Efficiency measurement for hierarchical network systems

The conventional data envelopment analysis (DEA) models for measuring the relative efficiency of a set of decision making units (DMUs), without considering the operations of the component processes, often produce misleading results, and network models have thus been recommended. This paper discusses the development of a network DEA model for systems with a hierarchical structure. It is shown that the hierarchical structure is equivalent to a parallel structure, with the components being the units at the bottom of the hierarchy. Due to the characteristics of a parallel system, the efficiency of a hierarchical system is thus a weighted average of those of the units at the bottom of the hierarchy. A hypothetic example shows that the proposed model is able to distinguish the order of the efficient DMUs evaluated by the conventional DEA model. Moreover, it provides the efficiencies of the functions of the DMU, which enables managers to identify areas of weakness, and thus better focus efforts to improve overall performance.