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• We propose a novel multi-criteria data envelopment analysis model. • The proposed two-stage DEA is first considered in the presence of ratio data. • Three states are considered (black-box, free-link, and fix-link). • A multi-criteria structure is used to demonstrate the validity of the models proposed. • An illustrative example on the efficiency of 60 sets of bank branches in Iran is provided. Data Envelopment Analysis (DEA) is a well-known technique for assessing efficiency levels of decision-making units (DMUs). Very often, available data may be expressed as ratios and, in such cases, traditional DEA models cannot be applied as long as biased efficiency results are produced, yielding the issues of efficiency underestimation and pseudo-inefficiency. In this paper, a novel two-stage MCDEA-R model to handle ratio data is developed observing three distinct assumptions – black-box, free-link, and fixed-link – offering a multi-criteria decision making (MCDM) perspective to the efficiency assessment problem in productive networks. While the proposed models are tested by evaluating the efficiency levels of a set of 30 bank branches in Iran, their distinctive features are highlighted in terms of previous literature to model ratio data under network structures. Precisely, there were not only gains in terms of mitigating pseudo-inefficiency and lack of discrimination power of weights issues, but there were also actual gains in terms of efficiency reliability as measured by information entropy. [ABSTRACT FROM AUTHOR]