Modeling loops and backhaul in maritime freight: A MILP extension for large-scale freight transport models

The paper presents LIFREM (Loops Including FREight Model), a model framework for improving the representation of maritime freight transport in large-scale freight transport models by integrating loops, cargo consolidation, and backhaul operations. Many large-scale freight models, such as the Swedish national freight transport model Samgods, calculate annual goods flows across different transport modes by minimizing firm-to-firm costs. These models generally restrict vehicles and vessels to direct routes, excluding the multi-stop routing patterns typical of maritime operations. This limitation reduces their ability to capture complex maritime dynamics such as port loops, consolidation, and backhaul. Using concepts from operational research and liner shipping network design, LIFREM uses a mixed-integer linear programming (MILP) framework to optimize freight assignments and incorporate loops and backhaul, thereby extending the representation of maritime transport in large-scale freight transport models and improving the representation of economies of scale in maritime transport. A case study of forest product exports from Northern Sweden illustrates how the inclusion of loops and backhaul in the modeled system can reduce transport costs and shift freight towards larger vessels, producing routing patterns qualitatively consistent with observed maritime transport structures in the Baltic Sea. The results also indicate that modal shifts may be non-linear, with transport modes remaining stable until threshold effects are reached. Computational scaling experiments assess the feasibility of applying the MILP formulation as a complementary module in large-scale freight transport models. The paper concludes by discussing limitations, computational tradeoffs, and possibilities for modular integration of the framework into large-scale freight transport models. • A new freight transport model with loops, consolidation, and backhaul is developed. • Maritime transport improved using concepts from the liner shipping network design. • A Baltic Sea case study of forest exports demonstrates model performance. • Results highlight importance of loops and backhaul in freight transport modeling. • Study shows potential and limits of integrating MILP in national freight models.