Network data envelopment analysis

Network data envelopment analysis models assess efficiency of decision-making unit and its sections using historical data but fail to measure efficiency of its units and their internal stages in the future. In this paper we aim to measure efficiency of stages of bank branches and obtain efficiency trend of stages during the time, then to estimate their efficiency in the future therefore we can be aware of stages inefficiency before occurrence and prevent them. First, a two-stage structure including deposit collection and loan giving was designed for bank branches using literature review and comments of experts. Human forces and fixed assets were considered as input variables of the first stage, deposit as mediator variable, delayed claims as interim variable, and loan amount as output variable of the second stage. Then, a dynamic network data envelopment analysis model was formulated and stages efficiency were obtained for 16 consecutive periods. Therefore, efficiency trend of stages was obtained during the time. In the following, efficiency of various stages of branches were estimated using artificial neural network and some recommendations are provided according to obtained amounts in order to prevent inefficiency before occurrence.

In this paper, we present a comprehensive approach for evaluating efficiency in complex networks by integrating network data envelopment analysis (NDEA) with the Malmquist productivity index. The proposed method addresses the inherent challenge of accommodating negative data within the network efficiency evaluation framework, which is a common occurrence in real-world network operations. Through the introduction of a two-stage structure, the model not only effectively manages the presence of negative values, but also provides a robust and insightful assessment of network efficiency. A case study from banking sector is employed to demonstrate the efficacy of the proposed approach, showcasing its capacity to offer valuable and actionable insights for decision-making in complex network environments. The results highlight the practical applicability and importance of the extended approach in addressing the complexities associated with evaluating efficiency in diverse network settings.

Objective : This study aims to evaluate the greenness and efficiency of the Iranian petrochemical supply chain, a sector that plays a vital role in both economic performance and environmental sustainability. Despite its importance, limited studies have comprehensively analyzed this industry’s efficiency using multi-dimensional and uncertainty-sensitive approaches. Methods : To address this issue, an integrated Network Data Envelopment Analysis (NDEA) framework combined with the Fuzzy Delphi Method was developed to assess the performance of ten leading petrochemical companies in Iran. Seventeen evaluation criteria were identified and validated, and the companies were analyzed under optimistic and pessimistic scenarios to capture a balanced and realistic view of their efficiency.  Results : The findings revealed that only a few companies were efficient under both scenarios, while others exhibited inefficiencies due to high environmental costs, excessive employment, and poor-quality management systems. Sensitivity analysis showed that reducing undesirable outputs and optimizing dual-role variables significantly improves performance. Efficient companies should also focus on sustaining competitiveness by optimizing their pessimistic efficiency scores. Conclusion : The results suggest that the proposed NDEA–Delphi approach provides a comprehensive and realistic tool for assessing the green efficiency of industrial supply chains. This framework can support decision-makers in identifying improvement areas, reducing resource waste, and developing environmentally responsible operational strategies in the petrochemical sector