Novel Multi-objective Green Supply Chain Model with $$CO_2$$ Emission Cost in Fuzzy Environment via Soft Computing Technique

In this investigation, a green supply chain (GSC) model has been developed for multi-objective optimization industrial problem. For this purpose, total cost of supply chain and total time including loading and unloading time of materials or products for transportation is minimized. The \(CO_2\) emission cost has been considered for environmental protection concern. Due to vagueness of various data of the proposed model, the parameters of the model have been taken as triangular fuzzy numbers. Expected value technique is used to remove the fuzziness of different parameters. A novel step method has been applied to convert the multi-objectives to a single one. The converted crisp model has been solved by Generalized Reduced Gradient (GRG) technique using LINGO 17.0. A practical numerical experiment with some sensitivity analyses has been carried out to validate the proposed model.