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This work focuses on freight consolidation in multimodal rail and road transportation. The transportation network comprises of a centralized source warehouse, a set of destination warehouses, and intermediate transshipment terminals. The paper formulates a single period integer programming model and a multi-period constraint programming model for optimizing multimodal freight transportation with volume discount on rail freight rate. The first model is aimed at consignee organizations with comparatively low shipment quantity and less frequent transportation, while the second model targets organizations which require continuous freight transportation on a massive scale. The single-period model is solved using a commercially available CPLEX solver. However, due to the computational complexity of the multi-period constraint programming model, a heuristic named Rail and Truck Allocation Algorithm (RATAA) is proposed. Computational experiments are carried out to prove the efficiency of the proposed solution approaches.

Multimodal transportation planning with freight consolidation and volume discount on rail freight rate