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

Abstract

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 nonlinear 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.

The Systematic Optimization of Train Formation in Loading Stations

“…However, the solving approach of the models and numerical examples were missing in this work. Zhao and Lin [22] proposed a linearized programming model based on the collection delay in loading stations, whereas the costs in unloading stations and intermediate reclassification yards were not taken into consideration, and the pattern of train formations was not universal.…”

“…However, the solving approach of the models and numerical examples were missing in this work. Zhao and Lin [22] proposed a linearized programming model based on the collection delay in loading stations, whereas the costs in unloading stations and intermediate reclassification yards were not taken into consideration, and the pattern of train formations was not universal. For other transportation modes, for example, maritime navigation, in the work of Iris et al [23], the flexible ship loading problem (FSLP) was optimized, including the management of loading operations, and the planning and scheduling of transport vehicles.…”

An Optimization Approach to the Low-Frequency Entire Train Formation at the Loading Area

“…A nonlinear 0-1 planning model was constructed, and the model was solved by a simulated annealing algorithm. Zhao and Lin [10] took the car hour cost at the loading station of stepped direct trains and non-direct trains, as well as the time delay caused by loading sequence as the optimization target, and took the train length and reclassification station capacity as constraints. In order to improve the railway rail freight services, many European companies and research institutes in the field of railway transport have focused on research and development projects.…”

“…As early as 1913, Harris [10] first proposed the importance of integrating transportation and inventory systems research, and discussed models with constant demand rates. He gave the classic economic order quantity (EOQ) model to minimize inventory cost and transportation cost.…”

Optimizing Train Formation Problem With Car Flow Routing and Train Routing by Benders-and-Price Approach

“…Chen et al [18] developed a binary linear model to minimize the total sum of accumulation costs and classification costs, and a novel tree-based decomposition algorithm was proposed. Zhao and Lin [19] formulated the multi-shipment train formation problem as a nonlinear binary model, which was linearized and then solved by LINGO. They reported the linear model has better performance than the nonlinear one in terms of solving efficiency.…”