An operational process at train marshaling yard is considered in this study. The inbound trains are decoupled and disassembled into individual railcars, which are then moved to a series of classification tracks, forming outbound trains after being assembled and coupled. We focus on the allocation plan of the classification tracks. Given are the disassembling and assembling sequence, the railcars connection plan, and a number of classification tracks. Output is the assignment of the railcars to the classification tracks. An integer programming model is proposed, aimed at reducing the number of coupling operations, as well as the number of dirty tracks which is related to the rehumping operation, and the order of the railcars on the outbound train must satisfy the block sequence. Tabu algorithm is designed to solve the problem, and the model is also tested by CPLEX in comparison. A numerical experiment based on a real-world case is analyzed, and the result can be reached within a reasonable amount of time. We also discussed a number of factors that may affect the track assignment and gave suggestions for the real-world case.
Railway transportation is known as one of the most significant modes of transport. Due to its advantages of the large capacity for both long-distance and short-distance transport, its full-time service, as well as the adaptation to different weather conditions, it is the most commonly used mode in freight transportation. In 2015, around 17.4% of inland cargo in European countries was transported via rail [
Train marshaling stations are terminals in the rail freight transportation network, where the inbound trains are disassembled into railcars to form outbound trains. Due to the complexity of the operation process at marshaling yards, railcars spend 10%~50% of their time in the marshaling yard during the whole trip [
The procedures at marshaling yard can be divided into four subproblems: railcar generation problem, train makeup problem, railcar classification problem, and outbound track assignment problem [
The typical layout of a train marshaling yard is shown in Figure
A schematic layout of a typical hump yard.
After the outbound train leaves the train marshaling yard, it will reach a number of intermediate train yards successively and unload railcars at their corresponding destination. In order to simplify the operation process both at marshaling yards and other following train yards, a group of railcars with the same origin and destination or belonging to the same train form a
In order to release the pressure at the marshaling station, this paper mainly concentrates on the process at classification bowl, and two problems are taken into account. Firstly, by deciding the railcar assignment, we try to reduce the rehumping operations and coupling operations. Secondly, the railcars on the same train should be arranged in a proper sequence (e.g., the block numbers of railcars on the same train appear consecutively), so that those railcars will arrive at their destinations successively, thus improving the efficiency of the whole rail freight network.
The classification track assignment is always regarded as a sorting problem, which is already reviewed by Gatto et al. [
The general train marshaling problem proved to be NP-complete [
A number of scholars propose graph theoretical approaches. Bohlin et al. [
Some scholars also analyze the rescheduling problem for the rehumping operation [
In China, very few scholars studied the classification track utilization, and the existing studies concentrate on the improvement of the track capacity [
Most previous studies only considered reducing the rehumping operations or satisfying the block sequence. Besides, due to the complexity to solve the OR model, the restriction on the order of the railcars in the outbound train is not always considered [
In this paper, the railcar allocation on the classification track is discussed in detail, especially how different types of railcar sequence influence the rehumping operations and coupling operations. Both the classification process and outbound train forming process are considered. In addition, both the assembling sequence and the block number sequence on the train are analyzed, so that the efficiency at the classification bowl, the departure yard, and the following train yards are improved. Many constraints related to the real-world case are also expressed in the paper, such as the track capacity and how the railcars from the former stage that have already on the classification track influence the classification track utilization. Basic studies have been made by the authors of this paper [
The paper consists of five parts. Section
The common sorting strategies can be divided into three types [
Figure
Clean track, temporary track, and dirty track.
Operations on the clean track are relatively simple, as the railcars can be directly moved to the departure yard. As for temporary track, more coupling operations are required. When a dirty track appears, rehumping operations are required. The existence of mixed tracks will lead to much more dwell time and greatly increase the difficulty in marshaling operations.
Figure
Coupling operation of the railcars from different tracks.
Apart from considering the assembling sequence, we also take the block sequence into account. Assume that the blocks from near to far are ordered from 1 to 5 and each railcar is unloaded at its corresponding destination. In order to simplify the unloading operation, the railcar next to the locomotive is the earliest to drop off at the nearest block. We note that the block number of each railcar on the classification track should be an ascending order, so that the outbound train can directly upload the railcars at their destination.
The core problem is to find a proper railcar sequence on the classification track, trying to make less mixed tracks and satisfying the requirements of the block sequence. To simplify the problem, two assumptions are made: The railcars with the same destination that do not depart at the end of the stage plan can be considered as an outbound train. The length of the trains and the classification tracks are measured by the number of railcars.
We consider all operations in one stage plan; the set of inbound trains
The set of railcars
According to Section
The definition of the destination sequence of the railcars.
There are
All the parameters and variables are described in Table
Parameters and variables.
| |
| Set of railcars in a stage plan (index |
| Set of railcars of inbound train |
| Set of the start and end time for disassembling and assembling (index |
| Set of classification tracks (index |
| Set of inbound trains (index |
| Set of outbound trains (index |
| |
| Index of the outbound train which railcar |
| Disassembling time of railcar |
| Assembling time of railcar |
| Destination of railcar |
| Capacity of track |
| Length of railcar |
| Binary parameter:1 if railcar |
| The maximum number of tracks outbound train |
| |
| Binary variable:1 if outbound train |
| Binary variable:1 if railcar |
| Binary variable:1 if track |
Dirty tracks require more rehumping operations, and temporary tracks mean more coupling operations. Our purpose is to minimize the number of mixed tracks, including both dirty tracks and temporary tracks. In the model, the number of temporary tracks is measured by the number of coupling times, while the number of rehumping times equals the number of dirty tracks.
The aim of the model is to minimize the number of dirty tracks and the coupling times for assembling operations, which is expressed in objective function (
The model is a 0-1 integer programming model, so that exact solutions can be reached by ILOG CPLEX. However, when the scale is expanded, there is a sharp increase in the solution time. It has been proved by many scholars that specific single-stage shunting and multistage shunting problem are strongly NP-complete, so a Tabu search is designed for the improvement of efficiency (see Figure
The procedure of Tabu search.
The computational experiments prove that the Tabu search algorithm offers a good solution in a very short time. Usually the optimal solution appears in the 50-100th iteration, so the maximum iteration is designed to be 100, and the Tabu length is 30 by a variety of tests.
The numerical experiment integrates with actual scenarios and randomly created data, which was cited in [
Disassembling and assembling sequence.
| | ||||||
---|---|---|---|---|---|---|---|
| | | | | | | |
1 | A2 | 9:40 | 9:55 | 1 | B1 | 9:55 | 10:10 |
2 | A1 | 9:55 | 10:10 | 2 | B3 | 10:10 | 10:25 |
3 | A3 | 10:10 | 10:25 | 3 | B2 | 10:25 | 10:40 |
4 | A4 | 10:25 | 10:40 | 4 | B4 | 10:40 | 10:55 |
5 | A6 | 10:40 | 10:55 | 5 | B5 | 10:55 | 11:10 |
6 | A5 | 10:55 | 11:10 | 6 | B6 | 11:10 | 11:25 |
7 | A7 | 11:10 | 11:25 | 7 | B7 | 11:25 | 11:40 |
8 | A8 | 11:25 | 11:40 | 8 | B8 | 11:40 | 11:55 |
9 | A9 | 11:40 | 11:55 | 9 | B9 | 11:55 | 12:10 |
10 | A12 | 11:55 | 12:10 | 10 | B10 | 12:10 | 12:25 |
11 | A11 | 12:10 | 12:25 | 11 | B11 | 12:25 | 12:40 |
12 | A10 | 12:25 | 12:40 | 12 | B12 | 12:53 | 13:08 |
Railcars information of inbound trains.
| | | | | | | | ||
---|---|---|---|---|---|---|---|---|---|
A0 | 1 | 1 | 4 | 6.4 | A7 | 33 | 3 | 22 | 24.2 |
2 | 3 | 4 | 4.4 | 34 | 5 | 4 | 6.4 | ||
3 | 4 | 6 | 6.6 | 35 | 7 | 12 | 13.2 | ||
A2 | 4 | 3 | 40 | 48.0 | 36 | 4 | 8 | 12.0 | |
5 | 4 | 4 | 6.4 | 37 | 3 | 20 | 24.0 | ||
6 | 5 | 10 | 15.4 | 38 | 7 | 8 | 10.4 | ||
7 | 3 | 20 | 26.0 | A8 | 39 | 2 | 30 | 48.0 | |
8 | 6 | 6 | 7.8 | 40 | 7 | 20 | 24.0 | ||
A1 | 9 | 1 | 30 | 40.0 | 41 | 5 | 4 | 4.4 | |
10 | 2 | 10 | 13.0 | 42 | 2 | 10 | 18.0 | ||
11 | 7 | 10 | 12.0 | 43 | 7 | 10 | 13.0 | ||
12 | 5 | 4 | 4.8 | A9 | 44 | 1 | 20 | 32.0 | |
13 | 1 | 18 | 21.6 | 45 | 2 | 26 | 31.2 | ||
A3 | 14 | 1 | 34 | 37.4 | 46 | 4 | 12 | 13.2 | |
15 | 2 | 16 | 19.2 | 47 | 2 | 16 | 17.6 | ||
16 | 4 | 6 | 6.6 | A12 | 48 | 6 | 2 | 2.4 | |
17 | 2 | 20 | 30.0 | 49 | 4 | 34 | 37.4 | ||
A4 | 18 | 3 | 40 | 44.0 | 50 | 5 | 12 | 13.2 | |
19 | 4 | 10 | 13.0 | 51 | 3 | 6 | 6.6 | ||
20 | 5 | 4 | 4.8 | 52 | 4 | 22 | 24.2 | ||
21 | 6 | 4 | 4.8 | A11 | 53 | 1 | 30 | 33.0 | |
22 | 4 | 12 | 15.6 | 54 | 6 | 6 | 9.6 | ||
23 | 7 | 4 | 4.8 | 55 | 2 | 10 | 12.0 | ||
A6 | 24 | 3 | 14 | 16.8 | 56 | 5 | 20 | 22.0 | |
25 | 5 | 20 | 24.0 | 57 | 1 | 6 | 9.6 | ||
26 | 4 | 4 | 6.4 | A10 | 58 | 3 | 20 | 26.0 | |
27 | 3 | 4 | 4.4 | 59 | 6 | 8 | 8.8 | ||
28 | 5 | 18 | 19.8 | 60 | 7 | 24 | 31.2 | ||
29 | 6 | 14 | 21.0 | 61 | 4 | 20 | 26.0 | ||
A5 | 30 | 1 | 40 | 56.0 | |||||
31 | 2 | 26 | 33.8 | ||||||
32 | 7 | 8 | 9.6 |
Railcars connection plan.
| |
---|---|
B1(3,4) | A0/3/6, A2/4/40, A2/7/20 |
B2(1,2) | A3/14/34, A3/15/16, A3/17/20 |
B3(1,2) | A0/1/4, A1/9/30, A1/10/10, A1/13/18 |
B4(3,4) | A0/2/4, A4/18/40, A4/19/10, A4/22/12 |
B5(5,6) | A2/6/10, A2/8/6, A4/20/4, A4/21/4, A6/25/20, A6/29/14 |
B6(1,2) | A5/30/40, A5/31/26 |
B7(3,4) | A6/24/14, A7/33/22, A7/36/8, A7/37/20 |
B8 | A1/11/10,A5/32/8, A7/35/12, A7/38/8, A8/40/20, A8/43/10 |
B9 | A8/39/30,A9/45/26 |
B10 | A3/16/6, A9/46/12, A12/49/34, A12/52/22 |
B11 | A9/44/20, A11/53/30, A11/57/6 |
B12(5,6) | A6/28/18, A7/24/4, A10/59/8, A11/54/6, A11/56/20, A12/50/12 |
| |
B13 | A6/27/4, A8/42/10, A9/47/16, A11/55/10, A12/51/6 |
B14 | A2/5/4, A6/26/4, A10/58/30, A10/61/20 |
B15 | A1/12/4, A8/41/4 |
B16 | A12/48/2 |
B17 | A4/23/7, A10/60/24 |
The numerical experiments are tested by both
Assume that there are 10 classification tracks. The capacity of each classification track is 100. The objective function is 27, where there are 0 dirty track and 10 temporary tracks. As it can be seen in Figure
Track assignment with 10 tracks (with block sequence considered).
In comparison, we also make the track assignment without considering the block sequence. By testing the model in [
Track assignment with 10 tracks (without considering block sequence).
More comparisons can be seen in Table
Comparison of the results for whether to consider the block sequence.
| | | | |
---|---|---|---|---|
Considering | 8 | 34 | 1 | 16 |
9 | 28 | 1 | 10 | |
10 | 27 | 0 | 10 | |
11 | 26 | 0 | 9 | |
| ||||
Not Considering | 8 | 29 | 4 | 8 |
9 | 20 | 2 | 1 | |
10 | 18 | 1 | 0 | |
11 | 17 | 0 | 0 |
As for the algorithm, the optimization solution can be found within 50 interactions. The calculation results show that this algorithm has good convergence (see Figure
The convergence rate of Tabu search.
In addition, the algorithm can reach the optimal solution in a shorter time compared to CPLEX as the scale expands. As it can be seen in Table
Computation time of CPLEX and Algorithm.
| | | ||
---|---|---|---|---|
Computation time(s) | Objective | Computation time(s) | Objective | |
8 | infeasible | infeasible | 14.12 | 34 |
9 | 456.92 | 28 | 11.04 | 28 |
10 | 113.34 | 27 | 13.56 | 27 |
11 | 10.29 | 26 | 17.79 | 26 |
The facilities and the operation strategies as well the stage plans will influence the track assignments. In order to find out to what extent the facilities influence such process, we vary the number and the length of tracks. Then we discuss how the wagon-flow allocation plan and railcars from the last stage affect the track allocation.
Both the track number and the track length represent the capacity of the classification bowl. Adding the number of classification tracks will decrease the possibility of forming dirty tracks or temporary tracks. Since more options and less restrictions are available for the railcars. However, in China, it is impracticable to build new tracks, and the track number is usually less than the block number. Most of the time, each track is assigned to a fixed block number, which will restrict the classification track assignment too. Due to the intense capacity, it is better to decide a reasonable assembling sequence while making the stage plan.
Usually, in a classification bowl, the tracks’ lengths are different due to the shape of the yard. For the limit of the track length, railcars of the same outbound train may be assigned to more than one classification track. We tested tracks with arbitrary length to see the impact. For the cases with 8~11 tracks (see Table
Variation in track length and track number.
| | | | |
---|---|---|---|---|
8 | | 34 | 1 | 16 |
8 | | 36 | 2 | 17 |
9 | | 28 | 1 | 10 |
9 | | 29 | 1 | 11 |
10 | | 27 | 0 | 10 |
10 | | 30 | 1 | 12 |
11 | | 26 | 0 | 9 |
11 | | 28 | 1 | 10 |
According to the wagon-flow allocation plan, railcar 5 and 12 cannot be assembled by the end of this stage, so that those tracks will be occupied throughout the whole stage (see track 6 in Figure
Usually, there are some railcars that cannot be assembled by the end of the stage, so that they may stay on the track for the next operational stage. Such railcars may influence the track assignment for the following procedure. As it is shown in Table
Due to the uneven traffic flow and the influence of the station layout, the classification track capacity at most marshaling stations is very tight. The optimization of classification tracks has an important influence on improving the efficiency for marshaling operations.
In this paper, the basic application of the classification tracks is analyzed. This paper requests a certain sequence of the railcars, in order to reduce the rehumping operations and the coupling operations at marshaling station, as well as simplify the operations at following train yards. It puts forward a holistic design thinking of the rail freight network, trying to decrease the whole time. Tabu search is designed for the real-world application, which proved to be efficient. A variety of factors such as track length, track number, wagon-flow allocation plan, and railcars from the last stage would influence the results. It illustrates that operations of railway system are continuous processes and should be considered as a whole.
The data used to support the findings of this study are from [
The authors declare that there are no conflicts of interest regarding the publication of this article.
This paper is supported by the National Natural Science Foundation of China No. U1434207 and No. U1734204.