Measurement and evaluation of multi-function parallel network hierarchical DEA systems

Many organisations are composed of multiple departments connected either in series or in parallel, which may be further decomposed into a number of functions arranged in a hierarchical structure. Several researchers have successfully used appropriate Data Envelopment Analysis (DEA) modelling techniques to assess complex structures. However, to our knowledge, no-one has yet examined the case of measuring and evaluating a parallel network structure combined with a hierarchical one. This paper discusses the development of a multi-function parallel system with embedded hierarchical network structures. A linear additive decomposition DEA model and a non-linear multiplicative aggregation DEA model are proposed as alternatives to evaluate the operating performance of such a structure. The system, the sub-systems, and the efficiencies of their internal units, as well as their relationships, are identified. The system efficiency of the additive model is shown to be greater than or equal to that of the multiplicative model. To verify the applicability of our proposed models, we consider a hypothetical example of the measurement and evaluation of the performances of several Business Schools across a number of universities. Other envisaged areas of application of our structure could include supporting the evaluation of the supply chain management of a firm, or the determination of the most desirable ship design considering maintenance issues.