Development of a Hybrid XGBoost–Fuzzy Robust DEA Model for Evaluating the Operational and Environmental Efficiency of Petrochemical Companies Considering Undesirable Outputs and Uncertainty

Seyed Morteza Mousavi; Javad Gerami; Mohammadreza Mozaffari; Roya M. Pour Ahari; Mohammadreza Feylizadeh

Authors

Seyed Morteza Mousavi Department of Industrial Engineering, Na.C., Islamic Azad University, Najafabad, Iran Author https://orcid.org/0009-0000-1526-5798
Javad Gerami Department of Industrial Engineering, Shi.C., Islamic Azad University, Shiraz, Iran Corresponding author https://orcid.org/0000-0001-6829-1412
Mohammadreza Mozaffari Department of Industrial Engineering, Shi.C., Islamic Azad University, Shiraz, Iran Author https://orcid.org/0000-0002-7043-5240
Roya M. Pour Ahari Department of Industrial Engineering, Na.C., Islamic Azad University, Najafabad, Iran Author https://orcid.org/0000-0002-8952-8682
Mohammadreza Feylizadeh Department of Industrial Engineering, Shi.C., Islamic Azad University, Shiraz, Iran Author https://orcid.org/0000-0002-1382-7328

Keywords:

XGBoost, Fuzzy DEA, Robust DEA, Operational Efficiency, Environmental Efficiency, Petrochemical Companies, Undesirable Outputs, Uncertainty

Abstract

This study aimed to develop a hybrid XGBoost–Fuzzy Robust Data Envelopment Analysis model for evaluating the operational and environmental efficiency of petrochemical companies while simultaneously considering undesirable outputs, nonlinear relationships, and uncertainty in input–output data. This quantitative applied study analyzed 30 petrochemical companies over the 2020–2025 period, yielding 180 company-year observations. Inputs included total assets, number of employees, operating costs, energy consumption, and feedstock consumption, while desirable outputs comprised sales revenue, value added, and marketable production. Undesirable outputs included CO₂-equivalent emissions, air-pollutant emissions, industrial wastewater, and process or hazardous waste. A non-radial slack-based DEA model with variable returns to scale was integrated with fuzzy α-cut analysis and robust optimization to account for uncertainty. XGBoost was applied to model nonlinear efficiency determinants, with five-fold cross-validation used for hyperparameter optimization. Model performance was assessed using R², RMSE, MAE, SHAP importance, Spearman rank correlations, and sensitivity analyses across alternative model specifications. Mean efficiency declined from 0.846 under conventional DEA to 0.781 after incorporating undesirable outputs, 0.754 under fuzzy DEA, 0.727 under robust DEA, and 0.713 under the final hybrid model. The number of efficient observations decreased from 31 to 8. XGBoost achieved a test-set R² of 0.881, cross-validated R² of 0.862, RMSE of 0.047, and MAE of 0.036. Energy intensity and CO₂ emission intensity were the most influential predictors, with SHAP importance values of 0.184 and 0.162, respectively. The correlation between conventional DEA and the hybrid model was ρ = 0.741 (p < 0.001), indicating substantial ranking changes. Removing energy consumption or CO₂ emissions reduced ranking stability more than removing wastewater or hazardous waste. The hybrid XGBoost–Fuzzy Robust DEA model provided a more discriminating and uncertainty-sensitive assessment of petrochemical efficiency than conventional DEA, demonstrating that operational performance should be evaluated jointly with environmental burdens, nonlinear determinants, and data uncertainty.

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