Fair Cost-Savings Allocation in Transportation Game

In this paper, we propose a transportation game which models a classical transportation problem (TP) using cooperative game theory (CGT) with logistic service providers (LSPs) as players. We noticed that merging LSPs leads to cost savings in the transportation game. This study explores different cooperative game theoretical solution concepts (Core, Shapley value, and Nucleolus) for cost savings (due to the merge) distribution among the stakeholders (LSPs). The game theoretic model assumes the products are substitutable. A real-world dataset has been used for the numerical illustration. For this real-world dataset, the proposed game is monotonic, superadditive, and convex for the two-player game but non-convex for the three-player game. In this dataset, we observed that the Nucleolus and Shapley value-based allocations turn out to be the same for two LSPs, while they are different for three LSPs. In either case, Nucleolus and Shapley value are inside the core.