A Robust Directional Distance Function for Fixed-Sum Undesirable Outputs: A Petrochemical Industry Study - Mousavi, Seyed Morteza; Gerami, Javad; Mozaffari, Mohammad Reza; Mohammadalipour Ahari, Roya; Feylizadeh, Mohammad Reza (Annals of Optimization With Applications, 2025)
Petrochemical industries, as energy-intensive and pollution-oriented sectors, operate under stringent environmental regulations, particularly regarding caps on total pollutant emissions. Under such conditions, the fixed-sum property of undesirable outputs creates interdependence among Decision-Making Units (DMUs) and violates the independence assumption of classical Data Envelopment Analysis (DEA) models. Moreover, operational data in these industries are inherently subject to uncertainty due to fluctuations in operating conditions and environmental variability, which may lead to instability in the estimated efficiency frontier. This study proposes a robust equilibrium framework based on the Directional Distance Function (DDF) to evaluate the environmental-economic performance of petrochemical complexes. In the proposed model, the fixed-sum constraint on undesirable outputs is explicitly incorporated into the production technology, and data uncertainty is addressed through a robust optimization approach. The model was applied to data from 36 active petrochemical complexes in 2024. The results indicate that the number of efficient units decreases from 7 in the classical DEA model to 1 in the robust equilibrium model, demonstrating increased discrimination power and improved realism of the proposed framework. Sensitivity analysis with respect to different uncertainty levels confirms the stability of the ranking results. The findings suggest that neglecting the fixed-sum property of undesirable outputs and data uncertainty may lead to misleading and unstable efficiency identification. The proposed framework can serve as an effective decision-support tool for managerial planning and environmental policy-making in the petrochemical industry.