Train trip package transportation is an advanced form of railway freight transportation, realized by a specialized train which has fixed stations, fixed time, and fixed path. Train trip package transportation has lots of advantages, such as large volume, long distance, high speed, simple forms of organization, and high margin, so it has become the main way of railway freight transportation. This paper firstly analyzes the related factors of train trip package transportation from its organizational forms and characteristics. Then an optimization model for train trip package transportation is established to provide optimum operation schemes. The proposed model is solved by the genetic algorithm. At last, the paper tests the model on the basis of the data of 8 regions. The results show that the proposed method is feasible for solving operation scheme issues of train trip package.
Railway transportation is one of the main types of modern transportation. Railway transportation has the features of fast speed, low costs, environmental friendship, high reliability, accuracy, and continuity. Before the completion of highspeed railway network, railway transportation in China heavily focused on passenger transport. For this reason, railway freight transportation was always restricted by the problem of insufficient capacity. With the operation of motor trains and highspeed railway in recent years, a large number of railway capacities have been released and applied to freight transportation. As the main form of railway freight transportation, train trip package transportation is becoming increasingly important. Meanwhile, it is also becoming more complex due to increased railway transport resources.
Train trip package transportation provides luggage and parcel transportation, fast freight, and joint logistics services. Train trip package transportation is based on the existing railway network and uses passenger baggage cars, train trip packages, and mail train lines as the carrier. With the rapid development of social economy and the growing requirement of perfecting transportation service, railway package transportation has been improving its level of service and has become the main body of rapid railway freight transportation. There are two main types of railway freight transportation: one is the package marshaled in the passenger train; the other is transport by a specialized train which consists of a certain number of baggage compartments and has fixed stations, fixed time, and fixed path. The second type is normally called the train trip package transportation. In the near future, train trip package transportation will become the main form of package transportation. Therefore, a reasonable train trip package operation scheme can help to improve the level of train trip package organization and the quality of service.
Most of the current researches have focused on the passenger train operation scheme, but few focused on train trip package operation scheme [
In this paper, the existing research results and experiences of passenger train operation scheme are studied. Then the related factors of train trip package operation scheme are analyzed from its organizational characteristics. A mathematical model is developed to optimize the train trip package operation scheme for practical situation. At the end, the proposed model is verified through an example, and some conclusions are obtained from the experiment.
The whole process of package transportation can be divided into three operational phases: reception and delivery in the stations of two ends and longdistance rail transportation between the stations. The whole process of package transportation and the relationship among the operational phases are shown in Figure
The whole process of package transportation.
In train trip package transportation, the train marshaling is composed of package trains with the same final station (single set of trains) or package trains whose final stations are in the same running path (grouped trains). The operation process of grouped trains is shown in Figure
The operation process of grouped trains.
Through the analysis of organizational characteristics of train trip package transportation, we first make the following assumptions before establishing the optimization model of train trip package operation scheme.
The path of train trip package has been already predetermined.
The transport capacity of train trip package is not restricted and the ability to receive and send trains of each package station can satisfy any traffic intensity; each path can satisfy any traffic intensity.
Operation details and operation process inside stations are not considered, because the operation of train trip package only reflects the influence on the operation scheme in some important links, such as loading costs, rejection, and hanging operations costs.
The operation of train trip package depends on the traffic situation and does not consider the constraints of facing operation.
All the expenses in the service process of train trip package are shown in Figure
Expenses in the service process of train trip package.
Train trip package transport is a kind of contractual transport and the contractors are obligated to organize shipments. In principle, the contractors of train trip package need to load and unload packages by themselves. Therefore, the cost of train trip package in loading place is considered as a constant which is denoted by the average loading cost.
A single set of trains do not need rejection and hanging operations in the middle station. Grouped trains need rejection and hanging operations in the operation stations along the way but do not need loading, unloading, and modifying marshaling operations. Therefore, the rejection and hanging cost only existed in the grouped trains and can be considered as a fixed value.
In the model established in this paper, the total cost of train trip package transportation consists of two parts: one is intransit cost such as locomotive traction cost and line usage cost which are decided by the cost per vehicle kilometer; the other is the rejection and hanging cost which is decided by the rejection and hanging costs for a train. Because the loading cost of train trip package can be considered as fixed, loading cost is not reflected in the model.
The optimization model of train trip package operation is
Constraint (
Constraint (
Constraint (
Constraints (
Because the formulation of train trip package operation scheme is a linear discrete optimization problem, the traditional method is difficult to get the optimal solution to the problem. Many literatures suggested that heuristic algorithm was often the first choice to solve this kind of complicated transportation optimization problems [
The decimal coding is employed to generate an array of numbers, namely, a chromosome. Each chromosome represents an operation sequence of train trip package (Figure
Representation of chromosome.
According to OD flows between package stations, we successively select each OD pair and find a path between stations to produce a feasible chromosome. Repeat the process until feasible chromosomes between each OD pair have been produced.
Clearly, some chromosomes may not satisfy all of the constraints in the model. Therefore, it is necessary to construct the fitness function. Adaptation function indicates the superiority of chromosomes. For the minimum value problem in this paper, the fitness function is
Roulette method is used as a selection mechanism. In the roulette method, chromosomes will be selected for reproducing a new generation with certain probability. The selection probability of a chromosome is related to its fitness. Generally, the higher the fitness value, the bigger the selection probability. Meanwhile, the elite strategy is also implemented, which means the chromosome with the maximum fitness value in each generation of populations will be copied to the next generation. The optimal policy makes the next generation not worse than the parent generation.
Crossover introduces random changes to the selected chromosomes by crossing two parent individuals to produce offspring individuals with a userspecified probability
Crossover operator of genetic algorithm.
Mutation introduces random changes to the chromosomes by altering the value of a gene with a userspecified probability
Mutation operator of genetic algorithm.
To compare the computation efficiency of different algorithms, different stopping times are set as the stopping criteria. When getting to the predetermined stopping time, the algorithm ends.
Based on “three vertical and four horizontal” train transportation physical network of China, eight package stations are chosen to build a spatial network graph of package transportation regions (as shown in Figure
Spatial network graph of package transportation regions.
As the spatial network graph of package transportation regions shown in Figure
Space distance of package transportation regions (km).
Region  1  2  3  4  5  6  7  8 

1  —  3768  —  —  —  —  —  — 
2  —  1288  2042  689  1463  —  —  
3  —  —  —  —  —  —  
4  —  1622  —  1100  2527  
5  —  998  —  1605  
6  —  —  1810  
7  —  1637  
8  — 
According to the statistics of China railway transportation, Table
OD flows by package among 8 package regions (tons/year).
Region  1  2  3  4  5  6  7  8 

1  —  139790  8284  34410  20431  80648  10753  44088 
2  50294  —  62909  136105  57034  140123  67275  108884 
3  7710  96678  —  —  —  32028  —  15421 
4  88962  172889  —  —  120854  119176  186317  100712 
5  13255  46392  —  26510  —  64381  —  31954 
6  44764  135649  42155  121667  104032  —  59998  109145 
7  20523  79930  —  106933  —  74529  —  73449 
8  31014  180416  39662  96321  79025  188766  65606  — 
In this paper, assume that the length of the design cycle is one day and the OD flows for each period are constant. It is known that the OD flows in Table
Since the volume of packages is difficult to accurately grasp in the actual operation, the deadweight constraint of package trains is considered as an alternative. The deadweight capacity of a package train is averagely 15 tons according to our survey and a year is calculated as 365 days. The result of the conversion is shown in Table
Daily OD train flows among 8 package regions (train/day).
Region  1  2  3  4  5  6  7  8 

1  —  26  2  6  4  15  2  8 
2  9  —  11  25  10  26  12  20 
3  1  18  —  —  —  6  —  3 
4  16  32  —  —  22  22  34  18 
5  2  8  —  5  —  12  —  6 
6  8  25  8  22  19  —  11  20 
7  4  15  —  20  —  14  —  13 
8  6  33  7  18  14  34  12  — 
The average operating cost is set to 90 per vehicle kilometer (
According to the regulation of the number of marshaling train trip packages,
Based on the above model parameters, the genetic algorithm is used to calculate model through C++ programming. The crossover probability of GA is set as 0.8 and the mutation probability is set as 0.05. The maximum evolution generation of GA is set as 100. The specific results are shown in Table
Calculation results train trip package operation scheme.
Number  Originating station  Final station  Running path  The number of train flows  Operation number  Organizational form 

1  1  2 

27  2  Single 
2  1  4 

12  1  Single 
3  1  5 

8  1  Single 
4  2  1 

11  1  Single 
5  2  3 

28  2  Single 
6  2  4 

50  3  Single 
7  2  6 

31  2  Single 
8  2  8 

33  2  Grouped 
9  3  1 

28  2  Single 
10  4  1 

16  1  Single 
11  4  2 

32  2  Grouped 
12  4  5 

32  2  Single 
13  4  6 

48  3  Grouped 
14  4  7 

48  3  Single 
15  4  8 

22  2  Single 
16  5  1 

11  1  Single 
17  6  2 

32  2  Single 
18  6  4 

35  2  Single 
19  6  5 

19  2  Single 
20  6  8 

31  2  Single 
21  7  4 

23  2  Single 
22  7  8 

27  2  Single 
23  8  2 

63  4  Single 
24  8  4 

18  1  Single 
25  8  6 

48  3  Single 
26  8  7 

23  2  Single 
As shown in Table
Figure
Result of each calculation.
It is known that the initial operation scheme consists of 48 single sets of trains. All OD flows are transported directly from the start station to the final station, without any operation in transit. Target cost of initial operation scheme is 9.8574 million yuan.
After optimization, the sample train transport service network consists of 26 kinds of train trip package transport services. In the optimized operation scheme, there are 52 operations within a day, including 45 operations of single set of trains and 7 of grouped trains. Compared with the initial scheme, the optimized scheme reduces the operation number of single set of trains in long distance and yet increases the operation number of both single set of trains and group trains in short/middle distance, thus reducing the total cost of train transportation. The total cost of the optimized scheme is 7.2561 million yuan, reduced by 26.4% compared with the initial one.
To evaluate the performance of the proposed scheme, the results of initial operation scheme and optimized scheme can be showed in Figure
Comparison of the results.
This paper focuses on how to arrange the train trip package operation scheme to lower the transportation cost. An optimization model is established based on the analysis of the organizational forms and characteristics of the train trip package transport, as well as the existing research results and experiences of passenger train plan. Computational tests show that the proposed model can effectively reduce the cost of transportation. The model can also optimize the operation number of train trip packages in the experiment, indicating that it has better applicability.
An issue of future research is the consideration of more constraints, such as the inconsistent loading cost between single set of trains and group trains and the constraints of facing operation. In further studies, these constraints will be considered in order to get closer to the actual situation.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This research is supported by Railway Ministry Science and Technology Management Project (2013X014C), China Railway Corporation Project (2014X010A), and Fundamental Research Funds for the Central Universities (Beijing Jiaotong University) under Grant no. 2014JBZ008.