A neutral cross efficiency approach for basic two stage production systems

•This paper proposes a neutral cross efficiency model for basic two-stage systems.•Proposed model can obtain more realistic weight scheme than basic two stage systems.•Proposed model can fully rank the units in overall (system) and sub-stages.•The system efficiency is the product of the sub-stages efficiencies. Cross efficiency evaluation in data envelopment analysis (DEA) is an effective tool for ranking the performance of decision-making units (DMUs). Numerous cross efficiency evaluations have been proposed with different secondary goals using both peer-evaluation and self-evaluation. The neutral cross efficiency evaluation is an important secondary goal in the classical black-boxes DEA models; that is, the internal processes of the DMUs are often ignored in the efficiency evaluation. This study extends the idea of neutral cross evaluation to measure the efficiency of the basic two stage network systems and proposes a new neutral cross efficiency model. The proposed model is able to rank DMUs in sub-stages and decompose the cross efficiency measure of the system into the product of those of the stages. The results from two real-world examples show that the neutral cross efficiency model proposed in this paper can increase the discriminating power of a two-stage system and their sub-stages and can obtain more realistic weight scheme than basic two stage DEA model.