# Research Methodology: Application of Railway Luggage and Package Transportation Scheme Formulation Based on a Dynamic Time–Space Service Network

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## Abstract

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## 1. Introduction

## 2. Literature Review

- Based on passenger schedules and demand information, we include the station-to-station transportation process in the research scope and construct a dynamic time–space service network of RLPT.
- The initial constructed time–space network is processed into a closed time–space network at both ends, and the improved A* algorithm adapted to the network is adopted to generate feasible path sets for all transportation demands. It is suitable for solving large-scale network problems.
- Considering the relevant important constraints, a flow distribution model is constructed. Feasible path search and traffic allocation are part of the important components in the two-stage method. The advantages of the two-stage method include the following: Based on the static timetable of passenger trains in a certain period of time, different timeliness paths can be found. Once the demand changes, only one-time traffic volume can be reallocated through the model to compile the RLPTS in a short period of time. Therefore, the two-stage solution method can not only guarantee the transportation timeliness of demand, but also meet the traffic volume transportation demand and greatly reduce the difficulty when solving the problem and improve the solving efficiency.

## 3. Methods

#### 3.1. Feasible Path Search Algorithm Based on Dynamic Time–Space Service Network

#### 3.1.1. Construction of Dynamic Time–Space Service Network

#### 3.1.2. Principles and Restrictions of Path Search

- Time limit of loading and unloading operations. The loading and unloading of goods must be completed before the departure of the train; otherwise, the goods will not be able to undergo loading and unloading at the station.
- Minimum transit operating time limit. At the transfer station, the time interval between the arrival of the previous train and the departure of the next train is the transfer connection time. If the transfer connection time does not meet the limit of the shortest transfer operation time, the goods will not be able to undergo transit operation at the station.
- Limited number of transits. Each transit of goods will be accompanied by a loading and unloading operation, which not only consumes a lot of transportation resources, but also increases the uncertainty and reduces the safety of the transportation process. Therefore, it is stipulated that the maximum number of transits should be two, and any path with more than two transit times will be ignored.
- Transport timeliness constraint. The transportation time of the searched feasible path should not be too long, and the path should be guaranteed to meet the timeliness requirements of the cargo owner.

#### 3.1.3. Preprocessing of Dynamic Time–Space Service Network before Path Search

#### 3.1.4. Feasible Path Set Generation Based on Improved A* Algorithm

#### 3.2. Flow Distribution Model Based on Feasible Path

#### 3.2.1. Assumptions and Parameter Descriptions

- Theoretically, the loading capacity of the train is limited by its own capacity, volume, and weight of goods. To simplify the solution, only the effect of weight on the train’s loading capacity is considered in the model.
- Without considering the restriction of mixed cargo loading, we studied the formulation of RLPTS from the perspective of system optimization.
- Assuming that RLPT handling station has no limitation on capacity, it can meet the requirements of large quantities of stacked goods.

Parameter | Description |

$D$ | OD set of cargo flows, $d\in D$ |

$A$ | Set of service arcs, $a\in A$ |

${d}^{k}$ | kth ($k=1,2\cdot \cdot \cdot $) path of demand $d$ |

${d}^{K}$ | Set of K shortest paths of demand $d$, ${d}^{k}\in {d}^{K}$ |

${\omega}_{{d}^{k}}$ | Cost of demand $d$ transported by path ${d}^{k}$, yuan/kg |

${x}_{d}$ | Demand $d$ for volume be transported through path ${d}^{k}$ |

${r}_{d}$ | Freight of demand $d$, yuan/t |

${x}_{{d}^{k}}$ | Demand $d$ for volume to be transported through path ${d}^{k}$ |

$\tau $ | Cost per kilogram of cargo loaded and unloaded, yuan/kg |

$\rho $ | Penalty charges for unmet demands, yuan/kg |

${\gamma}_{a}^{{d}^{k}}$ | If arc $a$ is selected by path ${d}^{k}$, the value is 1; otherwise, 0 |

${c}_{a}$ | Transportation capacity of arc $a$ |

${c}_{{d}^{k}}$ | Transportation capacity of path ${d}^{k}$ |

#### 3.2.2. Objection Function

#### 3.2.3. Constraint Conditions

#### 3.2.4. Evaluation Indices

## 4. Empirical Studies

^{k}) variables and (d + t + d

^{k}) constraints, and the global optimal solution was obtained within 180 min in this study (path search took 165 min and model solving took 15 min).

#### 4.1. Related Parameter Values

#### 4.1.1. Parameter Values in Path Search Algorithm

#### 4.1.2. Freight Rates and Costs in the Model

#### 4.2. Results and Discussion

#### 4.3. Result Comparison

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CRE | China Railway Express |

RLPTS | railway luggage and package transport scheme |

RLPT | railway luggage and package transportation |

TRA | train running arc |

DA | delay arc |

TA | transit arc |

VSN | virtual start node |

VEN | virtual end node |

VSA | virtual start arc |

VEA | virtual end arc |

ATT | average transit time |

TCUR | train capacity utilization ratio |

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**Figure 1.**Dynamic time–space service network for RLPT. TRA, train running arc; DA, delayed arc; TA, transit arc.

**Figure 2.**Comparison between (

**a**) initially constructed dynamic time–space network and (

**b**) dynamic time–space service network with virtual arcs at both ends.

**Figure 3.**Flowchart of K shortest path search algorithm under dynamic time–space service network based on A* algorithm.

**Figure 4.**Numbers of different types of paths. DP, direct path; OTP, one transit path; TTP, two transit path.

**Figure 8.**Timeliness comparison of paths calculated by model and algorithm and related products of S.F. Express.

Company | Indices | ||
---|---|---|---|

Service Levels | Delivery Time | Charges | |

S.F. Express | Arrive today | Before 22:00 today | 140 yuan ** |

Arrive next morning | Before 10:30 next day | 25 yuan*, 14 yuan/kg *** | |

Standard express | 1–2 days after receipt | 23 yuan*, 14 yuan/kg *** | |

Special express | 2–3 days after receipt | 18 yuan*, 4 yuan/kg *** |

Field | Definition | Data Type |
---|---|---|

node_id | ID index of time–space network node | Int |

train_code | Train code on which node is located | String |

station | Station corresponding to time–space node | Station class with attributes |

time | Time corresponding to time–space node | Double |

Field | Definition | Data Type |
---|---|---|

arc_id | ID index of time–space arc | Int |

type | Type of time–space arc | Int |

train_code | Train code on which time–space arc is located | String |

start_node | Head node of time–space arc | Node with attributes |

end_node | Tail node of time–space arc | Node with attributes |

weight | Time difference between nodes at both ends of arc | Double |

Time–space Arc | Type Index |
---|---|

TRA | 0 |

DA | 1 |

TA | 2 |

Virtual Node | Node_Id | Train_Code | Station | Time |
---|---|---|---|---|

VSN | N (total number of network nodes) + 1 | “0000” | VirtualStartStation | 0 |

VEN | N (total number of network nodes) + 2 | “0000” | VirtualEndStation | 0 |

Virtual Arc | Arc_Id | Type | Train_Code | Start_Node | End_Node | Weight |
---|---|---|---|---|---|---|

VSA | –1 | 3 | “0000” | SN | ${a}_{1}\text{}or\text{}{a}_{2\text{}}or\text{}{a}_{3}$ | 0 |

VEA | –2 | 3 | “0000” | ${b}_{1}\text{}or\text{}{b}_{2}\text{}or\text{}{b}_{3}$ | VEN | 0 |

**Table 7.**Start station code, end station code, batch, number, weight, time limit, and unit transport price (${r}_{d}$) of different demands.

Start Station Code | End Station Code | Batch | Number | Weight (kg) | Unit Transport Price (kg/yuan) | Time Limit (day) |
---|---|---|---|---|---|---|

0902 | 0102 | 5 | 6 | 21 | 2.19 | 2 |

0904 | 1201 | 1 | 3 | 21 | 5.20 | 1 |

1203 | 3226 | 3 | 3 | 21 | 2.81 | 3 |

1001 | 3341 | 2 | 1 | 21 | 2.63 | 2 |

4719 | 3348 | 4 | 1 | 21 | 0.98 | 2 |

0901 | 9887 | 25 | 772 | 10,480 | 3.69 | 2 |

1201 | 9887 | 28 | 1588 | 18,699 | 1.57 | 2 |

Demand ID | Start Station Name | End Station Name | RLPTS |
---|---|---|---|

1 | Changsha | Qiqihaer | (Changsha, 00T124A7,ShenyangBei)(ShenyangBei,0K1082A4,Qiqihaer *) |

1 | Changsha | Qiqihaer | (Changsha,00T124A8,ShenyangBei)(ShenyangBei,0K1082A4,Qiqihaer *) |

1 | Changsha | Qiqihaer | (Changsha,00T124A7,ShenyangBei)(ShenyangBei,0K1082A5,Qiqihaer *) |

1 | Changsha | Qiqihaer | (Changsha,00T124A8,Zhangchun *)(Zhangchun,0K1082A5,Qiqihaer *) |

1 | Changsha | Qiqihaer | (Changsha,000T14A5,ShenyangBei *)(ShenyangBei,0K1082A4,Qiqihaer *) |

1 | Changsha | Qiqihaer | (Changsha,00T254A0,Tianjin *)(Tianjin,0K1082A4,Qiqihaer *) |

1 | Changsha | Qiqihaer | (Changsha,000T14A5,ShenyangBei *)(ShenyangBei,0K1082A5,Qiqihaer *) |

1 | Changsha | Qiqihaer | (Changsha,00T254A0,Tianjin *)(Tianjin,0K1082A5,Qiqihaer *) |

1 | Changsha | Qiqihaer | (Changsha,000Z14A0,ShenyangBei *)(ShenyangBei,0K1082A4,Qiqihaer *) |

1 | Changsha | Qiqihaer | (Changsha,000Z14A0,ShenyangBei *)(ShenyangBei,0K1082A5,Qiqihaer *) |

2 | Botou | Qiqihaer | (Botou,0K1450A2,ShenyangBei)(ShenyangBei,00K546A3,Qiqihaer *) |

2 | Botou | Qiqihaer | (Botou,0K1450A1,Tianjin)(Tianjin,00K546A3,Qiqihaer *) |

2 | Botou | Qiqihaer | (Botou,00K956A2,Tianjin)(Tianjin,00K546A3,Qiqihaer *) |

2 | Botou | Qiqihaer | (Botou,001450A0,Tianjin)(Tianjin,00K546A3,Qiqihaer *) |

2 | Botou | Qiqihaer | (Botou,001450A0, Zhangchun)(Zhangchun,0K1082A4,Qiqihaer *) |

2 | Botou | Qiqihaer | (Botou,001450A0, Zhangchun)(Zhangchun,0K1082A5,Qiqihaer *) |

2 | Botou | Qiqihaer | (Botou,00K956A3,Tianjin)(Tianjin,0K1082A4,Qiqihaer *) |

2 | Botou | Qiqihaer | (Botou,0K1450A1,Tianjin)(Tianjin,0K1082A4,Qiqihaer *) |

2 | Botou | Qiqihaer | (Botou,00K956A2,Tianjin)(Tianjin,0K1082A5,Qiqihaer *) |

2 | Botou | Qiqihaer | (Botou,00K956A3,Tianjin)(Tianjin,0K1082A5,Qiqihaer *) |

Station Name | Transit Volume (kg) |
---|---|

Haerbinxi | 860 |

Qiqihaer | 3097 |

Zhangchun | 28,214 |

Shenyangbei | 20,662 |

Shenyang | 14,015 |

Jilin | 3424 |

Jinzhou | 31,063 |

Beijingxi | 1270 |

Beijing | 6412 |

Tianjin | 47,654 |

Shijiazhuang | 23,874 |

Train Code | Utilization Rate (%) |
---|---|

0000K5A0 | 0.11 |

0000T1A0 | 0.01 |

0000T2A0 | 0.04 |

0000T7A0 | 0.03 |

0000T8A0 | 0.12 |

0000T9A2 | 0.05 |

0000Z1A0 | 0.04 |

0000Z2A0 | 0.27 |

0000Z3A0 | 0.66 |

0000Z3A1 | 0.53 |

Path | Sent Time | Train Code | Transfer Station | Arrival Time | Customer Receipt Time | Door-to-Door Timeliness | Volume (kg) |
---|---|---|---|---|---|---|---|

1 | 00:51 | Z174 | — | 00:49 (2nd day) | 14:49 (2nd day) | 27 h, 58 min | 3409 |

2 | 00:51 | Z174 K292 | Suzhou | 05:34 (3rd day) | 10:00 (3rd day) | 47 h, 6 min | 0 |

3 | 00:51 | Z174 K378 | Suzhou | 05:24 (3rd day) | 10:00 (3rd day) | 47 h, 6 min | 0 |

RLPTS in This Paper | RLPTS Currently Used | ||||||
---|---|---|---|---|---|---|---|

Train Number | Transfer Station | Cost (yuan) | Time (min) | Train Number | Transfer Station | Cost (yuan) | Time (min) |

Z12 | – | 3281.06 | 1313 | T15 | – | 3210.06 | 1326 |

T12 | – | 2659.87 | 1320 | T29 | – | 2541.27 | 1348 |

2251, K93 | Chengde | 2226.74 | 1724 | T1, K93 | Changsha | 2353.09 | 1885 |

K48, Z12 | Tianjin | 977.46 | 1933 | K17, T25 | Zhengzhou | 1401.73 | 2013 |

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## Share and Cite

**MDPI and ACS Style**

Niu, K.; Liu, J.; Wang, Y.
Research Methodology: Application of Railway Luggage and Package Transportation Scheme Formulation Based on a Dynamic Time–Space Service Network. *Symmetry* **2019**, *11*, 1226.
https://doi.org/10.3390/sym11101226

**AMA Style**

Niu K, Liu J, Wang Y.
Research Methodology: Application of Railway Luggage and Package Transportation Scheme Formulation Based on a Dynamic Time–Space Service Network. *Symmetry*. 2019; 11(10):1226.
https://doi.org/10.3390/sym11101226

**Chicago/Turabian Style**

Niu, Kaige, Jun Liu, and Ying Wang.
2019. "Research Methodology: Application of Railway Luggage and Package Transportation Scheme Formulation Based on a Dynamic Time–Space Service Network" *Symmetry* 11, no. 10: 1226.
https://doi.org/10.3390/sym11101226