Iranian Journal of Operations Research

en Designing a Smart Efficiency Evaluation System in Petrochemical Industry: A Hybrid Machine Learning and Robust Data Envelopment Analysis Approach under Fixed-Sum Undesirable Outputs Decision Analysis and Decision Support Systems Decision Analysis and Decision Support Systems پژوهشی Original Evaluating the eco-efficiency of multi-plant petrochemical clusters operating under stringent regional environmental caps requires robust analytical frameworks capable of handling complex operational complexities and parameter ambiguity. Traditional Data Envelopment Analysis (DEA) models often fail to capture systemic fixed-sum undesirable output reallocation constraints and assume deterministic input-output parameters, leading to biased and overly optimistic performance benchmarks. To overcome these limitations, this study develops a novel hybrid predictive-optimization framework integrating Extreme Gradient Boosting (XGBoost) machine learning with a Robust Fuzzy Fixed-Sum Output Data Envelopment Analysis (R-FSODEA) model. The proposed approach utilizes an XGBoost regressor trained on multi-period operational data across 75 major petrochemical complexes to project baseline expectations and establish data-driven symmetric uncertainty bounds (<m:omath><m:ssub><m:ssubpr><m:ctrlpr></m:ctrlpr></m:ssubpr><m:e><m:r>x</m:r></m:e><m:sub><m:r>ij</m:r></m:sub></m:ssub><m:r>,</m:r><m:ssub><m:ssubpr><m:ctrlpr></m:ctrlpr></m:ssubpr><m:e><m:r>y</m:r></m:e><m:sub><m:r>rj</m:r></m:sub></m:ssub><m:r>,</m:r><m:ssub><m:ssubpr><m:ctrlpr></m:ctrlpr></m:ssubpr><m:e><m:r>y</m:r></m:e><m:sub><m:r>kju</m:r></m:sub></m:ssub></m:omath><img alt="" id="_x0000_i1025" src="data:image/png;base64,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" style="width:60pt; height:18pt" > ) based on out-of-sample prediction residuals. To address both epistemic fuzzy uncertainty and aleatory operational noise, fuzzy parameters are discretized via <m:omath><m:r>α</m:r></m:omath><img alt="" id="_x0000_i1025" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAoAAAAWCAIAAAB2RJoKAAAAAXNSR0IArs4c6QAAAAlwSFlzAAAOxAAADsQBlSsOGwAAAIJJREFUKFPdkbEVwjAMRM+MJe8jr5NsQmVtwAg09i5Cp4QABfREhZ/ufet8Ty7uju91+cEC/T+ettZaWLUZYC2adQKxFveugGgf0Y5FRFUgCxVxwlTPq4cMTKp9h5x+k0j9OftSvi31dh9xTmv1ivCKssaEGa3Tj9n4fpofduWsH/oA93N4xuA9xhkAAAAASUVORK5CYII=" style="width:7.5pt; height:16.5pt" > -cuts (<m:omath><m:r>α</m:r><m:r>∈(0,1]</m:r></m:omath><img alt="" id="_x0000_i1025" src="data:image/png;base64,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" style="width:46.5pt; height:16.5pt" > ), while cardinality-constrained uncertainty budgets (<m:omath><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>Γ</m:r></m:omath><img alt="" id="_x0000_i1025" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAkAAAAWCAIAAACdcyEJAAAAAXNSR0IArs4c6QAAAAlwSFlzAAAOxAAADsQBlSsOGwAAAF9JREFUKFNj/P//PwMOwIRLAihOCzmG//+3pWGxM23b//9A+zxn3p5gxWA14TbQySBwG6YYi1tUPEuBanG5UyX/6ExP2viBqHA5du02hjeR/Q7yMBJgHERxRJT/sMQhABuWMPfmIi1AAAAAAElFTkSuQmCC" style="width:6.75pt; height:16.5pt" > ) govern the level of decision conservatism. Multiple interdependent undesirable environmental emissions (<m:omath><m:ssub><m:ssubpr><m:ctrlpr></m:ctrlpr></m:ssubpr><m:e><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"><m:nor></m:nor></m:sty></m:scr></m:rpr>CO</m:r></m:e><m:sub><m:r>2</m:r></m:sub></m:ssub></m:omath><img alt="" id="_x0000_i1025" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB0AAAAWCAIAAACzNgCbAAAAAXNSR0IArs4c6QAAAAlwSFlzAAAOxAAADsQBlSsOGwAAARdJREFUSEvVk80VgjAMx1NnEQ88J8AJvDlFWQfX8C5swAheyi41aZu2QMvz8XGwFw1NfknzT4TWGg44pwOYhPxjblcLPrfnANDVdTfqUuQgxORu1k7UTWvVVHhRNcpYbINsne0c8jb7+V9gSoC6u1Z6Lv6Ns0a5Z1EMRq6JCqX4lKqR9gEZB/vIRCDFgI3K5mVsymEpcsucFSUW3H9UagW2cA2vKos0dymribg/sFOJsob3qwe4Xs7Jlc03EHVxovwyD6qVJCM+wKhNc+YUH4mH0FiqqfYJ27oj3syI5QY2vymhv2XxycwXbRBdBe5sZdZ8wJm3Cffk0iLx5u/G9ZXioo36u+bZ0c5Pei+oFweczfuWqeko7hc8USYC4gHvAwAAAABJRU5ErkJggg==" style="width:21.75pt; height:16.5pt" > , <m:omath><m:ssub><m:ssubpr><m:ctrlpr></m:ctrlpr></m:ssubpr><m:e><m:r><m:rpr><m:nor></m:nor></m:rpr>NO</m:r></m:e><m:sub><m:r>x</m:r></m:sub></m:ssub></m:omath><img alt="" id="_x0000_i1025" src="data:image/png;base64,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" style="width:23.25pt; height:16.5pt" > , <m:omath><m:ssub><m:ssubpr><m:ctrlpr></m:ctrlpr></m:ssubpr><m:e><m:r><m:rpr><m:nor></m:nor></m:rpr>SO</m:r></m:e><m:sub><m:r>2</m:r></m:sub></m:ssub></m:omath><img alt="" id="_x0000_i1025" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABwAAAAWCAIAAABc9GulAAAAAXNSR0IArs4c6QAAAAlwSFlzAAAOxAAADsQBlSsOGwAAAQxJREFUSEvllcEVgjAMhouzyMURYAIdpBx1FDjqIDCBjuCl7FKTlLS0hCdPe/GZi5SGL2n+v8/CWqtyxy43EHm/Bh27unBRd6MammaIpzI00zb+pJvCAEGoXitVtQaerDVtBUm6p4X0YpHgM8ODcswZBV/4Je75glEd7kJgWoBSbTmHmFFB+TgJGaCuV4yULPbpP1jvlSx1vLp2H5dymxDlAbOfZsXk7NP9+c4t307kgbdRHcq1HJxpG8SO9f98pnDyWIuZHbaob3qNNgRJ9ORLVj9oTNMNVVJfCmunGLD5O4Li8dkBkocciGNpMX9Npi2yVI4wbbgyeaBAnIudARp65Pv9NVSad/HffycvD+NTNjBlMDkAAAAASUVORK5CYII=" style="width:21pt; height:16.5pt" > , <m:omath><m:ssub><m:ssubpr><m:ctrlpr></m:ctrlpr></m:ssubpr><m:e><m:r><m:rpr><m:nor></m:nor></m:rpr>PM</m:r></m:e><m:sub><m:r>10</m:r></m:sub></m:ssub></m:omath><img alt="" id="_x0000_i1025" src="data:image/png;base64,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" style="width:27.75pt; height:16.5pt" > , and <m:r><m:rpr><m:nor></m:nor></m:rpr></m:r><m:omath>COD</m:omath><img alt="" id="_x0000_i1025" src="data:image/png;base64,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" style="width:25.5pt; height:16.5pt" > ) are simultaneously constrained under strict aggregate regional fixed-sum emission ceilings (<m:omath><m:nary><m:narypr><m:chr m:val="∑"><m:limloc m:val="undOvr"><m:subhide m:val="on"><m:suphide m:val="on"><m:ctrlpr></m:ctrlpr></m:suphide></m:subhide></m:limloc></m:chr></m:narypr><m:sub></m:sub><m:sup></m:sup><m:e><m:ssub><m:ssubpr><m:ctrlpr></m:ctrlpr></m:ssubpr><m:e><m:r>y</m:r></m:e><m:sub><m:r>kju</m:r></m:sub></m:ssub></m:e></m:nary><m:r>=</m:r><m:ssubsup><m:ssubsuppr><m:ctrlpr></m:ctrlpr></m:ssubsuppr><m:e><m:r>C</m:r></m:e><m:sub><m:r>k</m:r></m:sub><m:sup><m:r>u</m:r></m:sup></m:ssubsup></m:omath><img alt="" id="_x0000_i1025" src="data:image/png;base64,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" style="width:61.5pt; height:18pt" > ). The empirical results reveal a dynamic trade-off between operational conservatism and systemic performance: as the uncertainty budget increases from nominal (<m:omath><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>Γ</m:r><m:r>=0</m:r></m:omath><img alt="" id="_x0000_i1025" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACYAAAAWCAIAAAAjJXlUAAAAAXNSR0IArs4c6QAAAAlwSFlzAAAOxAAADsQBlSsOGwAAAPpJREFUSEvtlc0RgyAQhTG1WAVWkMklp5QAR1vRYxqRCrQCx4PQC9kloBLNDE42nuQi+PM+eLtvzKy17NhxORaHtBP5J8/BWCWz9ZCKAmiULLx2IZXxktCxVlec8UrjFFeNYEw0fvXDBWVBCHXd1CPYGuleIEDizueD4Op9kM2Ozcv2ef001tTBo406FHVwbfrMjD3jj1vub1zvwOxHeC09JLCP7ya3ZZCekHrottshHUnRTk4jHbnXWFTvBr3eaTpyr7Fz8Rx1UdrQsSSxiIvtm9SFZNG+EBL3xA2CZMRQXQnIIw4uptxn58+LLBeRUHrHkvFPJJmVsdALHpfn3phVRY0AAAAASUVORK5CYII=" style="width:28.5pt; height:16.5pt" > ) to fully robust configurations (<m:omath><m:r><m:rpr><m:scr m:val="roman"><m:sty m:val="p"></m:sty></m:scr></m:rpr>Γ</m:r><m:r>=4</m:r></m:omath><img alt="" id="_x0000_i1025" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACYAAAAWCAIAAAAjJXlUAAAAAXNSR0IArs4c6QAAAAlwSFlzAAAOxAAADsQBlSsOGwAAAPNJREFUSEvtlbsVgyAYhSGzeDKETuACtnZSmiadZQaQ0jKtA8gEOkIa3IX8mERRID6OWHkbCx7f5XI5YiEEOlaXY3GSdiIdZQ7BMoJ1EbYjsKUBxv2OgAwLnvvIzzmUV4pXyY44hFoa3xplR0N9vPAOFvYSI3EZ5eohjI310roIp8wuHZsC2ho9MvJAWZ1e1cHljwR8fJM3fOrU05FgEoCa+eXItUnDFZbRcwQED7JEXWFG9bGcRU6yaijfb7Wlg0klliPtqc6PSD7APuqDbV58bXRb5wsxRNAbmfe9YsZ0f3z+vLZe1v917t6llXsi3VwlegMQq1YX3KXtywAAAABJRU5ErkJggg==" style="width:28.5pt; height:16.5pt" > ), mean industry eco-efficiency monotonically decreases from <m:omath><m:r>0.8514</m:r></m:omath><img alt="" id="_x0000_i1025" src="data:image/png;base64,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" style="width:36pt; height:16.5pt" >  to <m:omath><m:r>0.6524</m:r></m:omath><img alt="" id="_x0000_i1025" src="data:image/png;base64,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" style="width:36pt; height:16.5pt" > , representing the analytical efficiency penalty required to guarantee feasibility under bad-case data perturbations. Furthermore, statistical correlation analyses (Spearman's <m:omath><m:r>ρ</m:r><m:r>>0.908</m:r></m:omath><img alt="" id="_x0000_i1025" src="data:image/png;base64,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" style="width:51.75pt; height:16.5pt" > , Kendall's <m:omath><m:r>τ</m:r><m:r>>0.907</m:r></m:omath><img alt="" id="_x0000_i1025" src="data:image/png;base64,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" style="width:50.25pt; height:16.5pt" > ) confirm that while individual complexes undergo localized rank shifts due to operational variance sensitivity, the global efficiency hierarchy remains highly stable. The proposed framework equips industrial executives and environmental regulators with an intelligent, policy-relevant decision-support tool for dynamic emission quota allocation, targeted technical retrofits, and eco-efficiency benchmarking under operational parameter uncertainty.   Data Envelopment Analysis, Fixed-Sum Output, Robust Optimization, Operational Parameter Uncertainty, Eco-Efficiency, Petrochemical Industry 117 138 http://iors.ir/journal/browse.php?a_code=A-10-6101-3&slc_lang=en&sid=1 Seyed Morteza Mousavi seyedmortezamousavi4044@iau.ac.ir 00031947532846003232 00031947532846003232 No Department of Industrial Engineering, Na.C., Islamic Azad University, Najafabad, Iran Javad Gerami javadgerami@iau.ac.ir 00031947532846003233 00031947532846003233 Yes Department of Industrial Engineering, Shi.C., Islamic Azad University, Shiraz, Iran Mohammadreza Mozaffari mozaffari854@iau.ac.ir 00031947532846003234 00031947532846003234 No Department of Industrial Engineering, Shi.C., Islamic Azad University, Shiraz, Iran Roya M. Pour Ahari Roya.ahari@iau.ac.ir 00031947532846003235 00031947532846003235 No Department of Industrial Engineering, Na.C., Islamic Azad University, Najafabad, Iran Mohammadreza Feylizadeh mo.feylizadeh@iau.ac.ir 00031947532846003236 00031947532846003236 No Department of Industrial Engineering, Shi.C., Islamic Azad University, Shiraz, Iran