Keywords

1 Introduction

Compared with other modes of transportation, air transportation can fully meet the timeliness requirements of logistics services for medium and high value-added goods with its technical and economic advantages such as speed, mobility and flexibility. Civil aviation cargo transportation plays an irreplaceable role in medium and long haul distance and transnational transportation. The relevant research by the International Air Transport Association (IATA) suggests that a one-percentage-point increase in air cargo accessibility boosts trade by about six percentage points. With the rapid development of China’s air cargo in recent years, its transportation volume has reached nearly 8 million tons in 2019, ranking second only to the United States in the world. Especially in the epidemic situation, air freight and logistics ensure the supply and stability of materials to a certain extent, and play a great role in epidemic prevention and fighting. As of the end of 2019, there were 13 airlines operating all-cargo aircraft in mainland China, with a total of 174 cargo aircraft. There are 8 main cargo airlines, SF Airlines, China Post Airlines, China International Air Cargo Company, China Southern Air cargo Company, Jinpeng Airlines, YuanTong Airlines, China Cargo Airlines and Longhao Airlines. As China’s air cargo has been carrying cargo in the belly warehouse for a long time, the number of cargo aircraft is insufficient and the cargo aviation network is not sound enough, the growth rate of air cargo is gradually slowing down. According to the data from Civil Aviation Administration of China, the average annual growth of cargo and mail transportation volume of the whole industry from 2014 to 2019 was 5.0%, and the year-on-year growth in 2019 was 2.1%. In this context, the research on the development status and trend of China’s cargo aviation network is of great significance to promote the healthy development of aviation industry and improve the development efficiency and quality of national economy.

Complex network theory is a tool commonly used to analyze networks. The characteristics and main applications of complex networks in different practical fields are systematically compared and analyzed by Boccaletti et al. (2006) [1] and Costa et al. (2011) [2]. The use of complex network theory to study aviation network has also been a hot spot and focus in recent years, but the results of existing research on cargo airline network are still very limited. Starting from the air cargo routes, this paper studies the freight network relationship between cities and regions, and finds that China’s air cargo network presents clear centralized characteristics (PAN Kunyou et al. 2007) [3]. XIE Fengjie and CUI Wentian (2014) analyzed the topological structure of specific enterprise’s express route network and proposed that its network has the characteristics of a small-world network [4]. Dang Yaru (2012) concluded from the study: China’s freight network is a scale-free network that has formed a relatively high agglomeration group, and the level of freight is very clear, but the network distribution is not balanced [5, 6]. Li Hongqi et al. (2017) studied the basic statistical characteristics and correlation of China’s air cargo network from the perspective of complex network, obtained the statistical characteristics of China’s air cargo network, and pointed out that China’s air cargo network has scale-free and small world characteristics, large clustering coefficient and small average path length [7]. Mo Huihui et al. (2017) studied the cargo network of aviation enterprises from the perspective of Chinese cargo airlines, and concluded that Chinese cargo airlines are a hub-structured network with smaller scale and higher organizational efficiency, and maintained a stable network expansion trend [8].

Most of the existing researches on the network of China’s cargo airlines are based on the passenger transport network, which is carried out in the manner of carrying cargo in the belly warehouse. Few people have discussed in depth the freight network composed of all-cargo aircraft. And most of the research is based on the network topology, the main indicators used are degree, strength, characteristic path length, clustering coefficient and so on, but less attention is paid to the economic characteristics of airlines. This can only evaluate the current status of the air cargo network, but cannot reflect the development and changes of the future network. Based on this, this paper comprehensively considers the existing network topology and economic benefit characteristics of cargo airlines to comprehensively evaluates their network development capabilities.

2 Chinese Cargo Airlines Network

China’s cargo aviation network is mainly composed of 8 Airlines: SF Airlines, China Post Airlines, China International Air Cargo Company, China Southern Air cargo Company, Jinpeng Airlines, Yuantong Airlines, China Cargo Airlines and Longhao airlines. By the end of 2019, China had 236 civil airports in operation. Among them, there are two airports in Beijing and Shanghai, one airport in other areas. In order to facilitate analysis and statistics, we merged the data of Beijing Capital Airport and Beijing Daxing airport as one node, and so did Shanghai. The data in this paper includes the data volume from March 1 to 7, 2021. The total freight network contains 56 nodes and 324 edges (Figs. 1 and 2).

Fig. 1.
figure 1

Chinese cargo airlines network map

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Different cargo airlines have different networks. SF Airlines connects 27 airport nodes, China Post Airlines 41, Jinpeng Airlines 12, Yuantong Airlines 7, China Cargo Airlines 45 and Longhao Airlines 14. China International Air Cargo Company and China Southern Air cargo Company mainly operate international cargo routes, but this paper mainly studies the air cargo network in china, so we did not join these two companies when studying each airline network in detail.

Fig. 2.
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Different cargo airlines network

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3 Network Measurement Index System of Cargo Airlines

3.1 Index System

From the two aspects of network topology index and economic benefit index, among them, the network topology index reflects the current situation of the network, and the economic index reflects the development ability of the network. The evaluation index system is shown in Fig. 3.

3.2 Network Topology Index

Network topologies are widely exist in various social phenomena, basic transportation and biological systems. Different network topologies represent different network connections and dynamic processes (Hossain et al., 2013) [9]. Therefore, the analysis of network topology depends on specific indicators.

Fig. 3.
figure 3

Evaluation index system of Cargo Airlines

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Degree.

Degree is one of the important basic attributes of nodes in the network, and it is the embodiment of the most basic connection characteristics of nodes in the network. Degree ki refers to the number of nodes directly connected to node i or the number of edges connected to node i.with that of node i defined as:

$$ k_i = \sum_{j = 1}^n {a_{ij} } $$
(1)

If node i is connected to node j, it is 1, otherwise it is 0. Generally speaking, the importance of degree is that the larger it is, the better the airport accessibility of the node corresponds, and the more important the node is. For the network, some very important indicators are formed, including the average degree k, which is a comprehensive index used to represent the average degree of all nodes. It can be written as:

$$ k = \frac{1}{n}\sum_{i = 1}^n {k_i } $$
(2)

Strength.

Degree is the total number of nodes associated to a node. It only considers whether the nodes in the network are connected. However, cargo capacity, number of available seats and flight frequency can be used as weights to affect the connection between airport nodes. This paper selects the number of flights between node i and node j in a week as the weight wij, the introduction strength Si can be expressed as:

$$ S_i = \sum_{j = 1}^n {w_{ij} a_{ij} } $$
(3)

The average strength S of all nodes is the average strength, which can be expressed as:

$$ S = \frac{1}{n}\sum_{i = 1}^n {S_i } $$
(4)

Clustering Coefficient.

The clustering coefficient Ci is the ratio of the number of edges actually connected to node i and all nodes connected to it to the maximum possible number of connected edges. It describes the proportion of network nodes that are also connected to each other. It shows the closeness of the nodes in the small groups in the network. The larger the value, the higher the closeness. Ci can be written as:

$$ C_i = \frac{1}{k_i (k_i - 1)}\sum_{i,j,k} {a_{ij} a_{jk} a_{ik} } $$
(5)

The average clustering coefficient C is the average value of the clustering coefficient of the whole network and can be expressed as:

$$ C = \frac{1}{n}\sum_i {C_i } $$
(6)

where n is the total number of network nodes, \(0 \le C \le 1\). The average clustering coefficient is used to describe the local properties of the whole network. If all nodes in the network are independent of each other, then C = 0; if all individual nodes in the network have edge connections with other nodes, then C = 1.

Characteristic Path Length.

The characteristics path length L of the network is the average number of shortest paths for all node pairs. Node i and another node connected to i form a node pair. It can be written as:

$$ L = \frac{1}{n(n - 1)}\sum_{i \in V} {\sum_{j \ne i \in V} {d_{ij} } } $$
(7)

where dij is the number of edges of the shortest path between node i and node j in the network, and n is the total number of nodes. The characteristic path length is usually used to measure the transmission efficiency of the network. The larger the characteristic path length value, the more edges the network passes through, and the lower the transmission efficiency.

3.3 Economic Benefit Index

Airlines obtain operating revenue and profits by transporting passengers and cargo. In order to further develop enterprises and meet the needs of the market, airlines will invest in opening up new routes. In the case of poor market conditions and poor business operation, the routes will be reduced, and the aviation network will be changed. Based on this, the cargo and mail turnover reflecting the market scale and the investment of aviation companies in aviation network are selected as important economic indicators.

  1. 1.

    Cargo and mail turnover is the total output produced by air cargo companies in a certain period of time. It is a composite index of transportation volume and transportation distance. It comprehensively reflects the total task and total scale of air transportation production. It is not only the most important index of civil aviation transportation companies, but also one of the main indicators for the state to assess air cargo companies.

  2. 2.

    Growth in the number of aircraft: The growth in the number of aircraft of airlines in recent years can reflect the economic situation and operation management of the company in recent years, and to a certain extent,it can also reflect the expansion speed of the company’s network. Only when market conditions are good and economic operation management is good, airlines will increase flight density of routes or invest in new routes and purchase new aircraft.

3.4 Measurement Method

Based on the analysis of network topology index and economic benefit index, the entropy weight method is used to calculate the weight of each index, and then TOPSIS model is used to comprehensively evaluate the airport network of each cargo airlines.

Principle of Entropy Weight Method.

Entropy weight method is an objective weighting method widely used in various fields. It weights different indicators according to the amount of information of different evaluation indicators, avoiding the differences between evaluation index data and reducing the difficulty of evaluation and analysis (Wang and Lee, 2009) [10]. The specific steps are as follows:

  • Step 1: According to relevant index data \(a_{ij}\) (i = 1, 2, …, 6, j = 1, 2, …, 6; i is the number of evaluation objectives; j is the number of indicators), in the future, the values of i and j are the same, and the original evaluation index system matrix Amn is established.

    $$ A = \left[ {\begin{array}{*{20}c} {a_{11} } & {a_{12} } & \cdots & {a_{1n} } \\ {a_{21} } & {a_{22} } & \cdots & {a_{2n} } \\ \vdots & \vdots & \vdots & \vdots \\ {a_{m1} } & {a_{m2} } & \cdots & {a_{mn} } \\ \end{array} } \right] $$
    (8)

  • Step 2: The extreme value method is used to eliminate the errors caused by the possible differences in the properties, dimensions, orders of magnitude and other characteristics of each index, and then the data are standardized. The formula is as follows:

    $$ b_{ij} = \frac{{a_{ij} - a_j^{\min } }}{{a_j^{\max } - a_j^{\min } }}\;({\text{Standardization}}\;{\text{of}}\;{\text{positive}}\;{\text{indicators}}) $$
    (9)
    $$ b_{ij} = \frac{{a_j^{\max } - a_{ij} }}{{a_j^{\max } - a_j^{\min } }}\;({\text{Standardization}}\;{\text{of}}\;{\text{negative}}\;{\text{indicators}}) $$
    (10)

    The data is normalized to form matrix \(B_{mn}\) after processing.

    $$ B_{mn} = \{ b_{ij} \}_{m \times n} $$
    (11)

  • Step 3: Calculate the information entropy Ej of the group j.

    $$ E_j = - (\ln \,m)^{ - 1} \sum_{j = 1}^m {P_{ij} \,\ln \,P_{ij} } $$
    (12)
    $$ P_{ij} = \frac{{b_{ij} }}{{\sum_{i = 1}^m {b_{ij} } }} $$
    (13)

  • Step 4: The weight is calculated according to the information entropy of each index.

    $$ W_j = \frac{1 - E_j }{{n - \sum_{j = 1}^n {E_j } }} $$
    (14)

TOPSIS Mothed.

TOPSIS is “a method to identify the schemes closest to the ideal solution and furthest away from the negative ideal solution in a multi-dimensional computing space”(Qin et al., 2008) [11]. Its advantage lies in its simplicity and easy of programming. TOPSIS has been applied in many fields, such as supply chain management and logistics, design, engineering and manufacturing systems, business and marketing management (Velasquez, M., and Hester, P. T., 2013) [12]. The application of TOPSIS method in this paper is mainly based on two points: one is that the TOPSIS method has good application effect in transportation, logistics, commerce, marketing and other fields; the other is that the method can eliminate the interference of different dimensions in network topology index and economic index. The specific steps are as follows:

  • Step 1: Construct a weighted normalization matrix Rij.

    $$ R_{mn} = \{ r_{ij} \}_{m \times n} = W_j \times b_{ij} $$
    (15)

  • Step 2: Calculate the optimal solution and the worst solution.

    $$ {\text{The}}\;{\text{optimal}}\;{\text{solution}}\;X^+ = \{ r_1^+ {,}r_2^+ {,} \ldots r_n^+ \} {,}\;r_j^+ = \max (r_{ij} ) $$
    (16)
    $$ {\text{The}}\;{\text{worst}}\;{\text{solution}}\;X^- = \{ r_1^- {,}r_2^- {,} \ldots r_n^- \} {,}\;r_j^- = \min (r_{ij} ){,} $$
    (17)

  • Step 3: Calculate the distance from the weighted evaluation normalized vector to the optimal solution and the worst solution.

    $$ D_i^+ = \sqrt {\sum_{j = 1}^n {(r_{ij} - r_j^+ )^2 } } $$
    (18)
    $$ D_i^- = \sqrt {\sum_{j = 1}^n {(r_{ij} - r_j^- )^2 } } $$
    (19)

  • Step 4: Calculate closeness.

    $$ G = \frac{D_i^- }{{D_i^- + D_i^+ }} $$
    (20)

  • Step 5: Use the value of G as the evaluation result. The larger the value, the better the evaluation result, and the smaller the evaluation value, the worse the result.

4 Data Acquisition and Result Analysis

4.1 Data Acquisition

Network Topology Index.

During data processing, we merged the data of Beijing Capital Airport and Beijing Daxing airport as one node, and so did Shanghai. The data in this paper includes the data volume from March 1 to 7, 2021. For the strength index, the number of flights between airports in a week is selected as the weight for calculation. The calculation of the network topology index of each airline is shown in the following table.

Table 1. Main indicators of each airline
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Fig. 4.
figure 4

Main indicators of each airline

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From Table 1 and Fig. 4, it can be seen that China Cargo Airlines, China Post Airlines and SF Airlines have a large number of nodes, indicating that they have opened routes in more airports, and Yuantong Airlines has the least number of nodes, that is, fewer airports have opened on their routes. The two indicators of degree and strength generally have the same trend. The more edges a node has on the network, the more flights may be allocated to the node. Therefore, the greater the degree of the node, the greater its strength. China Cargo Airlines, China Post Airlines and SF Airlines are all relatively large in degree and strength, while Jinpeng Airlines has the smallest degree and strength. In terms of clustering coefficient, China Cargo Airlines is the largest, indicating that a node in China Cargo Airlines network has a higher degree of correlation with its neighboring nodes, while Longhao and Yuantong airlines have the smallest clustering coefficient. The characteristic path length is an indicator reflecting the convenience of transmission. The smaller it is, the more convenient the transmission. In terms of the characteristic path length, China Post Airlines is the largest and Jinpeng Airlines is the smallest.

Economic Index.

The analysis of the aircraft growth of the 6 Chinese cargo airlines from 2017 to 2020, using the average value as the analysis data.

Table 2. Aircraft growth of different Cargo Airlines
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Table 3. Cargo and mail turnover of different cargo airlines in 2018
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4.2 Evaluation Results

Combine Table 1, Table 2 and Table 3 to form the original matrix data.

Table 4. Original matrix data
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The matrix is obtained according to the data in Table 4, and then the data is standardized to form a standard matrix to eliminate the impact of the difference between each index on the final result. The information entropy of each index is calculated by entropy weight method. As shown in Table 5.

Table 5. Information entropy of each index
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As shown in Table 6, the weight of each index can be calculated according to the formula.

Table 6. The weight of each indicator
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Through the evaluation of the TOPSIS method, the optimal solution and the worst solution are calculated as follows:

$$ \begin{gathered} X^+ = \{ 0.{1125}0{,}0.0{8173,}0.{17}0{24,}0.{77991,}0.{3167}0{,}0.{24}0{85}\} \hfill \\ X^- = \{ 0{,}0{,}0{,}0{,}0{,}0\} \hfill \\ \end{gathered} $$

The final calculated ranking result are: China Cargo Airlines 0.339, SF Airlines 0.290, China Post Airlines 0.201, Jinpeng Airlines 0.185, Longhao Airlines 0.112 and Yuantong Airlines 0.111. Compared with the results only considering topology indicators, China Cargo Airlines, SF Airlines and China Postal Airlines are still ranked high, indicating that they are not only outstanding on existing networks, but also excellent in future network development.

4.3 Sensitivity Analysis

TOPSIS method does not consider the weight of each index when calculating, assuming that all indexes are equally important. Therefore, it cannot reflect the difference between the weight of existing network and future network characteristic indicators. The weight setting of network topology index and economic index is changed from 1:1 to 1:2 and then to 2:1, so as to further analyze the impact of weight change on each airline. These three weight changes represent that airlines pay more attention to the development of future network, pay equal attention to the current network structure and future network development, and pay more attention to the structure of existing network, which are expressed as the initial stage, growth stage and maturity stage of each airline.

Initial Stage.

When the ratio is 1:2, it is the initial stage of the airline. And the weight is recalculated, as shown in Table 7 below.

Table 7. The weight of each indicator when the ratio is 1:2
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The calculation results are arranged as follows: China Cargo Airlines: 0.589, SF Airlines: 0.520, Jinpeng Airlines: 0.312, China Post Airlines: 0.270, Yuantong Airlines: 0.172, Longhao Airlines: 0.171.

Growth Stage.

When the ratio is 1:1, it is the growth stage of the airline. And the weight is recalculated, as shown in Table 8 below.

Table 8. The weight of each indicator when the ratio is 1:1
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The calculation results are arranged as follows: China Cargo Airlines: 0.634, SF Airlines: 0.506, China Post Airlines: 0.410, Jinpeng Airlines: 0.382, Yuantong Airlines: 0.222, Longhao Airlines: 0.221.

Mature Stage.

When the ratio is 2:1, it is the growth stage of the airline. And the weight is recalculated, as shown in Table 9 below.

Table 9. The weight of each indicator when the ratio is 2:1
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The calculation results are arranged as follows: China Cargo Airlines: 0.719, SF Airlines: 0.628, China Post Airlines: 0.568, Jinpeng Airlines: 0.451, Yuantong Airlines: 0.275, Longhao Airlines: 0.273.

According to the above three tables, the results of each index under different weights are different. No matter at any stage, China Cargo Airlines and SF Airlines have outstanding performance, while China Post Airlines has caught up from behind. The results of growth and maturity stages are consistent with those of TOPSIS method.

5 Conclusions and Recommendations

5.1 Conclusions

This paper uses network topology index and economic index to evaluate the current situation and development potential of the network, so as to effectively evaluate different freight airlines in China. From the analysis of network topology index, it is concluded that each airline has its own different characteristics, merit and demerit. China Cargo Airlines has the most connected cities and has the greatest advantages. It also performs well in terms of flight density and network accessibility. Sf Airlines has a large number of navigable cities, and the flight density of its routes is good, but poor network accessibility and inconvenient transfer. Although China Post Airlines does not connect so many cities and has poor transit performance, the density of routes between the cities and airports that have already been connected is high, and the network connectivity is good. Jinpeng Airlines, Longhao Airlines and Yuantong Airlines are all connected to a relatively small number of airports. The network density of Longhao Airlines and Yuantong Airlines is general, but the network connectivity is not good. On the contrary, Jinpeng Airlines has the worst network density, but the connectivity is good, and the traffic between the two nodes is convenient. From the perspective of economic indicators, each airline has its own advantages and disadvantages, and only Longhao Airlines and Yuantong Airlines are relatively average.

5.2 Recommendations

  1. 1.

    Cargo airlines should reasonably divide their development stages. The development focus of different development stages is different. In the initial stage, attention is paid to market development based on freight turnover and increasing the number of aircraft to improve the ability of market supply capabilities. In the mature stage, attention is paid to connotative development, that is, the optimization of existing route network. In the growth stage, it is necessary to redevelop route network optimization, expand the market and increase market supply. Only in this way can we be in a relatively leading position in the market.

  2. 2.

    Cargo Airlines reasonably determine benchmarking enterprises in different stages. In the initial stage, China Cargo Airlines, SF Airlines and Jinpeng Airlines should be the benchmark enterprises, and in the growth and maturity stages, China Cargo Airlines, SF Airlines and China Postal Airlines should be the benchmark enterprises.

  3. 3.

    When introducing air cargo enterprises to establish bases, local governments should comprehensively consider the current network of air cargo enterprises and the economic indicators affecting the future network development. Under controllable conditions, the economic indicators affecting the future development of air cargo network should be the key factors to be considered.