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Conventional Data Envelopment Analysis (DEA) assesses the performance of Decision-Making Units (DMUs) by measuring only one type of efficiency using definite data. However, due to the vastness of some industries, such as banks, calculating only one type of efficiency cannot confirm DMUs as efficient or inefficient. Also, real-world cases are often faced with uncertain data, and conventional DEA lacks the power to consider these uncertainties in evaluation. In this paper, we develop a multi-objective DEA model to calculate three types of efficiencies, including profitability, operational, and transactional for bank branches when there are uncertain data. First, we apply a modified DEA model which is capable of calculating the common weight of all inputs and outputs by solving only one linear programming model. Then, we employ a robust approach to handle the uncertainty in data. The uncertainty in data is described with discrete scenarios. Discrete scenarios require a set of possible values for each parameter with uncertain nature. Finally, we apply a fuzzy programming method to convert the proposed multi-objective model into a single-objective one. Our main goal is to calculate three types of efficiencies for bank branches under four different scenarios. To validate the accuracy of the proposed model, a real case of 45 Agriculture bank branches located in West Azerbaijan in Iran is examined. The results show that the proposed model can produce accurate results under different scenarios. We also perform a comparative analysis on each efficiency aspect to specify the benchmark branches and also inefficient branches. Comparative analysis can help managers recognize where improvement should be prioritized. [ABSTRACT FROM AUTHOR]

• 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]