Allocation method for transit lines considering the user equilibrium for operators

The purpose of this study is to address the allocation of transit lines problem in operation-sharing. An allocation method for urban transit lines is proposed to guide public authorities to pursue an optimal plan considering the User Equilibrium for operators (UE-O). The method utilizes the concepts from mathematical programming and game theory to present the UE-O and proposes a set partitioning formulation considering the benefits of both passengers and operators. A branch-and-price algorithm employing both column generation and branch-and-bound is used to tackle the problem. The proposed method is validated through a case study using data from the Development District of Dalian. Results show that the proposed line allocation method considering the UE-O can reduce the potential competitions among operators. This method and findings can provide a guidance to the problems in operation-sharing regarding allocation of transit lines.