A Gibbs entropy adjusted cross-efficiency analytics framework for robust biomass decision making

This research introduces a Gibbs entropy-adjusted cross-efficiency analytics framework for robust biomass decision making. The proposed method combines optimistic and pessimistic Ideal-Distance cross-efficiency perspectives with Gibbs entropy to improve ranking stability and reliability. The framework diverges from traditional cross-efficiency methods, which predominantly depend on average performance, by explicitly quantifying uncertainty and variability in cross-efficiency scores. The method is validated through two case studies: a benchmark numerical example with six nursing homes and a real-world biomass selection problem involving thirteen materials. The findings suggest that decision-making units exhibiting lower Gibbs entropy values, indicative of more stable peer evaluations, consistently attain higher entropy-adjusted performance indices ( S i ∗ ). In the biomass case study, Palm Kernel Shell achieves the highest entropy-adjusted score of 1.000, whereas Oil Palm Frond receives the lowest score of 0.2112, indicating poor performance and significant evaluation dispersion. A comparative analysis reveals a perfect rank correlation ( ρ = 1 . 000 ) between the Aggressive and Ideal Distance cross-efficiency models, along with a high consistency ( ρ ≥ 0.98) with the Benevolent model. The findings indicate that the proposed framework enhances ranking robustness while maintaining the relative ordering of decision-making units. This study presents a novel, computationally efficient, and theoretically robust method for uncertainty-aware biomass selection, offering practical insights for renewable energy planning and decision-making in agriculture-focused economies.