Data envelopment analysis of systems with multiple modes of functioning

Many systems can operate in different modes of functioning. Conventional data envelopment analysis (DEA) would ignore that fact and consider instead that the system is a black box, paying attention just to the overall input consumption and output production. In this paper a more fine-grained approach is proposed consisting of explicitly modelling the different modes of functioning as specific processes and using the observed data on the input consumption and output production in each of the modes of functioning to infer the corresponding mode-specific technology. The system technology results from composing these mode-specific technologies according to the corresponding time allocations. The proposed approach allows computing efficient operating points for every mode of functioning, looking for improvements in the overall system performance. Two efficiency assessment DEA models are presented depending on whether the observed time allocation is maintained or the model is free to modify it. An application of the proposed approach to assessing the efficiency of NFL teams, operating in defence and offence modes in a given game, is presented.