A fuzzy strategic game solution for a green supply chain model

This article deals with a pollution-sensitive production-transportation supply chain (SC) model, based on a fuzzy strategic game matrix approach. We know, the environmental pollution that comes from several industrial set-ups has some adverse effects throughout the globe. Therefore, in this study we develop a cost minimization SC problem with the effect of pollution. The amount of pollution exhausted from the production plant is estimated by percentage through defining some pollution functions and they are considered as constraints of the proposed problem. We convert our original problem into an equivalent game problem via fuzzification (because of natural flexibilities) of all the model parameters in which the producer plays the role of player I in one side and the customers play the role of player II on the other side exclusively. Moreover, this game problem has been solved with the help of random strategic weight vectors, the Gaussian strategy vectors and bi-objective optimization techniques respectively. For numerical computations, few novel C programming via solution algorithm (For data validation a hyperlink is also given in the numerical section) have been established. Numerical illustrations with comparative study are also provided to validate the model. The basic advantage of this study is that the use of random strategic weight vectors could ultimately optimize the model compared to some other new existing methods as per literature survey concerned. Finally, the sensitivity analysis and the graphical illustrations are made followed by a conclusion to justify the proposed model.