The Multi-Shipment Train Formation Optimization Problem Along the Ordered Rail Stations Based on Collection Delay

In the domain of freight transportation, road transport has occupied a leading position over the past years. Unfortunately, this has contributed to increasingly air pollution. Consequently, countries around the world have been concentrated on attracting freight transportation into rail. To improve the rail transportation efficiency and then to motivate shifting bulk cargo transportation to rail, the optimization of rail operation plan becomes ever-important. As part of operation plan, the multi-shipment train formation problem (MSTFP) is studied in this paper. It not only involves which direct train should be built in the loading area but also obtains the optimal combinatorial strategy of shipments to form a train. The primary objective is to minimize the delay incurred from the collection processes of all the original stations of shipments. A non-linear 0-1 integer programming model is proposed given train sizes, classification capacities, uniqueness condition of each shipment, and several logical constraints among decision variables. Then a linearization approach is introduced to transform the model into a linear one. The validation of the model is confirmed via a small-scale artificial case. A real-world case is carried out using the data from China rail system, based on which the effectiveness of both non-linear and linear models is compared. Finally, a sensitivity analysis is provided to evaluate the effects of enlarging the scale of shipments.