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Due to increasing air pollution, which is a consequence of the environmentaleffects of production in various industries, green supply chain management(GSCM) has attracted the attention of both scholars and practitioners. Greensupplier selection is one of the most important problems in GSCM, whichsatisfies a firm's environmental goals as well as its economic targets. In thispaper, for the first time, a green supplier selection problem considering bothgreen and non-green evaluation criteria in a closed-loop supply chain isstudied, and a cap-and-trade mechanism as a way of controlling the airpollution caused by manufacturers is proposed. To solve the described problem,a multi-objective robust optimization (RO) model, as an effective approach tohandle uncertainty, is proposed. A numerical example using randomly generateddata, accompanied by the analysis based on the proposed approach is elaboratedto validate the presented model. The results prove that the developed model forgreen supplier selection is able to effectively enhance the decision-makingprocess of the experts. By illustrating the trade-off in robustness between themodel and proposed solutions, as well as the effect of the deviation penalty onthe closeness of results to the achieved solution, we show how firms can makeoptimal decisions when assigning the parameters. Furthermore, analyses showthat allowance amount (cap) and allowance prices in the cap-and-trade systemimpact the firms' costs and the amount of carbon released. Finally, we showthat the cap-and-trade mechanism results in a better solution in terms of thetotal utility of the supply chain compared to the penalty-based system.

A robust optimization model for green supplier selection and order allocation in a closed-loop supply chain considering cap-and-trade mechanism