiency is found to be very close to a measure contained in the proposed model. The proposed model can thus be used for both efficiency decomposition and aggregation.