Document Type : Research Paper

Authors

• Hossein Sayyadi Tooranloo ¹
• Mohammad Zarei Mahmoudabadi ²
• Reza Norouzi Avargani ³

¹ Professor, Department of Industrial Management, Meybod University, Meybod, Iran.

² Associate Professor, Department of Industrial Management, Meybod University, Meybod, Iran.

³ PhD student, Department of Industrial Management, Meybod University, Meybod, Iran

Abstract

Over the past decade, the development of Network Data Envelopment Analysis (NDEA) models has enabled researchers to capture the internal structures and interrelationships among sub-units of decision-making units (DMUs). Compared to conventional DEA models, this approach provides deeper managerial and analytical insights into performance evaluation. The purpose of this study is to systematically review and clarify the overall trends in the development and application of NDEA models, with a particular focus on uncertainty-based approaches, over the period from 2014 to 2024. This research employs Microsoft Excel and VOSviewer software tools to conduct co-word analysis, visualize scientific networks, and identify research clusters. The reviewed articles were classified into two major dimensions: research domain (application areas) and research logic (deterministic or non-deterministic). The results indicate that most NDEA applications are concentrated in industrial sectors, and that deterministic logic dominates the existing body of literature. The term “network data envelopment analysis” was identified as the second most frequent keyword following “data envelopment” analysis. Based on the synthesis of reviewed studies, this research proposes a conceptual framework for NDEA and outlines potential future research directions centered on the integration of NDEA with uncertainty theories. To the best of our knowledge, no comprehensive study has simultaneously addressed network data envelopment analysis and uncertainty. By identifying research gaps, mapping the scientific structure of the field, and highlighting emerging themes and future avenues, this study provides a valuable reference for researchers and practitioners interested in performance evaluation under uncertainty.
Introduction
Over the past decade, Network Data Envelopment Analysis (NDEA) has emerged as a powerful extension of conventional Data Envelopment Analysis (DEA), enabling researchers to explicitly model the internal structures, intermediate products, and complex interrelationships among sub-processes within decision-making units (DMUs). Unlike traditional “black-box” DEA models, NDEA provides richer analytical and managerial insights by decomposing overall efficiency into stage-wise and network-based components. As real-world systems increasingly operate under uncertain, imprecise, or incomplete information, integrating uncertainty into NDEA models has become a critical methodological challenge. Despite the growing number of studies addressing NDEA and uncertainty separately, a comprehensive and systematic synthesis of the literature that jointly examines network DEA structures and uncertainty approaches remains limited.
Research Gap and Objective
Existing review studies on DEA and NDEA have primarily focused on methodological classifications, application domains, or dynamic and hierarchical extensions, while the uncertainty dimension has often been treated marginally or in isolation. Moreover, prior reviews rarely employ scientometric techniques to map the intellectual structure, thematic evolution, and research clusters within the NDEA–uncertainty literature. To address these gaps, the present study aims to systematically review and map the scientific landscape of Network Data Envelopment Analysis with an uncertainty approach. Specifically, this research seeks to (i) identify publication trends and influential sources, (ii) classify NDEA studies based on application domains and research logic (deterministic vs. non-deterministic), (iii) examine the dominant uncertainty modeling approaches adopted in NDEA, and (iv) propose a conceptual framework to guide future research in this field.
Methodology
This study adopts a systematic literature review combined with science mapping and bibliometric analysis. A structured search strategy was implemented in the Scopus and Web of Science databases, covering peer-reviewed journal articles published between 2014 and 2024. Keywords related to “Network Data Envelopment Analysis,” “Two-Stage DEA,” and “Uncertainty” were applied to titles, abstracts, and keywords. Following a multi-stage screening and filtering process based on time span, document type, language, and journal quality, a refined dataset of relevant articles was obtained. Bibliometric analyses, including co-word analysis and visualization of scientific networks, were conducted using Microsoft Excel and VOSviewer. The reviewed studies were systematically classified along two main dimensions: (1) research domain (application areas) and (2) research logic (deterministic versus non-deterministic modeling). Qualitative synthesis was then employed to interpret thematic patterns and methodological trends.
Results
The results reveal a steadily increasing trend in NDEA-related publications over the examined period, with a noticeable surge after 2020. Industrial and production systems constitute the dominant application domain, followed by energy, healthcare, transportation, banking, and supply chain management. The analysis indicates that deterministic NDEA models still prevail in the literature; however, uncertainty-based approaches—such as fuzzy sets, robust optimization, grey systems, stochastic programming, and rough sets—have gained growing attention in recent years. Keyword co-occurrence analysis identifies “data envelopment analysis” as the most frequent term, with “network data envelopment analysis” emerging as the second most prominent keyword. The findings further highlight that two-stage and multi-stage network structures are the most commonly employed configurations. Based on the synthesis of reviewed studies, this research develops a conceptual framework that links NDEA structures, uncertainty modeling techniques, and application domains, while outlining potential future research directions focused on hybrid and advanced uncertainty integration.
Discussion
The findings demonstrate that incorporating uncertainty into NDEA models significantly enhances their realism and applicability in complex decision-making environments. However, the dominance of deterministic logic suggests that many real-world uncertainties remain insufficiently addressed. From a methodological perspective, the study underscores the need for more integrated and hybrid uncertainty frameworks that combine multiple uncertainty theories within network DEA structures. From a practical standpoint, uncertainty-aware NDEA models provide decision-makers with more robust efficiency assessments, particularly in volatile sectors such as energy, healthcare, and supply chains. The scientometric mapping also reveals underexplored research clusters, indicating opportunities for interdisciplinary collaboration and methodological innovation.
Conclusion
This study represents one of the first comprehensive systematic and bibliometric reviews focusing explicitly on Network Data Envelopment Analysis under uncertainty. By simultaneously examining publication trends, research structures, uncertainty approaches, and application domains, the study offers a holistic understanding of the field. The proposed conceptual framework and identified research gaps provide valuable guidance for future theoretical development and empirical applications. Overall, this research contributes to advancing performance evaluation methodologies in uncertain environments and serves as a reference point for researchers and practitioners interested in NDEA and efficiency analysis under uncertainty.

Keywords

• Network Data Envelopment Analysis (NDEA)
• Data Envelopment Analysis (DEA)
• Uncertainty
• Systematic Review
• Science Mapping
• Decision-Making

Main Subjects

• Industrial management