Optimized load planning for motorail transportation

• The real-world problem of loading vehicles onto motorail wagons is studied.
• Two novel formulations of the problem are proposed.
• New formulations provide a tighter LP relaxation than the original problem formulation.
• Computational comparisons between all formulations.

This paper studies a real-world problem arising in the area of motorail transportation. The considered problem deals with the loading of cars and motorcycles onto motorail wagons under realistic technical and legal constraints. The load planning problem, introduced as motorail transportation problem (MTP), occurs during the booking process and afterwards during the loading process at motorail terminals. Optimization based decision support is highly valuable due to the combinatorial nature of these problems. In practical applications, the fast generation of good solutions is essential. Previous model formulations in literature reveal considerable optimality gaps in real-world instances. Hence, we propose and evaluate two novel integer linear programming formulations of the MTP. The first formulation is a simplified reformulation of the original problem, uses less variables and provides a tighter LP relaxation. The second model is a column-generation formulation of the reformulated model which is solved using branch-and-price. Both novel model formulations are compared and evaluated on the basis of real-world data sets and considerably outperform previous approaches in terms of solution quality and speed.