Intuitionistic fuzzy sustainable multi-objective multi-item multi-choice step fixed-charge solid transportation problem

Embedding sustainability in a distribution system solves major concerns appearing during wielding a distribution process. Therefore, this study explores a novel integrated model by developing sustainability in a multi-objective multi-item multi-choice step fixed-charge solid transportation problem under an intuitionistic fuzzy environment by considering economic, customers’ satisfaction and social aspects. Uncertainty in the parameters of the proposed model is handled by treating those as triangular intuitionistic fuzzy numbers. A new ranking concept with the help of total integral values is developed to defuzzify the above mentioned uncertainty. Apart from fixed-charge, an extra charge is calculated conjointly when the load is bigger than a particular quantity of product during shipping the commodities by different transportation modes. Herein, two different equivalent models are presented from the intuitionistic fuzzy model by utilizing the ranking concept and the possibility measure, respectively, thereafter these models are further transformed into fully deterministic models by converting the multi-choice parameter into a single choice using binary variables. A new method namely, intuitionistic fuzzy game-theoretic method is originated to solve the deterministic models, and then we compare the solutions with another extended method namely, augmented Tchebycheff method for showing the superiority of the new method. The competency of our findings is clarified with an industrial-based application example. Finally, a comparison study is drawn among the other existing techniques. Lastly, managerial implications, conclusions and future scopes are depicted.