Robust closed-loop supply chain network design for economic-environment-social sustainable development problems

In globalized and highly uncertain business environment, it is necessary to ensure the sustainable development of enterprises. Aiming at this problem, a multi-objective global robust optimization model for steel production is established to design a sustainable closed-loop supply chain network with fluctuation parameters. Firstly, for the sustainable development of enterprises, the model considers not only the recyclability of steel products, optimal production techniques and changes in retailers, but also the economic, environmental and social dimensions of sustainability. Secondly, to deal with the uncertainty of the raw material and demand parameters, a more relaxed global robust optimization method is adopted to convert the model into a tractable robust counterpart under the box and box-ellipsoid perturbation sets. Finally, for solving the model, the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon$$\end{document}-constraint method is used to transform the model into a single objective model. Meanwhile, a new sequential quadratic programming filter algorithm is constructed. Numerical results show: the robust model is effective in an uncertain environment and provides more reliable decision results than the deterministic model; the established model has certain reference value for the sustainable development of enterprises; the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.37\%$$\end{document} reduction in economic profit, the adverse environmental impact can be reduced by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$18.9\%$$\end{document}.