A knowledge based freight management decision support system incorporating economies of scale: multimodal minimum cost flow optimization approach

This study developed a framework incorporating economies of scale into the multimodal minimum cost flow problem. To properly account for the economies of scale observed in practice, we explicitly modelled economies of scale on quantity, distance and vehicle size in a given multimodal freight network. The proposed multimodal minimum cost flow problem formulation has concave equations due to economies of scale for quantity, non-linear equations due to economies of scale for both quantity and distance, and non-continuous equations due to the economies of scale for vehicle size. A genetic algorithm was applied to find acceptable route, mode, and vehicle size choices for the multimodal minimum cost flow problem. We demonstrated how the economies of scale influenced system (mode), route choices, and total cost under various demand/service capacity scenarios. Our results will lead into more realistic assessments of intermodal system by explicitly considering the three types of economies of scale.