An exact approach for the service network design problem with heterogeneous resource constraints

•We study the service network design problem with heterogeneous resource constraints.•We present two mathematical formulations: node arc and cycle models.•We present a B&P approach.•Computational results demonstrate effectiveness and efficiency of our method. In this paper, we study the service network design problem with heterogeneous resource constraints (SNDHRC) for one freight consolidation carrier. In this problem setting, there are a finite number of heterogeneous resources assigned to each terminal in the network, and the resources must ultimately return to a home terminal after the transportation service. The SNDHRC is to select services and their schedules, build routes for the heterogeneous resources performing these scheduled services, and move the commodities through the resulting service network such that the total transportation cost is minimized. We first present two formulations for the SNDHRC: node-arc formulation and cycle-path formulation. With the cycle-path formulation, we then propose a branch-and-price approach where cycles for resources and paths for commodities are dynamically constructed. The proposed approach integrates new branching strategies and an acceleration strategy for rapidly finding integer solutions. Computational results are provided and demonstrate efficacy of the proposed exact approach.