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Data envelopment analysis (DEA) is a methodology for assessing the relative efficiency of a set of homogeneous decision-making units (DMUs), i.e., a set of DMUs belonging to the same technology and having the same input and output indicators. However, in many practical settings, the assumption of homogeneity does not hold. Especially in a multi-function parallel system, each subunit may not have the same function, so it may produce different outputs (e.g., the professors in a university have the responsibilities of teaching and research which consume same inputs while produce different outputs). How to compare a subunit to others in a multi-function heterogeneous parallel system? Therefore, in this study, we extend the DEA model to consider the one-sided heterogeneous problem in a multi-function parallel structure, handling subunit sets that have heterogeneity in outputs. Here, we propose parallel DEA-based methods and the results show that if the non-existent outputs are replaced with zeros or missing values will lead to overestimate the efficiency of the DMU. Then, an application of our proposed approach to the regional innovation systems' performance evaluation regarding 30 provinces in China from 2012 to 2016 is provided and concludes with several findings. (C) 2020 Elsevier Ltd. All rights reserved.