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Assessing the efficiency of a supply chain (SC) is of great importance for managers and policy makers. For this aim, we propose a network data envelopment analysis (NDEA) model to reflect the internal structure of networks in efficiency evaluation. For many of the real-world performance evaluation problems, data of inputs and outputs are available, and their ratio conveys important messages to managers. However, conventional data envelopment analysis (DEA) models are no longer able to deal with ratio data. This paper aims to extend the NDEA models with the ratio data (NDEA-R) to evaluate the performance of SCs. Therefore, given the internal structure of a supply chain, relationships among different divisions of an SC are determined under two assumptions of free-links and fixed-links. Applicability of the proposed models is illustrated by evaluating supply chain of 19 hospitals in Iran over 6 months. By performing sensitivity analysis, we find out that the overall efficiency score of decision-making units (DMUs) under the fixed link assumption is greater than or equal to the overall efficiency of DMUs under free link assumption. Our proposed model overcomes the underestimation of efficiency and pseudo-inefficiency scores. [ABSTRACT FROM AUTHOR]