A carbon sensitive transport-based deteriorating supply chain model under type-2 fuzzy bi-matrix game

Abstract

The sustainable use and disposal of carbon materials without affecting the profit (gain) of an industry is an important task of the policy makers recent times. The present study deals with a vendor–buyer inventory model for deteriorating and imperfect quality items considering the carbon emissions under different environments, namely general fuzzy and triangular interval type-2 fuzzy environments. In fact, we develop a vendor-buyer inventory model under a fuzzy bi-matrix game approach and construct a joint payoff function along with a joint effective emission cost function. Carbon emission is related to the fuel consumption during transportation, disposal of the deteriorating items and warehouse energy consumption per unit item. The notion of this study is to optimize the total average inventory cost along with the amount of carbon emission cost under flexible demand rate and uncertain cost parameters. Basically, we have developed a new optimization problem incorporating vendor–buyer’s objective function with carbon emission based on the expected payoff function of the bi-matrix game. Numerical findings reveal that a type-2 fuzzy system could be able to optimize the average inventory cost as well as total emission cost all the time. Finally, sensitivity analysis graphical illustrations are made to validate the model.