This paper navigates the economic efficiency in a two-stage fixed-cost transportation problem (TS-FCTP), employing cooperative game theory (CGT) for fair allocation in a shared transportation network. Collaboration among Logistics Service Providers (LSPs) in a multi-echelon supply chain network, such as in TS-FCTP, emerges as a pivotal strategy to reduce costs and enhance network efficiency. The allocation of these cost savings among LSPs becomes a crucial question, prompting the introduction of a transportation game (TG) with LSPs as players. Diverse CGT solution concepts are explored to distribute cost savings among participating LSPs. We consider both synthetic and real datasets. For these datasets, we notice that the transportation game is monotonic and superadditive, and the core is non-empty. These properties indicate the willingness of players to form a coalition. Additionally, we determine the most stable cost savings allocation using the core center concept. The optimal coalition formation sequence has been identified using the Shapley monotonic path. Our findings illustrate that LSPs bear lower costs when cooperating with other LSPs. In this TG, individual players’ utility is computed by solving a TS-FCTP.
This can be computationally intensive, even for medium-sized problem instances. We propose two valid inequalities (VIs) that significantly reduce the computation time.