Synchromodal transport planning with flexible services: Mathematical model and heuristic algorithm

As a critical feature of synchromodal transport (ST), service flexibility plays an important role in improving the utilization of resources to reduce costs, emissions, congestions, and delays. However, none of the existing studies considered flexible services under the framework of synchromodality. This paper develops a Mixed Integer Linear Programming (MILP) model to formulate service flexibility in ST planning. In the MILP model, vehicles with flexible services as well as fixed services are both considered, and vehicle routes and request routes are planned simultaneously. Due to the computational complexity, an Adaptive Large Neighborhood Search heuristic is designed to solve the problem. Several customized operators are designed based on the characteristics of the studied problem. The proposed model is compared with the models developed in a highly-cited paper and a newly published paper that do not consider service flexibility. Case studies on small instances verified that the proposed model with flexibility performs better on all scenarios, including scenarios with different weights for the individual objectives, scenarios under congestion, and dynamic optimization scenarios. On large instances (up to 1600 shipment requests), the proposed model with flexibility reduces the cost by 14% on average compared with the existing models in the literature.