Efficiency decomposition for general multi-stage systems in data envelopment analysis

• This paper measures the system and stage efficiencies of general multi-stage systems.
• The system efficiency is decomposed into stage efficiencies in product form.
• A sharp drop in efficiency in one stage is more serious than a moderate drop in every stage.
• Dynamic systems share the same properties of the general multi-stage system.

Conventional data envelopment analysis (DEA) models only consider the inputs supplied to the system and the outputs produced from the system in measuring efficiency, ignoring the operations of the internal processes. The results thus obtained sometimes are misleading. This paper discusses the efficiency measurement and decomposition of general multi-stage systems, where each stage consumes exogenous inputs and intermediate products (produced from the preceding stage) to produce exogenous outputs and intermediate products (for the succeeding stage to use). A relational model is developed to measure the system and stage efficiencies at the same time. By transforming the system into a series of parallel structures, the system efficiency is decomposed into the product of a modification of the stage efficiencies. Efficiency decomposition enables decision makers to identify the stages that cause the inefficiency of the system, and to effectively improve the performance of the system. An example of an electricity service system is used to explain the idea of efficiency decomposition.