Application of game theory on optimizing multilevel green transportation problem under multi-stakeholder’s condition

Game theory, a branch of applied mathematics, which has been recently used to study strategic behavior, i.e. the conditions in which the desirability of each factor depends on the decisions made by the players. The paper proposes a multilevel green transportation model under multi-stakeholder’s condition, that game theory could be used to selects the best interactive mode by presenting different scenarios so that all stakeholders in a game achieve their maximum benefits.In this paper, a comprehensive multi-level supply chain model consisting of several simultaneous stakeholders has been considered. An optimal model was developed to achieve the lowest cost at different levels of the chain. The optimal model includes the lowest costs of purchase and production, maintenance, shortage, and warehousing. The model also includes various components of products transportation and distribution for all members of the chain. The produced Co2 at different stages of production and transportation for both involved parties was accounted in the model to minimize the environmental impacts. Furthermore, a competition in the context of a game to select the optimal situation between the stakeholders of the supply chain has been considered make the best decision in terms of a participatory game by considering different scenarios. In this paper, Excel and Gams software were used to model and solve the numerical example. The results confirmed the superiority of the optimal values of the game theory model.