Express delivery with high-speed railway: Definitely feasible or just a publicity stunt

Transportation Research Part A 120 (2019) 165–187

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Express delivery with high-speed railway: Definitely feasible or just a publicity stunt Mingkai Bia, Shiwei Hea, , Wangtu (Ato) Xub, ⁎

a b

T

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MOE Key Laboratory for Urban Transportation Complex Systems Theory and Technology, Beijing Jiaotong University, Beijing, PR China Department of Urban Planning, Xiamen University, Xiamen, PR China

ARTICLE INFO

ABSTRACT

Keywords: High-speed railway express delivery (HSReD) Adaptability HSR network Transportation capacity Levels of service China

When the construction of a large-scale high-speed railway (HSR) network is completed, how to make use of its transportation capacity is a consequent problem that needs to be resolved. Over the past few years, railway managers have launched the concept of high-speed rail express delivery (HSReD), with the aim of effectively utilizing the remaining passenger transportation capacity for express delivery services. This study analyzes the adaptability of HSReD to the HSR network according to the capacity utilization ratios of various HSR lines. First, the definition of the transportation capacity of the HSReD on the HSR network is proposed. Second, the level of service (LoS) of HSReD is measured. Then, the relationships among the LoS of HSReD, train schedule, and target market are analyzed. Next, based on the real operating environment, including different LoSs and capacity occupancies, an improved Arc-Route mathematical model for calculating the transport volume of HSReD parcels on the HSR network is built. A solution algorithm is designed. The proposed mathematical model is used to empirically analyze the adaptability of the HSReD on China’s HSR network, on which express parcels among 27 provinces are carried. Results show that: (a) the average utilization rate of transportation capacity of HSReD accounts for approximately 5.5% of the total transportation capacity of the entire HSR network. That is, currently, the capacity of the network is in a good state of adaptation, which can fully meet all transport demands. (b) Based on the annual growth rate of 50% of the express delivery amount in China, the transportation capacity of HSReD can meet the transport demand for only 5 years. In 2021, the transport volume of the HSReD parcels on China’s HSR network will reach the limit of the transportation capacity. Accordingly, this study provides policy suggestions for the current and future development of the HSReD on China’s HSR network.

1. Introduction The global express delivery industry has developed rapidly in recent years. The overall number of express deliveries has also multiplied in a short period of time. According to the latest statistics, by 2016, the annual global express delivery industry reached 70 billion parcels, and the global logistics market value has exceeded 9 trillion dollars (Armstrong & Associates, Inc., 2016). The increase in the number of express delivery parcels can be partly attributed to the rapid growth of the scale of e-commerce. For example, in 2016, the quantity of express delivery parcels in China reached 31.35 billion pieces, with a growth of 51.67% over that in 2015 (Statistical Office of the People’s Republic of China, 2017). With such a large and rapidly growing demand, sufficient transportation ⁎

Corresponding author. Corresponding author. E-mail addresses: [email protected] (S. He), [email protected] (W.A. Xu).

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https://doi.org/10.1016/j.tra.2018.12.011 Received 25 June 2018; Received in revised form 11 November 2018; Accepted 13 December 2018 0965-8564/ © 2018 Elsevier Ltd. All rights reserved.

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supplies in the form of low cost, large volume, fast speed, and good continuity are urgently needed to carry the express parcels. Express transportation in developed countries adopts two main modes of transportation: airplane and highway. The shortage of express transportation capacity is the bottleneck restricting the further development of the express industry in developed countries. For instance, the average delivery time of a parcel is longer than two days. Compared with other modes of transportation, high-speed railway (HSR) has numerous advantages, such as fast speed, high punctuality rate, less economic investments required, little environmental impact, and low energy consumption (Chai et al., 2018). In this context, a kind of transport service that uses HSR passenger trains to carry parcels, which is called high-speed rail express delivery (HSReD), has been introduced in China. Cargo express transportation has been launched in many countries, such as Germany, Denmark, and France, and the hardware conditions of the existing infrastructure are adequate to meet the basic requirements for the organization of HSReD (Plotkin, 1997). Moreover, China has developed a large-scale HSR network in recent years, providing the conditions for the implementation of the new transport service. HSReD would not only bring considerable economic benefits but also promote the sustainable and healthy development of the express delivery market (D’Alfonso et al., 2015; Chen et al., 2016; Jia et al., 2017; Wang et al., 2017). HSReD also has the potential to become an important part of the express market in China. The evaluation of the transportation capacity of HSReD is the prerequisite for the rational utilization and strengthening of transportation capacity on the entire HSR network. By contrast, scientific analysis of the transportation capacity of the HSReD on the HSR network can help the transportation planning and management departments master the practical operations and make the right decision-making policies on transport service establishment (Abril et al., 2008; Zhang, 2015). Definitely, determining how many parcels can be transported through the HSReD service on the HSR network is necessary. However, no previous studies of this essential topic have been conducted. The main reason is that countries, except for China, have had a HSR network with sufficient scale for sharing a part of passenger transportation capacity as cargo transportation capacity. For this reason, the passenger demand cannot be within the scope of this paper. And the current study proposes an evaluation method for evaluating the adaptability of the transportation capacity of the HSReD on current and future HSR networks. The adaptability of HSReD transportation capacity is equivalent to the supply-demand relationship of HSReD in this paper. Therefore, the adaptability of HSReD transportation capacity is defined as the degree of mutual coordination and promotion between the supply of HSReD transport capacity provided by HSR trains under a certain LoS and the transport demand of HSReD parcels under certain economic and social conditions in a HSR network. What’s more, the capacity utilization ratio of HSReD is used to quantify the adaptability. Therefore, this study considers the LoSs and capacity occupancy of HSReD and proposes an improved ArcRoute mathematical model with K shortest paths. And the improved model is developed to calculate the distribution scheme of HSReD parcels, which is the main parameter of the capacity utilization ratio to evaluate the adaptability. The remaining parts of the paper are presented as follows. Section 2 presents a review of previous studies and analyzes the shortage of studies on this topic. Section 3 analyzes and defines the LoS of HSReD in practical operations and illustrates the relationships among LoSs, train schedule, and target market. Section 4 proposes a specific evaluation method and an improved ArcRoute mathematical model based on different LoSs and capacity occupancies. Section 5 presents the algorithm solution to solve the problem. Section 6 takes China’s HSR network as a practical case, calculates the utilization rate, and further analyzes the development prospects in the next five years. Section 7 provides some concluding remarks for policy formulation and future research directions. 2. Literature review For carrying out the transportation capacity evaluation of railway networks, we need to explore how much transport demand can be met by the network, which can also be called the maximum transport volume or transportation capacity. In the study of railway transportation capacity, many studies focused on the line capacity of the railway and defined the capacity of the HSR line as the maximum number of trains or passengers that can pass through or be carried on a HSR line during a unit of time (usually overnight) (Ortega Riejos et al., 2016). Correspondingly, methods for calculating the railway line transportation capacity are mainly divided into four types, namely, the methods specified in the International Union of Railways (UIC, 1983, 1996, 2004) codes 405 and 406, the analytical method (Hansen and Pachl, 2014), the optimization method (Delorme et al., 2004), and the simulation method (Kaas, 1998). However, railway freight transportation is a complete system with strong integrity and relevance, that is, the transportation capacity of the railway network is not equal to the total transportation capacities of all lines. In addition, according to the actual operation of railway freight transportation, the transportation capacity of HSReD on the HSR network belongs to the category of railway network capacity (Fu et al., 2015; Pazour et al., 2010; Cao et al., 2012; Lovett et al., 2013). Thus, it is of little significance to the overall HSR operation by taking the HSR line as a unit to study the transportation capacity of HSReD. What’s more, theories and methods for railway line capacity determinations are unsuitable for investigating the transportation capacity of the HSReD on the HSR network, which is mainly due to that no uniform model for determining the transportation capacity of the HSR network has been presented thus far. The railway network capacity refers to the number of trains or cars that can be carried by the entire railway network within a certain period of time (Abril et al., 2008; Harrod, 2009; Assadipour et al., 2015). According to this definition, a variety of models for accurately determining the railway network capacities are constructed. At the same time, the corresponding research methods are mainly divided into three types. The first type is the operation research (OR) method, for instance, the queuing theory, service level, K shortest paths, and capacity reliability were applied to calculate the transportation capacity of the railway network (Morlok and Riddle, 1999; Huisman et al., 2017; Park, 2005; Ortega Riejos et al., 2016; Canca et al., 2016). The second type is the estimation method. In this type of method, the railway network capacity is defined as having three combinations, namely, 166

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overall, effective and potential capacities. Moreover, this type of method is suitable for determining the capacity of a large-scale railway network (Harrod, 2009). The third type is the analytical method. This type of method focuses on the best use of railway systems, the maintenance and the technological adaptation of available resources (Abril et al., 2008). The evaluation and improvement methods for railway network capacity have been proposed, with the influencing factors as constraints (Kontaxi and Riccia, 2011, 2012; Harrod, 2009). The existing research on railway network capacities indicates that that the HSR network capacity is not a simple summation of all HSR stations and lines (Lindfeldt, 2010). The main factors influencing network capacity include the layout of the infrastructure, timetable, train speed, and external interferences. In addition, the concept and calculation methods of railway network capacity have been continuously developed and extended to the multimodal and express freight networks (Ceselli et al., 2008; Pazour et al., 2010; Armacost et al., 2002; Steadieseifi et al., 2014; Park and Regan, 2005). Thus, among the three methods mentioned above, the capacity calculation method of railway network is more inclined to the network flow model method, which is considered a representative optimization method in the field of transportation (Fernández et al., 2003; Nuzzolo et al., 2011; Ortega Riejos et al., 2016; Canca et al., 2016). At the same time, the network flow model methods for railway network capacity determination are mainly divided into Node-Arc and Arc-Route Models (Shafahi and Khani, 2010). In contrast to the Node-Arc model, the Arc-Route model does not consider the station operations, but can significantly reduce the scale of computation and is suitable for large-scale network optimization problems (Cepeda et al., 2006). This bibliographic review is concluded by indicating that, although numerous applications exist for analyzing HSR cargo transportation and railway network capacity, a few of these have focused on the capacity calculation of the HSReD, even its definition and LoSs. For this reason, more research must be conducted in this specific field owing to its high contribution to the use of the transportation resources of HSR. Moreover, given that express delivery on the railway network has high requirements on the LoS, such as the cost and delivery time, the computation of the transportation capacity of the express delivery service needs to consider the LoS factor. However, no existing research proposed related models or methods to determine the express delivery service on the railway network, let alone the HSReD on the HSR network. Therefore, the present research attempts to deal with these issues by proposing a definition of the capacity and LoSs of HSReD. An improved Arc-Route model (IARM) is constructed to calculate the transport volume of HSReD on each HSR line based on the basic Arc-Route model (BARM), which is commonly used in the literature to calculate the transportation capacity of the railway network. An effective solution procedure is also given. Then, the capacity utilization rate of each HSR line, which is used to evaluate the adaptability of the HSR network, is calculated. The results provide a reference for policy makers to formulate relevant policies for the future development of HSReD. 3. Concepts 3.1. Transportation capacity of HSReD Although the transportation capacity of the network is different from that of lines, the latter is not only an important parameter in the calculation process of the former, but also an important basis for evaluating the adaptability of transportation capacity of the network. Next, we draw lessons from different types of capacity measures of railway lines, and put forward the definition of the transportation capacity of HSReD. In practical operations, the capacity of the railway line on the network varies based on major influencing factors, namely, infrastructure conditions and operational organization levels, which enrich the connotation of the transportation capacity and derives many related concepts (Ortega Riejos et al., 2016). Theoretical capacity: This denotes the maximum number of trains that could be used by a railway line in ideal conditions during a given time period. Theoretical transportation capacity is only determined by the railway infrastructure. Practical capacity: This denotes the traffic flows that can be provided under normal operating conditions, that is, driving on the railway line with an acceptable level of reliability. Practical capacity reflects the effective number of actual delivery tasks and typically corresponds to between 60% and 75% of the theoretical capacity as it depends on the priorities established among different kinds of trains and on the traffic clustering. The transportation capacity of HSR lines mentioned below mainly refers to the practical capacity, which can be obtained from the train timetable during the peak period, such as the Spring Festival. Potential capacity: This refers to the transportation capacity that has the use conditions but has not yet been used. Potential capacity is due to the fact that the structure of traffic flow is unformed, the associated lines are incomplete, and the transport organization method is limited. Available capacity: This refers to the maximum transportation capacity that can be obtained by strengthening the traffic transport organization and line construction in practical operations and is generally the sum of practical and potential capacities. This means that, based on practical capacity, a series of measures is adopted to maximize the utilization of potential capacity. Unavailable capacity: This denotes the part of the capacity that cannot be used due to the overhaul of fixed equipment, maintenance sky-light, complex external environment, climate change and human error. As we known, the transportation capacity of HSReD in HSR network is the spare practical capacity of HSR network after satisfying the passenger demand. So the transportation capacity of HSReD is equal to the remaining passenger capacity of HSR network. Meanwhile, HSReD parcels are transported by the passenger transport equipment. Therefore, the practical capacity of HSR network is divided into two parts: the passenger and freight practical capacities, not only the former. In this paper, the freight practical capacity is regarded as the transportation capacity of HSReD. So we propose the definition of the transportation capacity of the HSReD on the HSR network, which refers to the maximum number of express parcels that can be carried per unit time on the HSR network under the 167

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Transportation capacity Invalid capacity

Unavailable

Potential capactiy

Available

Transportation capacity of HSReD Transportation capacity of passengers

Theoretical capacity Practical capacity

Fig. 1. Types of capacity measures of HSR network.

existing hardware and software circumstances, including current equipment, manpower, LoS requirements and railway traffic organization conditions. And it can also be understood as the remaining capacity of the overall practical capacity of HSR network after deducting the passenger practical capacity. The different types of capacity measures are illustrated in Fig. 1. 3.2. Definition of LoS of HSReD on the HSR network In addition to the circumstances of stations and lines and the transport path, the calculation of the transportation capacity of the HSReD on the HSR network should consider the different LoS requirements (Yum et al., 2015). More broadly conceived, the LoS of general cargo transportation is indeed affected by many factors, such as fleet size, transportation timeliness, timetable, cargo integrity, train load, informatization level and so on. However, in a narrow sense, the delivery time and cost are the most important concerns for shippers, while the modes of transport and transport conditions are less considered. So the LoSs can be divided into terms of the delivery time. The LoS of HSReD studied in this paper belongs to the latter. Generally speaking, goods can be classified as the time-sensitive and cost-sensitive types (Plotkin, 1997; Ceselli et al., 2008; Steadieseifi et al., 2014). As express parcels are mainly high value-added items, their time value is greater than their cost value. HSReD is one of the ordinary express transports, but the means of transport are different, that is, HSReD parcels also have the same transportation demands with ordinary express cargo, such as timeliness, cost and safety. Therefore, this paper divides different LoSs of HSReD according to the arrival time, which is also suitable for evaluating the performance of transporting the express parcel on the HSR network. From a practical business perspective, we summarize the practical LoSs of the express delivery services of UPS, S.F. Express and EMS in 2016, as shown in Table 1. As presented in Table 1, we classified the LoS requirements of HSReD based on “delivery time-sensitivity” into four types: “Arrived today”, “Arrived next morning”, “Arrived next day” and “Arrived the day after tomorrow” according to the business situation of current express delivery companies (Armstrong & Associates, Inc., 2016). (1) “Arrived today” includes two seed products, namely, “18:00 today” and “22:00 today.” The service radius of “18:00 today” is 500 km and is promised to be delivered before 18:00 on the same day. The product is mainly for customers such as enterprises and official departments and is required to be delivered before work. The service radius of “22:00 today” is 1000 km and is Table 1 Practical LoSs and related indexes of S.F. Express, EMS and UPS in 2016. Indexes Company

Service levels

Delivery time

Charges

S.F. Express

Arrived Today Arrived Next Morning Standard Express Special Express

Before 22:00 today Before 10:30 next day 1–2 days after receipt 2–3 days after receipt

140 yuan** 25 yuan*, 14 yuan/kg*** 23 yuan*, 14 yuan/kg*** 18 yuan*, 4 yuan/kg***

EMS

Arrived Next Morning Fastest Express Economic Express

Before 10:30 next day 2–3 days after receipt 3–6 days after receipt

20 yuan**, 12 yuan/kg*** 20 yuan**, 18 yuan/kg*** 8 yuan*, 4 yuan/kg***

UPS

Global Express Global Fastest Express Global Fast Express

Before 10:30 next day 1–3 days after receipt 3–5 days after receipt

Related to geographical conditions 22 yuan*, 14 yuan/kg*** Related to geographical conditions

Notes: *, **, *** represent the price of first weight 1000 g, first weight 500 g and continued weight. 168

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Table 2 Related indexes of four LoSs of HSReD in practical. Service levels

Cut-off time

Delivery time

Priority

Service radius

First weight price

Arrived today Arrived next morning Arrived next day Arrived the day after tomorrow

9:30–12:00 15:00–18:00 18:00 18:00

22:00 today 10:00 a.m. of the next day 18:00 next day 18:00 other day

Focus Secondary focus General Ordinary

1000 km 1600 km 2400 km > 2400 km

120–150 yuan 10–22 yuan 10–18 yuan 8–15 yuan

Maintenance sky-light

0:00

2:00

4:00

Arrived the day after tomorrow Arrived next day Arrived next morning Arrived today

Arrived next morning

6:00

8:00

10:00 12:00 14:00 16:00 18:00 20:00 22:00 24:00

Fig. 2. Time intervals of four LoSs and maintenance sky-light within a day.

promised to be delivered before 22:00 on the same day. The product is mainly for individual customers and is required to be delivered before their break. (2) “Arrived next morning” includes “8:00 a.m. of the next morning” and “10:00 a.m. of the next morning.” The service radius of the former is 1350 km and is promised to be delivered before 8:00 a.m. of the next day. The product is mainly for customers of enterprises and government agencies and is required to be delivered before work. The service radius of the latter is 1600 km. (3) The service radius of “Arrived next day” is 2400 km and is promised to be delivered before 18:00 of the next day. (4) The service radius of “Arrived day after tomorrow” is greater than 2400 km and is promised to be delivered before 18:00 of the third day. The service time intervals of the four service levels based on the Table 2 are shown in Fig. 2. In Fig. 2, the time intervals of the latter two service levels are similar. Thus, to simplify the issue, we reclassify these four levels into three levels (“Arrived today”, “Arrived next morning” and “Arrived next day”). 3.3. Relationship between LoS and HSR train operational plan As mentioned above, the transport carrier of HSReD is HSR trains, which operates in strict accordance with train schedules. Meanwhile, the transport demand of HSReD with different LoSs is satisfied by the remaining passenger transportation capacity. Hence, it is affirmative that the LoS is closely related to the operational plan of HSR trains. Taking the example of a HSR section consisting of four high-speed stations (A, B, C, and D) shown in Fig. 3, we describe the relationship between the LoS of HSReD and the train operational plan. In Fig. 3, we suppose there are nine HSR trains in the operational plan, on the basis of which, the corresponding high-speed train diagram can be set, as shown in Fig. 4. The colored lines in the figure indicate different types of high-speed trains. The red line indicates the non-stop direct train, and the blue line indicates the stopped direct train. Moreover, the yellow and green lines indicate the short-distance high-speed trains. The time intervals on the horizontal ordinate corresponding to three types of LoS are also shown. For express parcels sent by A to D, if the departure and arrival times of the train are within the time interval of a certain LoS, then the train can meet the LoS requirements of the HSReD service. For example, the arrival time of Train 4 is within the time interval of “Arrived today,” but the departure time is earlier than 10:00 a.m., which is not within this time interval. As a result, Train 4 cannot meet the LoS requirement of “Arrived today” between A and D. According to the relationship between the LoS and the train operational plan, express parcels with the “Arrived today” LoS requirement from A to D can be carried by Trains 3, 6 and 8 or by a combination of Trains 5 and 7. Similarly, express parcels with the “Arrived next morning” LoS requirement can be transported by Trains 2 and 9 and express parcels with “Arrived next day” LoS requirement can be transported by all trains. Consequently, if no train meets the “Arrived today” requirement to carry express parcels from A to D, then these parcels could not be delivered between these sections. In this case, trains from A to D can only deliver express parcels with the two other types of LoS requirements. 3.4. Target market of HSReD Although the previous section elaborated on the concept of capacity and LoS of HSReD, HSReD is an emerging transport product with the ultimate goal of serving the express demand in the transport market. Moreover, the key to satisfying the demand is to determine a reasonable target market, which will play an essential role in the development of HSReD. Therefore, we need to subdivide the transportation market according to the transportation distance and determine the target market for HSReD. 169

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Fig. 3. An example of HSR train operational plan among stations A, B, C and D.

Fig. 4. An example of HSR train diagram among stations A, B, C and D based on the operational plan.

According to the analysis of Armstrong & Associates, Inc. in 2016, the express transportation market can be divided into four categories according to service scopes: the short-distance market (0–500 km), the medium-distance market (500–1000 km), the medium/long-distance market (1000–2400 km), and the long-distance market (2400 km or more). As specified in the definition proposed by the UIC (1989), the average travel speed of the HSR train is approximately 250 km/h. Thus, the travel time for the shortdistance market is only 1–2 h and the service time for both ends of the short and medium/long-distance markets would not exceed 5 h. As a result, the total transit time for the short-distance market is expected to be within 10 h. Therefore, the “Arrived today” and “Arrived next morning” service products of HSReD should be given priority in the short-distance market. Similarly, for medium/longdistance transportation, the total transit time would be within 24 h and the “Arrived next day” service products should be given priority. According to the discussion of the four categories of the express transportation market, the appropriate target markets for different LoSs of HSReD can be determined. The target markets with various distances corresponding to different types of LoSs are presented in Fig. 5. 4. Mathematical model 4.1. Prerequisites The adaptability of transportation capacity to a practical HSR network has been the subject of tactical research that aims to determine the potential of this emerging freight delivery service. Specifically, in determining the adaptability, the OD demand of 170

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Fig. 5. Relationship between four LoSs and target transportation markets (by distance).

goods is initially assigned to the railway network to obtain the transport volume of goods on each railway line. During this process, a distribution method, that is, the Arc-Route model, is used and the distribution scheme can be got based on the minimum transport cost. According to the results of traffic assignment, we analyze the capacity utilization of each railway line. Finally, we conduct a reasonable evaluation of the adaptability of the entire railway network on the basis of the average and maximum utilization ratios of all rail lines. Specifically, the greater (or smaller) the utilization ratio of the capacity is, the worse (or better) the adaptability of the railway network. Notably, the maximum transport volume of the railway network, which is approximately equal to the freight transportation capacity, can be determined by increasing the quantity of goods reasonably until there is no solution for the mathematical model. The most important feature of the Arc-Route model is applying the K shortest path method to determine the alternative route for cargo delivery on the railway network. Specifically, the route search algorithm is applied to identify the K shortest paths of OD pairs among all nodes on the physical railway network, which will be described in Section 5.1. Then, after data preprocessing, the results are applied as the data source inputted into the Arc-Route model and solved. Here, we present the definition of cargo flow demoted by m, which refers to a group of goods that have the same origin and final arrival stations. This is done to illustrate the advantage of K shortest paths. Taking the simple railway network with 11 nodes in Fig. 6 as an example, the numbers (7,100) represent the mileage and the practical freight transportation capacity of the rail line, respectively. In order to simplify things, we calculate the K shortest paths and distances of three cargo flows, including a to d, b to e, and c to f, as shown in Table 3. When the three cargo flows take the first transport path, that is, the shortest path, all of them will pass through the line (i, j). The transport volume of goods on the line (i, j) reaches 150 pieces that is more than 100 pieces, which is the limitation of the transportation capacity. Therefore, such a traffic assignment scheme is unreasonable and infeasible because the total transport demand cannot be met. In addition, the traffic volumes allocated on paths (i, k, j) and (i, m, n, j), the parallel paths of (i, j), are equal to 0, indicating that the transportation resources do not play a full role. In the face of the imbalance of transportation resource utilization in the network, the best choice is to transfer one or more cargo flows to its second or third shortest path based on the minimum transportation cost or time. In this manner, the transportation pressure of lines is alleviated, and the transportation resources of parallel paths are fully utilized. Assuming that the cargo flow of c to f is transported by the second shortest path, c → i → k → j → f, the transport volume of (i, j) decreases to 100 pieces and those of (i, k) and (k, j) increase to 50 pieces. The transport volume of every line in the network is lower than its capacity limit, which indicates that this traffic assignment scheme is feasible. Based on the previously presented analysis, the K shortest paths perfectly overcome the drawback that cargo flows are concentrated on some lines that their capacity is insufficient and the traffic assignment scheme is infeasible. At the same time, the ArcRoute model simplifies the operation of the intermediate nodes and reduces the calculation scale on the basis of ensuring reliable and effective results.

Fig. 6. An example of a small network consisting of 11 stations and 12 lines marked with mileage (unit: km) and practical freight transportation capacity (unit: pieces).

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Table 3 The shortest paths and corresponding transport distances of three cargo flows in the example network. Origins

Arrivals

Traffic (pieces)

K shortest paths

Transport distances (km)

a

d

50

a→i→j→d a→i→k→j→d a→i→m→n→j→d

9 11 12

b

e

50

b→i→j→e b→i→k→j→e b→i→m→n→j→e

10 12 13

c

f

50

c→i→j→f c→i→k→j→f c→i→m→n→j→f

11 13 14

4.2. Assumptions and the Basic Arc-Route model Specifically, the two decision variables are set up to provide convenience for obtaining the distribution scheme of cargo flows. The first decision variable determines which shortest path in the set of K shortest paths should be selected to transport the corresponding cargo flow. The second decision variable counts the total transport volume of goods assigned to each rail line. In this manner, the distribution scheme of cargo flows is obtained, and the future adaptability of the transportation capacity is determined. Without the loss of generality, this study further makes the following assumptions: (1) In the entire decision-making process, the railway network remains constant. (2) During the decision period, the OD freight volume, the train operational plan, and the unit transportation cost of goods are known. (3) For any cargo flow, the transport path is the only one in the network. In other words, the goods in each cargo flow are bound together and will not be apart. The parameter and decision variable definitions of the basic model are as follows: The OD set of cargo flows, m

M

M

The set of railway lines, i L The set of K shortest paths of flow m, p The line set of path p selected by flow m

L m Lpm

m

The volume of cargo flow m The practical transportation capacity of the rail line i The transport cost of rail line i If the path p is selected by flow m, then the value is 1; otherwise, the value is 0

Nm Ci wi

m p aim ,p

The transport volume of cargo flow m of the line i on path p; when

m p

m = 1, aim , p = Nm , otherwise ai, p = 0

In fact, as a profitable company, railway operators prefer to economically and effectively utilize the transportation resources of the railway network and reduce the overall transport cost to a minimum. Thus, the object function of the model expressed in Formula (1) is to minimize the total cost of transporting all cargoes on the network.

Minimum m M p

m m i Lp

wi aim ,p

(1)

If path p in m of cargo flow m is selected to deliver goods ( pm = 1), then the transport volumes of all rail lines on path p will increase Nm . If pm = 0 , then the transport volumes of all rail lines on path p are equal to 0. Here, constraint set (2) calculates the transport volume of every rail line i in the network:

aim ,p =

m p Nm ,

m

M, p

m,

i

Lpm

(2)

Constraint set (3) ensures that the total transport volume of goods is less than the transportation capacity of line i:

aim ,p m M p

Ci ,

i

Lpm

(3)

m

According to the assumption (3), constraint set (4) guarantees that only one path p can be selected by flow m: m p p

= 1,

m

M

(4)

m

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Constraint set (5) ensures that the decision variable is nonnegative:

aim. p

0,

i

Lpm , m

M, p

(5)

m

Constraint set (6) ensures that the decision variable is boolean: m p

{0, 1},

m

M, p

(6)

m

4.3. Improved Arc-Route model HSReD is a special product of railway freight transportation. The basic attributes of HSReD parcels are the same as those of ordinary goods, but the difference is that the former require higher transportation timeliness, lower transportation cost, and different LoSs (Pazour et al., 2010). Therefore, drawing on the existing research results, analyzing the adaptability of the transportation capacity of HSReD by Arc-Route model is feasible. Here, the definition of HSReD flow (represented by m) is updated to a group of express parcels that have the same origin and final arrival stations under the same LoS. However, if the BARM is introduced to analyze the distribution scheme of HSReD flows in this paper, then two shortcomings should be solved. The first one is the failure to consider the diversification of transportation demand. HSReD has different LoSs, which is unavailable in the BARM. In response to this problem, a set of LoSs denoted by T is applied, with T = {“Arrived today”, “Arrived next morning”, “Arrived next day”}, t T . Correspondingly, an index dimension t is added to the set and parameters. For example, tm represents the set of K m m m m m, t shortest paths of HSReD flow m under LoS t, p t . The same is true for Lp, t , Nt , p, t and ai, p . When the LoSs are considered, the number of HSReD flows in the set increases. In addition, according to the discussion in Section 3.3, HSReD flows that do not meet the LoS requirements will be eliminated from the flow set. As such, the feasible set of HSReD flows represented by M could be obtained. The second shortcoming is denoted by the fact that that HSR trains with different speeds have different occupancy rates in terms of the transportation capacity of HSReD. Thus, HSReD parcels transported by HSR trains with different speeds are expected to have different occupancy rates—a condition that is ignored in the BARM. Here, we take 2 fast trains and 10 slow trains as an example. As illustrated in Figs. 7 and 8, the thick line refers to the fast train, the solid line represents the slow train, and the dashed line indicates the slow train that needs to be deducted because of the conflict with the fast train. In the operation diagram, the time interval of adjacent departure trains represented by t1 refers to the minimum time interval required for two trains running continuously because of the limitation of the infrastructure. The time interval between arriving and passing trains (or between passing and arriving trains) represented by t3 (or t4) refers to the minimum time interval from a train passing through (or arriving at) the station to the next train arriving at (or passing through) the station.

Fig. 7. The HSR train diagram with 2 fast trains and 7 slow trains in the fixed line section and time period (no overtaking).

Fig. 8. The HSR train diagram with 2 fast trains and 7 slow trains in the fixed line section and time period (overtaking). 173

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In the time period shown in the operation diagram, if only running slow trains, then the maximum transport volume of this railway section will be equal to 10 slow trains. When running two fast trains, two different situations for the operation diagram, namely, overtaking or not can be observed. Fig. 7 shows that, with fast trains running, two slow trains will be in conflict with them. In addition, although the fifth slow train is not in conflict with the first fast train, t2 is less than t3, which means that the minimum time interval is unsatisfied. Thus, the fifth slow train must also stop. Meanwhile, Fig. 8 shows that the fifth slow train stops at station d, where it is overtaken by the fast train. The departure time of the second fast train is delayed and the seventh slow train stops at station b to avoid the conflict with the second fast train. Moreover, the ninth slow train must stop because it comes in conflict with the seventh slow train (the time interval t5 is less than t1). By contrast, if the departure time of the seventh slow train does not change, then that train will be deducted (the time interval t6 is less than t1). Finally, we can determine the relationship of capacity occupancy between fast and slow trains in the case of the time interval of t1, that is, the capacity occupancy of two fast trains is more than equal to that of three slow trains based on the hypothesis. The previously presented analysis expounds on the relationship between fast and slow trains. Based on the relationship, uniform conversion into a standard train is necessary to make the calculation easy and reliable. In this study, the conversion coefficient mt of HSR trains is proposed. Here, we assumed that the HSR train with a lower speed is the standard train. From the analysis of the train operational plan (or operation diagram), the conversion factor mt can be determined by Formula (7). t m· nlow )

Cap (1·nfast ) = Cap (

(7)

where Cap (·) refers to the capacity occupancy function. In addition, the growth rate coefficient µtm of HSReD parcels is introduced into the model in order to obtain the maximum transport volume of HSReD parcels. In this manner, Ntm is replaced with Ntm·(1 + µtm ) in the IARM. In the IARM, the parameter cmt is set to represent the occupancy value of m on the line capacity under the LoS t. Thus, the constraint set (2) in the BARM is respectively replaced with Formulas (8) and (9). m t p, t cm,

,t aim ,p =

cmt

=

Ntm (1

m µtm ) mt,

+

m t ,

i

Lpm, t

M,p

m t ,

M,p m

(8)

i

Lpm, t

(9)

4.4. Mathematical formulation for determining the transportation capacity and adaptability of HSReD on the HSR network In the IARM, on the basis of the assumptions of BARM, we provide another premise: only HSR trains with speeds of 250 and 350 km/h are considered, and the train with a speed of 250 km/h is regarded as the standard HSR train. Generally, the formulation of the IARM used to determine the distribution scheme of HSReD flows on the HSR network is summarized as follows:

Minimum m m t i Lp, t

m M t T p

m t p, t cm,

,t S.T. aim ,p =

cmt = Ntm (1 + µtm ) m t

m M t T p

m t

p

m p, t

aim. p, t , cmt m p, t

,t aim ,p

= 1, 0,

{0, 1},

m i m

m t m,

,t wi aim ,p

m t ,

M,p m

Ci ,

M,t

(10)

m t ,

M,p

Lpm, t

i i

(11)

Lpm, t

(12)

Lpm, t

i

(13)

T

(14)

Lpm, t , m

M,p

M,p

m t ,

t

m t ,

t

(15)

T

(16)

T

where the object function of IARM is the same as that of BARM in order to minimize the total transport cost of HSReD parcels. Specifically, constraint set (11) calculates the transport volume of the HSR line i on path p selected by flow m under the LoS t, which is different from that expressed in Eq. (2). In constraint set (12), the capacity occupancy of m under LoS t is calculated. For HSReD flow m under LoS t, the capacity occupancy of the line cmt is equivalent to the product of the volume, the conversion coefficient, and the growth rate, rather than simply its own volume. Constraint set (13) ensures that the total transport volume of HSReD parcels must be less than the transportation capacity of line i. Constraint set (14) guarantees that only one route p can be selected. Constraint sets (15) and (16) play the same role as Eqs. (5) and (6), respectively. 5. Solution of the problem The IARM is a 0–1 mixed-integer linear programming model that is efficient for use in any size HSR network. Concretely, the traffic assignment of HSReD flows is a combinatorial optimization problem. Given that the problem includes trains and feasible flows, the scale of the problem is related to the number of HSReD flows (denoted by f ), the number of rail lines (denoted by n ), the types of 174

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LoS (denoted by l ), and the maximum value of k. Thus, the problem has in general (flk ) binary variables, (fnlk ) integer variables and (2fnk + n + fl) constraints. With respect to the algorithm, commercial optimization software, such as Lingo and CPLEX, has advantages in solving the problem of a certain scale. However, in solving large-scale practical cases, a heuristic algorithm is more appropriate under a more acceptable range of accuracy. In contrast to the conventional mathematical optimization model, the IARM proposed in this study is based on K shortest paths. The entire solution is divided into two aspects, namely, searching K shortest paths and solving the model. The first aspect uses the path search algorithm to search the K shortest paths of each feasible HSReD flow on the HSR network and stores them in tm . The data applied in the second aspect are the preprocessed K shortest paths, rather than the basic network data; this step considerably reduces the scale and difficulty of model solving. Therefore, commercial optimization software is sufficient to solve the model in this study. Based on previous research experience, the ILOG CPLEX software has a significant advantage in solving linear problems and has been widely used in solving different kinds of transportation problems (Shafahi and Khani, 2010). Specifically, the embedded algorithm set can be configured according to the needs of the solution, that is, single optimization program, limit optimization program, and mixed-integer optimization program (2009 User Manual for CPLEX 12.1). Therefore, among the existing general optimization software, ILOG CPLEX becomes the first choice to effectively solve this scale optimization problem. Finally, based on the distribution scheme obtained by IARM, the total transport volume of each HSR line can be determined. Thus, the utilization ratio of the transportation capacity of HSReD, which is used to evaluate the adaptability of the HSR network and identify the bottlenecks, could be obtained. 5.1. Overall solution algorithm According to the contents described previously, the overall solution algorithm to solve the problem is divided into five steps: Step 1: The transportation capacity of the HSReD of each HSR line on the network is calculated. The calculation method will be described in detail in Section 5.2. Step 2: The feasible set of HSReD flows is obtained. According to the relationship between LoS and HSR train operational plan described in Section 3.3, we can obtain the feasible set of HSReD flows represented by M . Step 3: The K shortest path sets of all HSReD flows on the HSR network are determined. Step 4: All feasible HSReD flows in M are assigned to each rail line based on the IARM. According to the previously presented parameters, the corresponding path k in the K shortest paths is selected for each HSReD flow. Ultimately, all HSReD flows under different LoSs can be assigned to each rail line on the HSR network. The distribution scheme of HSReD parcels could be obtained. Step 5: The utilization rate of each HSR line is calculated, and the bottlenecks on the network are identified. Visual Studio 2012 software (C# in short) is used to write the overall solution algorithm in this study in order to facilitate data input and output. Here, the overall algorithm is designed as described below. Algorithm. 1. Input “the set of HSReD flows:” M, m M Input “the set of LoSs of HSReD:” T, t T 2. Calculate the transportation capacity of the HSReD on each HSR line i Input “the number of HSR lines on the network:” n Input “the maximum number of HSR trains on line i:” hi Input “transport volume of HSR trains and the checking train:” Wunit and W0; For i = 1 to n Ci = hi × Wunit + W0 ; Endfor; 3. Get the feasible set of HSReD flows (or M ) Input “the proportions of different LoSs in M:” t ; Input “the time interval of HSR trains on line i:” [ , ]hi ;

Input “the time interval of LoS t:” [ t,

Set M = ; Foreach m in M , t in T For l = 1 to hi [ t, t ] then If [ , ]l

t ];

Ntm = Nm × t ; break;

Else Ntm = 0 ; Endfor; M =M {Ntm} ; Endfor; 4. Determine the K shortest paths Input K; Foreach m in M , t in T Set m t = ;

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Lpm, t = Lpm,t

path p} ;

{i i

Endfor; Endfor; 5. Assign feasible HSReD flows on the HSR network (or solve the IARM) Calling the core of CPLEX algorithm solver by C# code; Input Ci , M ,

m t ,

and Lpm, t where m

M,t

t m,

T, p

i

Lpm, t ;

Input “the conversion coefficient of the HSReD flow m under LoS t:”

t m;

Input “the growth rate coefficient of the HSReD flow m under LoS t:” µtm ; ,t Output the optimal solution of aim , p and

m p, t ;

6. Calculate the utilization of each HSR line i ,t Input aim , p and Ci where m

M,t

T, p

t m,

i

Lpm, t ;

For i = 1 to n Set i = 0, i =0;

Foreach m in M , t in T, p in i

=

i

,t + aim ,p ;

Endfor; i = i Ci ; Endfor; 7. Output the utilization rate

i

t m;

of each line and bottlenecks on the network.

Next, the transportation capacity of HSR lines, K shortest paths, and adaptability calculation are introduced in detail, including the key parameters and main calculation process. 5.2. Transportation capacity of HSR lines The transportation capacity of the HSReD on line Ci is not only applied to model computation (Step 5 of the overall algorithm) but is also an important parameter in adaptive computation (Step 6). In determining the capacity of the HSReD, the calculation process includes two steps, as discussed below: The first step is calculating the transport volume of the HSR train (Wunit ) by Eq. (17):

Wunit =

(17)

× wcar

where refers to the average number of cars that comprise a HSR train, and wcar is the number of HSReD parcels that a car can load. In general, the number of cars that constitute a HSR train is different. In China, HSR trains have the 8-car and 16-car versions. The 8-car version train is called the standard EMU train, that is, denoted by = 8. Therefore, the number of HSReD parcels loaded on HSR trains with different cars is also different. Here, we can calculate using Eq. (18). (18)

= (1 + Slong Sshort )

where Slong and Sshort refer to the total numbers of HSR trains with 16 and 8 cars, respectively. In the second part, according to the daily train schedule, hi can be obtained. Thus, we can obtain the transportation capacity of HSR lines using Eq. (19).

Ci = W0 + Wunit × hi , i

(19)

L

where W0 refers to the transport volume of the checking train, which is the first HSR train running daily, in order to check whether hidden dangers exist in the track and decide not to transport passengers. 5.3. K shortest paths In the fourth step of the overall algorithm, obtaining the K shortest paths of each HSReD flow is the prerequisite for the fifth step to solve the IARM. The existing methods include double-sweep algorithm, A* algorithm, and deviation path algorithm (Brander, 1995; Hershberger et al., 2007). The double-sweep algorithm has advantages in solving path mileage; however, obtaining path data requires reverse search, which is complex and difficult to understand (Rink et al., 2000). In addition, compared with the A* algorithm, the deviation path algorithm is easier to operate and has a higher solution efficiency (Chabini and Lan, 2002; Feng et al., 2011). Therefore, the deviation path algorithm is used to solve the K shortest path in this study. The core idea is to use the standard shortest path algorithm (such as Dijkstra’s algorithm) to determine the shortest path p1 from s to t and place it in the result list A. Then path pk+1 can be generated based on the already obtained path pk (k ≥ 1). Specifically, the goal of the deviation path algorithm is to construct the K shortest path tree. The path of each tree from the root node s to the leaf node

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Fig. 9. An example of K shortest paths tree from node 1 to node 5.

t is one path of K shortest paths. Assuming that the first three paths p1, p2, and p3 (pk represents the kth short path) from s = 1 to t = 5 in graph G are p1 = {1,2,5}, p2 = {1,3,4,5}, and p3 = {1,2,4,5}. The K shortest path trees corresponding to the three paths are shown in Fig. 9. Ultimately, the result list A is the set of the preferred K shortest paths (Paixão and Santos, 2008; Feng et al., 2011). 5.4. Adaptability of HSReD As stated above, the utilization ratio of the transportation capacity of HSReD is used to evaluate the adaptability of the HSR network in this paper. Next, based on the result of model, the specific steps to evaluate the adaptability of HSReD are given as following. ,t From the analysis of aim , p , we can obtain the transport volume of HSReD parcels on each HSR line (denoted as i ) using Eq. (20): i

= m t

m M t T p

,t aim ,p ,

i

L

(20)

Next, we analyze the utilization ratio of transportation capacity of HSReD (denoted as i

=

i

Ci

,

i

L

i ), as expressed in Eq. (21).

(21)

Generally, when the utilization ratio reaches 80% or more, the transportation capacity of the line appears to be tense, which means that the adaptability of the overall HSR network capacity is poor. Hence, this line is identified as the bottleneck of the entire network. 6. Empirical study: adaptability of the HSReD on the HSR network of China In 2017, HSR in China exceeded 25,000 km in total length, accounting for about two-thirds of the world’s HSR tracks in commercial service. This is the world’s longest HSR network and is also the most extensively used one, with 1.713 billion trips delivered in 2017, thereby bringing the total cumulative number of trips to 7 billion. 6.1. Network topology of China’s HSR The above analysis shows that the K shortest paths play a very important role in the whole algorithm process. In order to facilitate the construction of the K shortest path tree, the topology of China’s HSR network is drawn based on reality, as shown in Fig. 10. It should be noted that, on the one hand, some provinces of China, such as Inner Mongolia and the Ningxia and Xizang Provinces, do not have HSR lines. On the other hand, we would not consider operating the HSReD between mainland China and other regions like Hong Kong, Macao, and Taiwan. Provincial capitals are deemed as the occurrence sites of HSReD flows (as the black centroid points in Fig. 10). Furthermore, some important rail stations are the rail line bifurcation points, so these stations must be marked with the grey points on the topology as well. In addition, the mileage of HSR between adjacent sites is also illustrated on the topology. 6.2. Related parameter values (1) OD volume of HSReD with different LoSs According to the Statistical Office of the People’s Republic of China in 2016, 80%, 15%, and less than 5% of express parcels were transported by on-land vehicles, by air and by rail and other transport means, respectively. As a part of the whole express industry, HSReD service has the same basic nature with the whole express industry. Therefore, according to the total volume of express parcels of each province, we can confirm the total volume of HSReD parcels in different provinces, rather than the OD volume of HSReD flows among provinces. In this case, the gravity model is used to estimate the OD volume of HSReD among provinces, which entails analyzing the relationship between express parcel and four influencing factors: population, GDP, CPI and the added value of the tertiary industry, as shown in Fig. 11. The number of HSReD parcels is significantly related to population, GDP, and the added value of the tertiary industry. Therefore, the three main factors are substituted into the gravity model, proposed by Shao et al. in 2016.

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Harbin Changchun 298

Urumqi

Beijing 1,589

122 120 138

Baoding

Xi’ning

Taiyuan

Lanzhou

188

232

536

650 800

Xi’an

643

142

Province capital Bifurcation point Beijing Node name Existing railway and distance (unit: km)

Railway under con800 struction and distance (unit: km)

Chengdu

304

845

345 475

Kunming

710

Wuhan

815

Nanning

359

362

706

Hefei

574

157

530

740

Nanjing

295 181 161 256 202

Tongling

Hengyang

Bengbu

132 175

342

177 Nanchang 721

Tianjin

156

Zhengzhou

Changsha

Guiyang

284

362

523

Chongqing

Shenyang

661

Ji’nan Shijiazhuang 286 412 Xuzhou

536

Legend

475

240

547

582

Shanghai

Hangzhou

669 724

Fuzhou

Guangzhou

Fig. 10. The topology of the constructed HSR network of China as of 2016.

HSReD Population GDP CPI Added value of tertiary industry

Fig. 11. The proportions of HSReD and the four influencing factors in 2016 (unit: %).

According to the actual traffic volume statistics, the demands of three LoSs proposed in this paper account for approximately 10%, 30%, and 60% of each OD volume, respectively (ICANdata, 2017). Thus, the OD volume of HSReD flows Ntm can be obtained based on the data in Table 4 and the proportions of three LoSs. 178

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Table 4 Transport demand of HSReD parcels among 27 provinces of China in 2016 (unit: pieces/year). Provinces

Beijing

Tianjin

Hebei

Shanxi

Liaoning

Jilin

Heilongjiang

Shanghai

Jiangsu

Zhejiang

Anhui

Fujian

Jiangxi

Shandong

Beijing Tianjin Hebei Shanxi Liaoning Jilin Heilongjiang Shanghai Jiangsu Zhejiang Anhui Fujian Jiangxi Shandong Henan Hubei Hunan Guangdong Guangxi Chongqing Sichuan Guizhou Yunnan Shaanxi Gansu Qinghai Xinjiang

0 82335 40383 3028 11394 1361 2341 5656 1590 14214 1788 4592 1187 36895 10194 3287 1677 25334 650 291 3849 191 564 2869 400 38 901

321145 0 23654 1847 7951 932 1584 4278 6139 10529 846 3284 832 38664 6348 2085 1011 16241 418 455 2466 120 364 1819 260 23 577

245590 36882 0 44359 15601 2238 4225 18891 27446 46917 6247 14182 4203 197602 76645 13442 6816 90427 2266 2660 14595 679 19 14465 1641 148 2596

39913 6242 96159 0 5090 798 1580 6544 9913 17567 2311 6753 1736 33499 34222 6019 3117 42244 1063 1681 9328 394 1081 12529 1112 96 1631

27617 4941 6218 936 0 25329 19938 4517 5798 12867 1281 4714 1013 11473 4416 2266 1423 25168 662 656 3523 437 627 1847 333 34 1037

8188 1438 2214 364 62861 0 55087 2026 2489 5362 550 2292 469 4119 1817 1006 664 12490 334 322 1713 97 324 824 159 16 546

7087 1230 2103 363 24901 27722 0 2204 2658 5883 585 2640 524 3921 1872 1100 736 14636 395 372 1975 114 390 894 181 19 665

5579 1082 3064 490 1838 332 718 0 114456 872082 9808 28681 4675 10333 6159 6081 3895 56487 1137 783 3184 314 829 1995 291 28 707

4469 4423 12683 2113 6722 1163 2468 326085 0 1050617 210012 63124 20656 48624 36285 39081 14657 183936 3763 3193 11469 988 2701 8113 1151 100 2404

10583 2010 5744 992 3952 664 1447 658246 278344 0 26312 91458 19198 18201 13358 14641 9818 158074 3021 1778 6890 795 2086 4321 629 60 1527

15968 1937 9172 1565 4720 816 1725 88785 667303 315575 0 40273 21729 33480 28385 48136 14458 166848 3087 2829 8779 805 2109 6260 827 76 1680

2963 543 1504 330 1255 246 563 18759 14491 79249 2910 0 11253 3955 3527 7973 6223 223742 2119 1045 3752 504 1172 1790 292 29 818

5993 1077 3488 665 2109 394 873 23919 37099 130147 12282 88039 0 9024 8823 39601 31073 285472 4313 2248 6627 1103 2376 3899 517 49 1220

163783 44004 144239 11280 21012 3040 5750 46501 76808 108522 16644 27217 7937 0 75767 20123 9940 127360 3064 302 16746 1036 2844 14261 1528 145 3364

Provinces

Henan

Hubei

Hunan

Guangdong

Guangxi

Chongqing

Sichuan

Guizhou

Yunnan

Shaanxi

Gansu

Qinghai

Xinjiang

Beijing Tianjin Hebei Shanxi Liaoning Jilin Heilongjiang Shanghai Jiangsu Zhejiang Anhui Fujian Jiangxi Shandong Henan Hubei Hunan Guangdong Guangxi Chongqing Sichuan Guizhou Yunnan Shaanxi Gansu Qinghai Xinjiang

55027 8785 68027 14012 9833 1630 3338 33703 69694 96845 17158 29508 9435 92128 0 48062 18283 180670 4331 5228 28783 1489 3731 51686 2988 243 3696

12290 1998 8263 1707 3495 625 1358 23049 51990 73515 20153 46200 29332 16947 33288 0 64720 252552 5426 5016 14079 1378 3102 11328 1102 98 1944

8329 1288 5567 1174 2916 548 1208 19616 25909 65507 8043 47916 30582 11123 16826 85997 0 555084 12564 2943 10438 2094 1719 7068 878 81 1841

7233 1189 4245 915 2965 593 1380 16350 18687 60617 5335 99018 16148 8191 9556 19287 31903 0 30300 4062 14496 20762 8463 4926 820 81 2349

2360 389 1352 293 991 202 474 4185 4861 14729 1255 11924 3102 2506 2913 5269 9182 385279 0 4661 13285 4572 10647 534 328 37 925

963 381 1430 417 885 175 402 2595 3715 7806 1036 5294 1456 2285 3167 4386 1937 46514 4197 0 121502 7885 5693 5392 732 769 1082

6492 1066 4048 1193 2451 480 1100 5445 6883 15608 1658 9810 2214 6362 8994 6352 3544 85634 6172 62682 0 5662 16911 16026 2806 324 3446

1805 290 1052 282 1700 152 357 2997 3317 10066 850 7361 2061 2202 2601 3476 3975 685796 11876 22745 31662 0 17365 518 431 48 917

1539 254 9 224 706 147 351 2293 2622 7644 645 4958 1284 1748 1886 2264 944 80883 8002 4752 27358 5024 0 479 474 54 1109

9067 1474 7517 3004 2408 433 933 6393 9124 18345 2216 8767 2441 10154 30264 9577 4497 54531 465 5213 30031 173 554 0 3798 240 2134

2699 449 1820 569 927 178 402 1990 2763 5699 625 3056 691 2321 3733 1988 1192 19372 610 1511 11220 308 1171 8103 0 2486 2434

500 77 320 96 185 36 82 371 467 1064 112 588 127 429 590 343 215 3742 136 3092 2525 67 262 998 4845 0 678

607 100 323 83 288 61 148 483 576 1381 127 854 163 510 461 350 250 5540 171 223 1376 65 274 455 243 35 0

(2) The transportation capacity of HSR lines Ci According to the HSR train operating plan from the China Railway Corporation, there are about 1800 HSR trains with 8 cars and 360 trains with 16 cars running every day. Thus, 1 + Slong Sshort = 1.2 . In addition, hi can be obtained as well. Taking the 8-car version of trains as the standard ( = 8), and the load of each car is 20 pieces (wcar = 20 ). In addition, W0 = 16, 000 . Based on the calculation method in Section 5.2, the results are shown in Table 5.

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Table 5 The maximum running number of HSR trains and transportation capacity of HSReD on all HSR lines in China (2016). Rail lines

hi

Ci (pieces)

Rail lines

hi

Ci (pieces)

Heilongjiang-Jilin Jilin-Liaoning Liaoning-Tianjin Tianjin-Beijing Tianjin-Baoding Tianjin-Shandong Beijing-Baoding Baoding-Hebei Hebei-Shanxi Hebei-Henan Shanxi-Shaanxi Shaanxi-Gansu Shaanxi-Sichuan Gansu-Chongqing Gansu-Qinghai Qinghai-Xinjiang Sichuan-Chongqing Chongqing-Guizhou Shandong-Xuzhou Shaanxi-Henan Henan-Xuzhou Xuzhou-Bengbu Bengbu-Anhui Bengbu-Jiangsu

80 138 60 278 42 118 96 136 52 136 38 74 72 0 40 10 98 88 186 108 106 102 46 80

31360 42496 27520 69376 24064 38656 34432 42112 25984 42112 23296 30208 29824 16000 23680 17920 34816 32896 51712 36736 36352 35584 24832 31360

Henan-Hubei Chongqing-Hubei Hubei-Anhui Anhui-Jiangsu Jiangsu-Shanghai Jiangsu-Zhejiang Shanghai-Zhejiang Jiangsu-Tongling Anhui-Tongling Tongling-Fujian Hubei-Hunan Zhejiang-Jiangxi Jiangxi-Hunan Hunan-Guizhou Guizhou-Yunnan Zhejiang-Fujian Jiangxi-Fujian Hunan-Hengyang Fujian-Guangdong Guangdong-Hengyang Guangdong-Guizhou Guangdong-Guangxi Hengyang-Guangxi Guangxi-Yunnan

154 64 102 158 420 200 260 32 60 18 188 202 122 90 70 86 36 160 46 140 48 110 22 40

45568 28288 35584 46336 96640 54400 65920 22144 27520 19456 52096 54784 39424 33280 29440 32512 22912 46720 24832 42880 25216 37120 20224 23680

Table 6 The unit prices of different grades of seats at different speed levels. Speed (km/h)

Seat class

Unit price (yuan/km per capita)

250

First-class Second-class First-class Second-class

0.37 0.3 0.74 0.46

350

(3) The transport cost wi With the aim of effectively utilizing the remaining passenger transportation capacity for express delivery services, HSReD parcels are assumed to be the same as passengers. According to Fares Management Department of China Railway General Corporation, the unit prices of different grades of seats are shown in Table 6. Considering the average weight of parcels (3 kg) is different from that of passengers and luggage (100 kg), the cost should be reduced proportionally (3:100). In accordance with the relevant provisions of the state, 500 km for the full fare, 500 to 1000 km, the fare should be 10% off, and for a distance exceeding 1000 km, the fare should be 20% off. The transport cost of each rail line can be obtained, as shown in the Table 7.

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Table 7 The mileage, speed limit and transport cost of HSReD of all HSR lines in China (2016). Rail lines

Distance/km

Speed/(km/h)

Cost/yuan

Rail lines

Distance/km

Speed/(km/h)

Cost/yuan

Heilongjiang-Jilin Jilin-Liaoning Liaoning-Tianjin Tianjin-Beijing Tianjin-Baoding Tianjin-Shandong Beijing-Baoding Baoding-Hebei Hebei-Shanxi Hebei-Henan Shanxi-Shaanxi Shaanxi-Gansu Shaanxi-Sichuan Gansu-Chongqing Gansu-Qinghai Qinghai-Xinjiang Sichuan-Chongqing Chongqing-Guizhou Shandong-Xuzhou Shaanxi-Henan Henan-Xuzhou Xuzhou-Bengbu Bengbu-Anhui Bengbu-Jiangsu

240 298 661 120 138 284 122 142 232 412 536 650 643 800 188 1589 304 345 286 523 362 156 132 175

250 250 250 350 250 350 350 350 250 350 250 250 250 250 250 250 250 250 350 250 250 350 250 350

2.16 2.68 5.8 1.66 1.24 3.92 1.68 1.96 2.09 5.69 4.79 5.72 5.66 6.93 1.69 12.79 2.74 3.11 3.95 4.69 3.26 2.15 1.19 2.42

Henan-Hubei Chongqing-Hubei Hubei-Anhui Anhui-Jiangsu Jiangsu-Shanghai Jiangsu-Zhejiang Shanghai-Zhejiang Jiangsu-Tongling Anhui-Tongling Tongling-Fujian Hubei-Hunan Zhejiang-Jiangxi Jiangxi-Hunan Hunan-Guizhou Guizhou-Yunnan Zhejiang-Fujian Jiangxi-Fujian Hunan-Hengyang Fujian-Guangdong Guangdong-Hengyang Guangdong-Guizhou Guangdong-Guangxi Hengyang-Guangxi Guangxi-Yunnan

536 845 359 157 295 256 202 161 181 669 362 582 342 706 475 724 547 177 740 530 815 574 721 710

350 250 250 250 350 250 350 250 250 250 350 250 250 250 250 250 250 350 250 350 250 250 250 250

7.35 7.29 3.23 1.41 4.07 2.3 2.79 1.45 1.63 5.87 5 5.16 3.08 6.17 4.28 6.31 4.88 2.44 6.44 7.27 7.05 5.1 6.29 6.39

(4) Conversion coefficient

t m

Based on the research of the conversion coefficient of the Beijing-Shanghai HSR by Zhang (2015), the average conversion coefficient mt is determined to be 1.2. 6.3. Current transportation capacity adaptability The relevant parameters mentioned above are subdivided into the model and algorithm in order to obtain the allocation scheme of HSReD parcels and the utilization ratio of each HSR line on China’s HSR network. The results are shown in Table 8. Table 8 The total transport volume and the capacity utilization rate of HSReD parcels on all HSR lines of China in 2016 (obtained by IARM). Rail lines

Volume (pieces)

Utilization

Rail lines

Volume (pieces)

Utilization

Heilongjiang-Jilin Jilin-Liaoning Liaoning-Tianjin Tianjin-Beijing Tianjin-Baoding Tianjin-Shandong Beijing-Baoding Baoding-Hebei Hebei-Shanxi Hebei-Henan Shanxi-Shaanxi Shaanxi-Gansu Shaanxi-Sichuan Gansu-Chongqing Gansu-Qinghai Qinghai-Xinjiang Sichuan-Chongqing Chongqing-Guizhou Shandong-Xuzhou Shaanxi-Henan Henan-Xuzhou Xuzhou-Bengbu Bengbu-Anhui Bengbu-Jiangsu

617 810 1088 2355 1588 3082 1255 2843 1375 1863 566 223 882 235 222 155 1918 1557 3476 962 3116 5286 2411 2875

2.00% 1.90% 4.00% 3.40% 6.60% 8.00% 3.60% 6.80% 5.30% 4.40% 2.40% 0.70% 3.00% 1.50% 0.90% 0.90% 5.50% 4.70% 6.70% 2.60% 8.60% 14.90% 9.70% 9.20%

Henan-Hubei Chongqing-Hubei Hubei-Anhui Anhui-Jiangsu Jiangsu-Shanghai Jiangsu-Zhejiang Shanghai-Zhejiang Jiangsu-Tongling Anhui-Tongling Tongling-Fujian Hubei-Hunan Zhejiang-Jiangxi Jiangxi-Hunan Hunan-Guizhou Guizhou-Yunnan Zhejiang-Fujian Jiangxi-Fujian Hunan-Hengyang Fujian-Guangdong Guangdong-Hengyang Guangdong-Guizhou Guangdong-Guangxi Hengyang-Guangxi Guangxi-Yunnan

889 435 2048 4967 2204 6927 5067 814 2163 2977 2558 1408 1060 225 502 1507 1346 3302 4909 3024 2964 1532 278 453

2.00% 1.50% 5.80% 10.70% 2.30% 12.70% 7.70% 3.70% 7.90% 15.30% 4.90% 2.60% 2.70% 0.70% 1.70% 4.60% 5.90% 7.10% 19.80% 7.10% 11.80% 4.10% 1.40% 1.90%

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ArcGIS software is used to draw GIS maps based on the distribution results and the utilization ratio, as shown in Figs. 12 and 13, respectively. We must emphasize that the volume and utilization ratio is expressed through the color of the line. First, according to the data in Table 8 and Fig. 13, we can see that the capacity utilization ratio is quite low, and that the average

Harbin Urumqi

Huhhot

Fig. 12. Distribution scheme of China's HSReD flows obtained by IARM (2016, unit: cars/day).

Harbin Urumqi

Huhhot

Fig. 13. Utilization rate of the transportation capacity of HSReD on each HSR line (2016, unit: %). 182

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capacity utilization ratio of all lines on China’s HSR network is only 5.5%. This is mainly due to the face that the current HSReD in China is still in its infancy. And the calculation results show that China’s HSR network has a very good adaptability and can fully meet the transport demand of HSReD in 2016. In other words, on the one hand, the transportation resources can be further exploited in the future. On the other hand, the validity of the model and algorithm proposed in this paper is also verified by the results. Second, according to Table 8 and Fig. 12, we further analyze the adaptability of different regions in detail. Several findings can be obtained: (1) According to the geographical division, the transport volumes of HSReD parcels in the Eastern1, Central2 and Western regions3 are calculated, as shown in Table 9. The volume of the Eastern region is 62248 pieces per day, almost three and eight times those of the Central and Western regions, respectively. This is mainly due to the asymmetry of the economic development and population. Compared with the Central and Western regions, the economic development of the Eastern region is faster and better. This also leads to the increase in the transport demand of HSReD parcels in that region, which has resulted in the unbalanced transport volume of HSReD parcels, as shown in Fig. 11. Table 9 The total transport volume of HSReD parcels in different regions of China in 2016. Regions

The eastern

The central

The western

Transport volume (pieces) Proportion

62248 66.00%

24024 25.47%

8047 8.53%

(2) The express parcels are mainly transported on the following lines: Beijing–Shanghai, Beijing–Guangzhou, Hefei–Fuzhou, Fuzhou–Shenzhen, Zhengzhou–Xuzhou and Guangzhou–Guiyang HSR lines, which are most likely to become transportation bottlenecks on the overall HSR network. Furthermore, these lines are mostly located on the Eastern region in China. This is the main reason why the adaptability of the Eastern network is not good. (3) The generation and arrival nodes of the HSReD parcels are mainly distributed in the following cities: Beijing, Tianjin, Ji’nan, Shanghai, Nanjing, Hangzhou, Hefei, Guangzhou, Fuzhou, Guiyang, Wuhan and Xuzhou. Upon further analysis, we find that they are mainly distributed in the Beijing–Tianjin–Hebei region, the Yangtze River Delta region and the Pearl River Delta region, which are the core areas of China’s economic development and population agglomeration. Nevertheless, the assignment characteristics of the HSReD parcels can be obtained along with the imbalance of distribution. That is, the transportation demand of the HSReD parcels is unbalanced in the Eastern, Central and Western regions of China. In the Eastern region, the adaptability of the network is poor. Thus, the authorities should focus on the construction of parallel transportation channels in order to alleviate the transportation pressure of the bottleneck line in the Eastern network, thus ensuring the healthy and effective development of HSReD. The adaptability of the Central network is better, but its transportation capacity has not fully maximized. Therefore, the authorities should intensify the development of the transportation market and attract more high-quality goods. In addition, the necessary HSR line should be built in order to achieve the goal of optimizing the structure of the Central network. Finally, the adaptability between transport demand and network capacity in the Western region is at a low level, but the matching degree between the two is better compared with those in the other regions. 6.4. Applicability of the transportation capacity in the future To obtain the maximum transport volume of HSReD parcels on the HSR network, we analyze the adaptability of the HSR network by adjusting the growth rate parameter µtm . According to the statistical analysis of China’s express delivery industry, a growth rate of 50% shall be maintained in the future. Here, the results are shown in Table 10. The growth curves are drawn from 2016 to 2021, as presented in Fig. 14. We find that with the increase of HSReD parcels, the adaptability of China’s HSR network will undoubtedly decrease as well. Before 2020, the maximum utilization rate of all lines on the network would be less than 80%, indicating that the transportation capacity of HSReD on the network is still sufficient and adaptable. However, by 2020, the capacity utilization ratios of some lines in the network would be up to 99.99%, hence, the transportation demand will be difficult to satisfy, and the adaptability of the HSR 1

The Eastern regions include: Beijing, Tianjin, Hebei, Shandong, Jiangsu, Shanghai, Zhejiang, Fujian, Guangdong, Hainan, Heilongjiang, Jilin and Liaoning. 2 The Central region includes Shanxi, Henan, Hubei, Hunan, Jiangxi, Anhui and the Inner Mongolia Autonomous Region. 3 The Western regions include: Sichuan, the Guangxi Zhuang Autonomous Region, Guizhou, Yunnan, Chongqing, Shaanxi, Gansu, the Inner Mongolia Autonomous Region, the Ningxia Hui Autonomous Region, the Xinjiang Uygur Autonomous Region, Qinghai, and the Tibet Autonomous region. 183

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Table 10 The evaluation indexes of the adaptability of China's HSR network in diffierent time periods between 2016 and 2021. Utilization rate

2016

2017

2018

2019

2020

2021

Average Maximum

5.50% 19.80%

8.20% 29.70%

12.30% 44.50%

18.50% 66.70%

27.70% 99.99%

40.20% 99.99%

100% 90%

The average The maximum

Utilization ratio

80% 70% 60% 50% 40% 30% 20% 10% 0 0

2016

2017

2018

Year

2019

2020

2021

Fig. 14. The average and maximum utilization rates of HSR line on China's HSR network from 2016 to 2021. Table 11 The utilization rates of 6 bottleneck lines in diffierent time periods between 2016 and 2021. Rail lines

2016

2017

2018

2019

2020

2021

Xuzhou-Bengbu Jiangsu-Zhejiang Tongling-Fujian Fujian-Guangdong Guangdong-Hengyang Guangdong-Guizhou

14.85% 12.73% 15.30% 19.77% 7.05% 11.75%

22.30% 19.10% 23.00% 29.66% 10.58% 17.63%

33.46% 28.66% 34.46% 44.47% 15.87% 26.44%

50.13% 42.98% 51.68% 66.71% 23.80% 39.69%

75.18% 64.46% 77.53% 99.99% 35.69% 59.43%

99.99% 96.40% 91.81% 99.99% 80.69% 86.59%

100%

Xuzhou-Bengbu Railline Jiangsu-Zhejiang Railline Jiangsu-Zhejiang Railline Tongling-Fujian Railline Fujian-Guangdong Railline Guangdong-Hengyang Railline

90%

Utilization ratio

80% 70% 60% 50% 40% 30% 20% 10% 0 0

2016

2017

2018

Year

2019

2020

2021

Fig. 15. Growth curves of the capacity utilization rate of six HSR lines (or bottleneck lines) from 2016 to 2021. 184

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Table 12 The maximum transport volume of HSReD parcels with different LoSs on China's HSR network in 2020. Service levels

Arrived today

Arrived next morning

Arrived next day

Amount/pieces per day

27596

80410

217133

network will become very poor. Next, we focus on analyzing the bottleneck lines that limit the maximum transport volume of HSReD parcels on the whole HSR network. Here, only lines with utilization rate of over 80%, the bottlenecks of the HSR network, are shown in Table 11. In accordance with Table 11, the growth curves of utilization rates are shown in Fig. 15. With the growth of the HSReD demand, the first HSR line that would suffer the capacity shortage (capacity utilization rate reaching 80%) in 2020 would be Fujian–Guangdong HSR line, suggesting that the adaptability of the network is bad. Until 2021, all six HSR lines will face the dilemma of insufficient capacity and the adaptability will be at its worst. Meanwhile, the growth rates and the trends of the six lines would be roughly the same from 2016 to 2020. In 2020, the utilization of the HSReD transportation capacity of the Fujian–Guangdong HSR line will reach as high as 99.99% and there will be no increase in 2021. By 2022, the utilization rate of these lines will exceed 100%, resulting in no mathematical solution. Here, we can conclude that as the transport volumes of parcels on these HSR lines (e.g. Fujian–Guangdong and Xuzhou–Bengbu) approach the transportation capacity of HSReD, this can lead to the situation wherein the overall transport volume of the HSR network will also reach its maximum transportation capacity, even if one parcel cannot be added. Therefore, the maximum volume of HSReD parcels on China’s HSR network is equal to 325139 pieces per day, as shown in Table 12. In Fig. 15, we can see that: (1) the growth curves of the utilization rates of Jiangsu–Zhejiang and Guangdong–Hengyang have experienced a sharp increase from 2020 to 2021, about 35% and 45%, respectively; moreover, (2) the capacity utilization ratios of Fujian–Guangdong and Xuzhou–Bengbu in 2021 have reached as high as 99.99%, but that of Fujian–Guangdong remains unchanged from 2020 to 2021. The reason is that, when the transportation capacity of one line is limited, the HSReD flow on this HSR route will be transferred to others, which reduces the capacity utilization ratio of the line and leads to a sharp increase in others. This proves that the method proposed in this paper is effective and practical in analyzing the adaptability of the transportation capacity of HSReD on the HSR network. Furthermore, in order to eliminate the bottlenecks that affect the transport resource using in the HSR network in the future, the transportation capacity of HSReD can be improved from two aspects. On the one hand, the infrastructure construction of rail lines should be strengthened, such as double track, track quality improvement, and so on. On the other hand, relative optimization theories should be applied. Specifically, the reasonable HSR train schedule should be determined by constructing the mathematical optimization model. 7. Conclusions and discussion An improved Arc-Route mathematical model and overall solution algorithm are proposed in this paper to calculate the distribution scheme of HSReD parcels, which is an important parameter for the capacity utilization ratio of each HSR line to evaluate the adaptability of HSReD on the HSR network. Based on the definition of transportation capacity and LoSs of HSReD proposed in this paper, the target market, the relationship with the HSR train schedule, the capacity occupancy, and the unbalanced parcel distribution are analyzed as well. A case study of China’s HSR network is performed after collecting basic data. Some conclusions are drawn from the evaluation results in the case study. The results show that, in 2016, the utilization ratio of the transportation capacity of HSReD only reached 5.5%. This indicates that the transportation capacity of China’s HSR network is highly sufficient and the adaptability is excellent. As the demand of HSReD parcels grows at an annual rate of 50%, the adaptability will also decline annually, and the total transport volume will reach the limit of the transportation capacity in 2020. Moreover, six lines will become bottleneck lines after 2021, and they can no longer meet the transport demand of HSReD by that time. In the end, the maximum transport volume of the overall network is identified as 325139 pieces per day, which is the total volume of HSReD parcels in 2021. According to the results of our research and analysis, policies should be formulated from the following aspects to ensure the orderly development of HSReD. (1) At present, with the popularization and construction of HSR, many countries, such as China, France, Germany and Japan, have ripe infrastructure conditions for the development of HSReD. China has launched HSReD from 2010 and shows accelerated development trend nowadays. But the other three countries still aims at serving passenger travel demand by HSR, and has not yet shared the remaining passenger transport capacity with HSReD. On the one hand, HSReD makes full use of the idle transport capacity of HSR network to make up for the shortage of passenger ticket revenue, which provides economic support for the sustainable development of HSR. On the other hand, HSReD alleviates the pressure of express transportation by road and air. And it will attract more express parcels, which is conducive to enriching the revenue diversification of HSR operators. Therefore, these three countries should advocate to use the spare space of passenger trains to carry express parcels. Specifically, the Ruhr Industrial Zone in Germany, the Pacific coast in Japan and the northwest of Europe should give priority to HSReD business and further expand to the whole country. 185

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(2) In terms of the target market of HSReD mentioned in Section 3.4, there is no doubt that the rationality of the market positioning plan will have an important impact on the development of HSReD in various countries. Based on the study of this paper, countries can classify LoSs of HSReD into four categories, namely “arrival on the same day”, “arrival on the next morning”, “arrival on the next day” and “arrival on the next day”. Then, based on the speed and service scope of the HSR train, the target markets of the four LoSs can be determined. Specifically, the “Arrived today” and “Arrived next morning” service products should be given priority in the short-distance transportation, such as the “Arrived today” and “Arrived next morning” circles of the Beijing–Tianjin–Hebei area, the Yangtze River Delta and Nordrhein-Westfalen area. Similarly, in the medium/long-distance transportation, the total time should be within 24 h, and the “Arrived next day” service products must be developed, such as the “Arrived next day” circles of Tokyo–Nagoya–Osaka–Nagasaki, Beijing–Wuhan and Shanghai–Guangzhou. On the basis of the existing business, HSReD must be able to appropriately increase the ratio of “Arrived today” and “Arrived next morning” according to the transport demand of the express market. (3) According to the content described in the Section 6.3, the uneven distribution of HSReD parcels is mainly due to the different levels of the economic development among these regions. For this reason, the capacity adaptabilities of the HSR networks in different geographical regions also vary. In order to solve this problem, effective control measures should be implemented in different regions according to local conditions. The regions with poor adaptability are generally more economically developed areas, where the demand for parcel transportation is huge. However, a large number of bottleneck lines are also produced in this region due to the limited transportation capacity of the HSR network. Therefore, the authorities should strengthen the infrastructure construction in that region with poor adaptability, especially the construction of parallel transportation corridors among important economic development regions, such as the Yangtze River Delta region in China and Paris–Amsterdam–Rotterdam–Brussels region. In addition, the authorities must also design special equipment for parcel transportation, such as HSR cargo trains and special boxes for parcels. Taking the parcel box as an example, two boxes can be equipped on the train with 16 cars and one for the train with 8 cars. Assuming that the maximum load of a box can reach 500 kg, if all standard trains running on the Beijing–Shanghai line have 16 cars, then more than 13 tons of express parcels can be transported per day on this line. The economic development levels of regions with good adaptability are generally lower, such as the Central region of China and Osaka–Kobe–Nagasaki in Japan, where the transportation demand of HSReD parcels is far lower than that in a region with poor adaptability. In order to resolve this, the authorities should establish partnerships with private express enterprises to fully utilize transportation resources in their respective regions. First, they can design special equipment for parcel transportation, which is mentioned above, to lay the foundation upon which partnerships can be achieved with such courier companies as S.F., UPS, and EMS. Second, the operation organization of HSReD can be improved. The HSR is responsible for the intermediate transport, and the courier company is responsible for picking up and delivering at both ends, that is, collecting/sending the parcels to the HSR stations and collecting/delivering the parcels from the station. In order to ensure timeliness and stability, subways can be used as a means of transport during the pick-up and delivery operations. The third solution is income distribution. Courier companies do not have to pay transportation fees to the railway corporation first. Instead, the two companies jointly gain the total business income and share the profits and losses, which will place higher demands on railway departments to actively adapt to the market development. In general, the region, where the HSR network is excellent, is usually relatively backward in terms of economic development. For example, in the Western region of China, the HSR network size and structure in this area are generally smaller in scale, but it can fully meet the transport demand of HSReD parcels. In this area, some HSR lines with few passengers can be effectively utilized to deliver HSReD parcels, such as HSR lines in the Rhone River-Alps in France and Aomori area in Hokkaido. (4) Finally, the reform of relevant railway departments should be accelerated. For example, the railway companies should set up separate departments in charge of passenger transportation and freight transportation. Meanwhile, in the freight transportation department, commissioners should be appointed, who will be responsible for managing the HSReD business and ensuring the long-term development of HSReD in their respective regions. 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