Pricing Strategy for High-Speed Rail Freight Services: Considering Perspectives of High-Speed Rail and Logistics Companies

Abstract

It is well known that there is a significant conflict of interest between high-speed rail (HSR) operators and logistics companies. This study proposes an HSR freight pricing strategy based on a multi-objective optimization framework and a freight mode splitting model based on the Logit model. A utility function was constructed to quantify the comprehensive utility of different modes of transportation by integrating five key influencing factors: economy, speed, convenience, stability, and environmental sustainability. A bi-objective optimization model was developed to balance the cost of the logistics with the benefits of high-speed rail operators to achieve a win–win situation. The model is solved by the TOPSIS method, and its effectiveness is verified by the freight case of the Zhengzhou–Chongqing high-speed railway in China. The results of this study showed that (1) HSR has advantages in medium-distance freight transportation; (2) increasing government subsidies can help improve the market competitiveness of high-speed rail in freight transportation. This research provides theoretical foundations and methodological support for optimizing HSR freight pricing mechanisms and improving multimodal transport efficiency.

1. Introduction

Transportation modes primarily consist of railway, highway, waterway, aviation, and pipeline transport. Currently, highway transport remains the dominant component of China’s inland freight logistics. With the continuous development of high-speed rail and civil aviation infrastructure and the escalating demand for freight timeliness, the proportion of high-speed rail and aviation freight transportation have been increasing annually. By the end of 2024, the mileage of China’s high-speed railway had reached 47,000 km, forming an “Eight Vertical and Eight Horizontal” trunk line network covering the whole country. With the advantages of convenient transportation, high speed, high punctuality, and low carbon emissions, high-speed rail freight has become the core growth project of the multimodal transportation system. Compared with aviation, its downtown connection is more efficient. Compared with the highway, its speed and stability are better.

Although high-speed rail freight has many advantages, there are still some issues that need to be addressed among the parties involved in high-speed rail freight. There are significant differences of interest between high-speed rail operators and logistics companies in the pricing of freight transportation. The high-speed rail operators pursue maximum freight revenue to ensure sustained profitability while the logistics companies focus on minimizing costs. This difference in goals not only leads to a rigid pricing mechanism but also results in inefficient resource allocation, hindering the expansion of the high-speed rail freight market and the improvement of service quality. The conflict of interests between the high-speed rail operator and logistics companies needs to be balanced urgently. It is necessary to coordinate the objectives of both sides through a pricing strategy to optimize the comprehensive benefits. Consequently, developing a pricing strategy to coordinate the interests of both parties is of great practical significance for promoting multimodal transport synergy and enhancing logistics efficiency.

The primary objective of this study is to construct a high-speed rail freight pricing model that can comprehensively consider both high-speed rail operators and logistics companies. This article is structured into seven sections. Section 1 introduces the background and research objectives. Section 2 provides a literature review on high-speed rail’s interactions with other transportation modes, high-speed rail passenger transport, pricing optimization, and high-speed rail freight. Section 3 introduces freight transport and the influencing factors of transport mode selection. Section 4, the main part of this study, elaborates the establishment and solution approaches of the high-speed rail freight pricing model. Section 5 describes the case study. Section 6 conducts a sensitivity analysis of the case. Section 7 summarizes the findings and concludes this research.

2. Literature Review

This study focuses on the pricing of high-speed rail freight transportation. The development of high-speed rail freight is still in its early stages; therefore, focusing solely on related articles has certain limitations. Consequently, the review is structured around four interconnected domains: competition and cooperation among transportation modes, high-speed rail passenger transportation, pricing optimization, and high-speed rail freight transportation.

With the development of high-speed railways, various transportation modes cooperate and compete, which has had a wide-ranging impact on society and all parties involved in transportation. Adler et al. [1] constructed a game competition model among three transportation modes: high-speed rail, traditional aviation, and low-cost aviation. Albalate et al. [2] examined the effects of high-speed rail on airline service frequency and seat capacity in major European markets. Abrate et al. [3] explored both intramodal and intermodal price competition. Jiang et al. [4] established a game model to study the competition between high-speed rail and airlines. Z. Chen [5] investigated the impacts of high-speed rail on domestic air transportation in China utilizing both demand and supply perspectives and discovered that high-speed rail has a significant substitution effect on domestic aviation. Álvarez-SanJaime et al. [6] revealed that collaborative HSR airline models yield lower fares and higher passenger demand than pure competition. X. Sun et al. [7] demonstrated that high-speed rail and air transport interact competently. Su et al. [8] explored the impact of their competition level on urban economic growth. D. Cai et al. [9] demonstrated that the incorporation of high-speed rail into the domains of passenger and freight transportation can contribute to the enhancement of social welfare. Y. Zhang et al. [10] established a straightforward model for air–HSR competition in both passenger and cargo markets. They pointed out that the entry of high-speed rail into the freight market continues to improve social welfare.

There is a lot of research on passenger transportation. Dobruszkes [11] analyzed the competition between high-speed rail (HSR) and air transport in Europe from a supply-side perspective, showing that longer HSR routes and airline network adjustments significantly reduced flight frequency. H. Yang and A. Zhang [12] analyzed the impacts of price discrimination between business and leisure travelers on fare levels, operator revenues, and social welfare under HSR–aviation competition under the assumption that airlines maximize profits while HSR operators maximize the sum of profit and social welfare. D. Alfonso et al. [13] explored the environmental and social welfare implications of HSR–aviation dual-oligopoly competition, demonstrating that HSR entry might adversely affect the environment due to induced demand. Through empirical data analysis, Wan et al. [14] showed that operational speed and route distance constitute pivotal determinants in the competitive dynamics between high-speed rail and aviation transportation systems. Xia et al. [15] examined how HSR–aviation competition and cooperation under varying travel distances influenced pricing strategies, traffic flow distribution, and social welfare optimization. Zhang et al. [16] studied three major Chinese air routes, finding that HSR entry caused significant demand erosion in air transport markets and price sensitivity was the primary driver of passenger choice behavior. Tsunoda [17] developed a game-theoretic model to assess regulatory approaches governing HSR–aviation competition, concluding that optimal government intervention should balance passenger choice benefits and revenue differentials between transportation modes. In addition, some experts have conducted specialized research on the selection of transportation methods. Samimi et al. [18] constructed a two-binary-mode choice model using artificial neural networks to make freight mode choices and analyzed the factors influencing shippers’ choices. Arunotayanun et al. [19] constructed a shipper selection model and studied the heterogeneity characteristics of shippers. The application of the bi-level programming model in the railway field is relatively abundant. It can effectively solve numerous problems in the railway field. Zhao et al. [20] constructed a bi-level programming model based on Stackelberg game theory to optimize the line planning problem for the high-speed railway network. The model is solved under the framework of a Simulated Annealing Algorithm by a decomposition searching strategy. Huang et al. [21] constructed a bi-level programming model to optimize the high-speed train timetable and used heuristic algorithms to solve it.

Research on pricing optimization mainly focuses on passenger transportation. Brotcorne et al. [22] considered a bi-level programming formulation of a freight tariff-setting problem. At the upper level, the leader’s revenue corresponds to the total tariffs levied, whereas the shipper minimizes its transportation cost given the tariff schedule set by the leader. Bharill and Rangaraj [23] analyzed the Indian railway system, developed a passenger price sensitivity model to quantify travelers’ responsiveness to fare fluctuations, and investigated pricing strategies for passenger fares. Liu and Gerodimos [24] proposed an adaptive pricing strategy to update parking pricing (or congestion pricing) in a multi-region and multimodal transportation system that provides parking and transfer facilities. This can contribute to reducing the total social cost effectively. Xia et al. [25] studied the competition and cooperation between aviation and high-speed rail in a multi-airport system. They developed an analytical framework for a revenue-sharing mechanism between an airline and an HSR operator, each retaining its objective function. Banerjee et al. [26] developed an approximation framework for pricing and optimization in shared vehicle systems that considered a wide range of controls (pricing, matching, and rebalancing), objective functions (throughput, revenue, and welfare), and system constraints (travel times, welfare benchmarks, and post-price constraints). Ma et al. [27] studied the problem of pricing and dispatching in ridesharing platforms and proposed the Spatio-Temporal Pricing mechanism, which solves the welfare-optimal matching of drivers to trips and sets prices that are appropriately smooth in both space and time.

Research on high-speed rail freight systems includes economic benefit evaluation, optimization of the train operation schedule, and optimization of freight transportation plans. Pazour et al. [28] used a network design model considering highway traffic and transit times to quantify the economic benefits of HSR systems. Zhen et al. [29] introduced a two-stage mixed-integer linear programming model to address vehicle arrangement, station selection, freight allocation, and the optimization of HSR freight routes. Zhen et al. [30] establish a stochastic mixed-integer programming model with the goal of maximizing the net profit of the HSR express system to plan the amounts of freights transported by each HSR express mode and the arrangement of capacity resources of each mode. Li et al. [31] designed the multi-objective nonlinear mixed-integer programming model of HSR passenger train and freight train line planning with passengers and freight, which is designed on the basis of comprehensive consideration of passenger and freight transport demand. Zhang et al. [32] addressed the problem of robust train composition and carriage arrangement for the mixed transportation of passengers and freights in a high-speed railway network while considering the uncertainty in freight demand.

In summary, despite the recent growth of high-speed rail freight, empirical research on optimizing high-speed rail freight pricing remains scarce. Against this backdrop, this study takes an approach that integrates the perspectives of two key stakeholders—high-speed rail operators and logistics companies—to address this research gap.

3. Freight Transport and Influencing Factors

3.1. Freight Transport Process

A complete package transportation process comprises three stages: collection, transportation, and delivery. In the collection stage, the customers or the logistic companies transport parcels from the senders’ locations to the service point (logistics distribution center). After that, the staff select appropriate transportation modes and routes based on parcel destinations, transporting them to the service points near the destination and facilitating final delivery to the destinations.

Since logistics companies undertake the collection and delivery stages, the transportation between service points is mainly portrayed in the study of this problem, taking the transportation chain between two service points (OD) in the city cluster as the object of study. The service points and the starting and ending points of high-speed railway or aviation are selected as the key nodes to construct the transportation network, as shown in Figure 1.

3.2. Analysis of Influencing Factors

• Economy

As a logistics company, the primary objective is to obtain profits by completing the customers’ transportation tasks. Therefore, the cost of transportation is used as a measure of economy to describe the service expense of each transportation mode. For the same OD pair, multiple transportation modes exist, each with different costs, and this difference affects the proportion of modes selected. Therefore, economics is one of the important influencing factors to be considered.

2.

Rapidity

With the rapid development of the economy, the transportation industry has also expanded significantly. The user’s requirements for the timeliness of the package are constantly increasing. And the prompt arrival of the package at the destinations can enhance user satisfaction. Therefore, the rapidity of the transportation mode is also an essential factor that needs to be considered.

3.

Convenience

The convenience of the transportation mode is mainly reflected in the transfer efficiency between different modes. For example, when road transport is used throughout the entire process, no conversion of transportation mode is needed, making it more convenient and efficient. In contrast, high-speed rail and aviation transport require road transport for the early and late stages, involving the transformation of the transportation mode. The time consumed for loading and unloading and the convenience of transshipment in each link also affect the choice of transportation mode. Therefore, convenience is also a key factor.

4.

Stability

The stability of different transportation modes has specific differences. High-speed rail operates according to a fixed timetable, with relatively stable departure and arrival times. Aviation is more susceptible to the influence of weather conditions, which may result in flight delays. And road transport can also be affected by various external factors, leading to instability of arrival time. Hence, the punctuality of high-speed rail is usually higher than that of aviation and road transport. Most customers typically have an expected delivery time when mailing packages or goods, so stability should also be a factor that logistics companies must consider.

5.

Green and low-carbon

As one of the largest sources of greenhouse gas and air pollutant emissions, the transportation sector accounts for 15% of global greenhouse gas emissions, a proportion that continues to rise. With the proposal of carbon peaking and carbon neutrality goals, the government and companies are paying more and more attention to green and low-carbon practices in production and life, so green and low-carbon are also essential factors that need to be considered.

There are many factors influencing transportation mode selection, and we have selected the five more popular factors mentioned above [18,33,34,35]. These factors can largely determine the choice of transportation mode.

4. High-Speed Rail Freight Pricing Model

4.1. Problem Assumption

As an emerging transportation mode, high-speed rail freight has broad application prospects in express freight transport. High-speed rail freight has many advantages, such as great stability, large load capacity, and environmental friendliness. Therefore, we should consider both railways and logistics companies to construct a bi-objective optimization model to maximize the total profit of the railway operator and minimize the generalized cost of the logistics companies.

Before model construction, the following assumptions are made to simplify the problem, eliminate interference from secondary factors, and facilitate model calculation:

• The sum of the total transport capacity of all transportation modes can meet the freight demand of the logistics companies.
• As an economic agent, the behavior of the logistics company is rational. Thus, the logistics company will choose the optimal transportation mode based on cost–benefit analysis.
• The government provides subsidies for high-speed rail freight operations, which are allocated to the high-speed rail operators.
• The goods primarily consist of high-value and time-sensitive products, such as fresh food, business urgent items, biopharmaceutical products, electronic products, etc.

Table 1. Symbols and their representations.

Symbols	Representations
$Q$	Actual freight volume
$w$	Lowest generalized costs in equilibrium
$c$	Average cost of high-speed rail freight transportation
$m$	Government subsidies
$s$	Haul distance
$x$	High-speed rail pricing
$U_i$	Utility function of mode i
$E_i$	Economic indicator
$V_i$	Rapidity indicator
$C_i$	Convenience indicator
$S_i$	Stability indicator
$G_i$	Green and low-carbon indicator
${\mathrm{q}}_{\mathrm{r}\mathrm{a}\mathrm{i}\mathrm{l}}$	High-speed rail transportation capacity
$P_i$	Proportion of transport mode i

shows the symbols and meanings involved in this paper.

4.2. Logit Model for Transport Mode Selection

Based on the Logit model, the transportation mode selection mechanism is constructed. The utility value is comprehensively calculated through multiple indicators of each transportation mode, and then the market share is determined. The Logit model is widely used in the study of mode choice in the field of transportation. The Logit model is based on the theory of random utility, assuming that travelers choose a path based on its utility. It is used to estimate the probability of each path being selected in the transportation network.

To model the freight mode selection behavior of logistics companies, a multinomial Logit model is adopted, which quantifies the utility of each transportation mode and converts utilities into market share probabilities. The model integrates five key indicators: economy $E_i$, rapidity $V_i$, convenience $C_i$, stability $S_i$, and green sustainability $G_i$. The calculation methods for some indicators are shown in Equations (1) and (2).

$$\begin{array}{c}{\mathrm{E}}_{\mathrm{i}}={\mathrm{a}}_1\times \mathrm{s}\times \mathrm{x}\end{array}$$

(1)

$$\begin{array}{c}{\mathrm{V}}_{\mathrm{i}}={\mathrm{a}}_2\times {\displaystyle \frac{\mathrm{s}}{{\mathrm{v}}_{\mathrm{i}}}}\times \mathrm{t}\end{array}$$

(2)

where $s$ is the transportation distance, $x$ is the price per kilometer, $v_i$ is the speed of the transportation mode $i$, $t$ is the time value, and $C_i,S_i,G_i$ can be obtained by the Delphi method.

First, the original indicators of each mode are normalized to eliminate dimension effects. The normalization formula is shown in Equation (3):

$$\begin{array}{c}{Y}_{norma i}={\displaystyle \frac{Y_i-\underset{i}{\min }{Y}_i}{\underset{i}{\max }{Y}_i-\underset{i}{\min }{Y}_i}}\end{array}$$

(3)

where $Y_i$ can be substituted into $E_i$, $V_i$, $C_i$, $S_i$, and $G_i$.

After the previous normalization process, the utility function $U_i$ of each mode of transport is obtained by Equation (4):

$$\begin{array}{c}{\mathrm{U}}_{\mathrm{i}}=-{\mathrm{w}}_1{E}_{norma i}-{\mathrm{w}}_2{V}_{norma i}+{\mathrm{w}}_3{C}_{norma i}+{\mathrm{w}}_4{S}_{norma i}+{\mathrm{w}}_5{G}_{norma i}\end{array}$$

(4)

with negative signs for economic and rapidity indicators (cost-type indicators) and positive signs for convenience, stability, and green and low-carbon indicators (benefit-type indicators). According to the Delphi method, the importance ratio of the five influencing factors in the utility function is set to 6:1:1:1:1.

Finally, based on the utility values, the market share of each transportation mode is calculated using the Logit model’s probability formula:

$$\begin{array}{c}{P}_i={\displaystyle \frac{\exp \left({\mathrm{U}}_{\mathrm{i}}\right)}{{\sum }_{\mathrm{j}=1}^3\exp \left({\mathrm{U}}_{\mathrm{j}}\right)}}\end{array}$$

(5)

This formula converts the utility value into a selection probability. The transportation mode with a higher utility value will have a higher probability of being selected, that is, a larger freight share.

4.3. Bi-Objective Optimization Model

Based on the transportation mode selection mechanism constructed by the Logit model, a bi-objective optimization model with the minimization of transportation costs of logistics companies and the maximization of revenue of high-speed rail operators is further established. The model depicts the interaction between the interests of both parties and solves the optimal pricing strategy that takes into account the interests of both parties.

The revenue $R\left(x\right)$ of the high-speed rail operator is determined by the combination of pricing strategy, market share, and transportation scale, and is expressed as follows:

$$\begin{array}{c}R\left(\mathrm{x}\right)=\left(\mathrm{x}-\mathrm{c}+\mathrm{m}\right)\times \left(P_{HSR}\times \mathrm{Q}\right)\times \mathrm{s}\end{array}$$

(6)

where $(\mathrm{x}-\mathrm{c}+\mathrm{m})$ is the unit profit after deducting operating costs $c$ and adding government subsidy $m$; $P_{HSR}\mathrm{\ast }\mathrm{Q}$ is the high-speed rail freight volume, determined by the market share $P_{HSR}$ calculated by the Logit model and the total freight volume $Q$; and $s$ is the haul distance.

The total cost of the logistics company $C\left(x\right)$ is the sum of the costs of each mode of transport and is expressed as follows:

$$\begin{array}{c}C\left(x\right)={\sum }_{\mathrm{i}=1}^3(P_i\times Q)\times p_i\times s\end{array}$$

(7)

where $P_i$ is the market share of the transport mode $i$ and $p_i$ is the transportation cost per unit of freight volume. $s$ is the haul distance.

In summary, the bi-objective function of the model can be expressed as follows:

$$\begin{array}{c}\mathrm{O}\left(\mathrm{x}\right)=\mathrm{m}\mathrm{a}\mathrm{x} \mathrm{R}\left(\mathrm{x}\right)+\min \mathrm{C}\left(\mathrm{x}\right)\end{array}$$

(8)

There are three constraints for this model.

The pricing of high-speed rail needs to meet the dual requirements of cost coverage and market competition:

$$\begin{array}{c}\mathrm{c}\left(1-\mathrm{m}\right)<\mathrm{x}<{\mathrm{x}}_{\mathrm{m}\mathrm{a}\mathrm{x}}\end{array}$$

(9)

The sum of freight volumes for each mode of transport is equal to the total demand:

$$\begin{array}{c}{\sum }_{\mathrm{i}=1}^3(P_i\times Q)=Q\end{array}$$

(10)

Due to high-speed rail capacity constraints, high-speed rail freight volume does not exceed its transportation capacity:

$$\begin{array}{c}{P}_i\times \mathrm{Q}\le {\mathrm{q}}_{\mathrm{r}\mathrm{a}\mathrm{i}\mathrm{l}}\end{array}$$

(11)

4.4. Solution Method

There is a natural contradiction in the bi-objective optimization problem (minimizing the cost of logistics companies and maximizing the revenue of high-speed rail). Although reducing the pricing of high-speed rail can reduce logistics costs, it may compress the profit margin of high-speed rail. Traditional single-objective optimization cannot take into account the interests of both parties. The TOPSIS method effectively deals with multi-objective conflicts by quantitatively resolving the relative distance from the ideal solution. Compared with other heuristic methods, the TOPSIS method directly selects the optimal solution through a mathematical distance measure, which has low computational complexity and strong convergence. The specific solution process is as follows:

(1)

Select 100 discrete points within the pricing range and calculate the market share for each price point by the Logit model. Calculate the revenue function $R\left(x\right)$ and the total cost of logistics $C\left(x\right)$ to form a solution set.

(2)

Revenue normalization:

$$\begin{array}{c}\overline{{\mathrm{R}}_{\mathrm{k}}}={\displaystyle \frac{{\mathrm{R}}_{\mathrm{k}}-{\mathrm{R}}_{\mathrm{m}\mathrm{i}\mathrm{n}}}{{\mathrm{R}}_{\mathrm{m}\mathrm{a}\mathrm{x}}-{\mathrm{R}}_{\mathrm{m}\mathrm{i}\mathrm{n}}}}\end{array}$$

(12)

where $R_{min}, R_{max}$ are the minimum and maximum values in the solution set. Make sure $\overline{R_k}\in \left(\mathrm{0,1}\right)$. The higher the value of $\overline{R_k}$, the higher the revenues of the high-speed rail operator.

Cost reverse-normalization:

$$\begin{array}{c}\overline{{\mathrm{C}}_{\mathrm{k}}}={\displaystyle \frac{{\mathrm{C}}_{\mathrm{m}\mathrm{a}\mathrm{x}}-{\mathrm{C}}_{\mathrm{k}}}{{\mathrm{C}}_{\mathrm{m}\mathrm{a}\mathrm{x}}-{\mathrm{C}}_{\mathrm{m}\mathrm{i}\mathrm{n}}}}\end{array}$$

(13)

where $C_{min},C_{max}$ are the minimum and maximum values in the solution set. Make sure $\overline{C_k}\in \left(\mathrm{0,1}\right)$. The higher the value of $\overline{{\mathrm{C}}_k}$, the lower the cost of the logistics companies.

Use standardized revenue and cost to represent the bi-objective: $A=(\overline{R_k},\overline{C_k})$.

(3)

Define ideal and negative ideal solutions. The ideal solution $A^{*}$ = (1, 1), which represents the maximization of high-speed rail revenue ($\overline{R_k}=1$) and the minimization of logistics costs ($\overline{C_k}=1$), usually does not exist in practice. The negative ideal solution $A^{-}$ = (0, 0), which represents the minimization of high-speed rail revenue and the maximization of logistics costs, is the worst benchmark for decision-making.

(4)

Calculate distance and relative proximity.

Distance to the ideal solution:

$$\begin{array}{c}{\mathrm{D}}_{\mathrm{k}}^{+}=\sqrt{{\left(\overline{{\mathrm{R}}_{\mathrm{k}}}-1\right)}^2+{\left(\overline{{\mathrm{C}}_{\mathrm{k}}}-1\right)}^2}\end{array}$$

(14)

where the smaller the distance to the ideal solution, the better the solution.

Distance to negative ideal solution:

$$\begin{array}{c}{\mathrm{D}}_{\mathrm{k}}^{-}=\sqrt{{\left(\overline{{\mathrm{R}}_{\mathrm{k}}}-0\right)}^2+{\left(\overline{{\mathrm{C}}_{\mathrm{k}}}-0\right)}^2}\end{array}$$

(15)

where the greater the distance to negative ideal solution, the better the solution.

Relative proximity:

$$\begin{array}{c}{\mathrm{I}}_{\mathrm{k}}={\displaystyle \frac{{\mathrm{D}}_{\mathrm{k}}^{-}}{{\mathrm{D}}_{\mathrm{k}}^{+}+{\mathrm{D}}_{\mathrm{k}}^{-}}}\end{array}$$

(16)

When ${\mathrm{I}}_{\mathrm{k}}$ = 1, the solution is the ideal solution.

(5)

Select the solution with the largest $I_k$ to correspond to the optimal pricing x. And the revenue of high-speed rail and the cost of the logistics company are balanced.

5. Case Study

5.1. Case Description

Taking the freight transportation between Zhengzhou and Chongqing as an example, this paper analyzed the cargo sharing rate of high-speed rail in the freight delivery process between Zhengzhou and Chongqing and studied the optimal pricing scheme of high-speed rail freight.

Zhengzhou is the capital of China’s Henan Province, located in central China. Chongqing is a municipality directly under the central government of China, located in the southwest of China. These two cities have successfully launched the Zhengzhou–Chongqing high-speed rail freight demonstration line. Zhengzhou–Chongqing high-speed rail utilizes a verification train, which is operated by the China Railway Group affiliated companies. The high-speed rail (HSR) freight services provided by the Zhengzhou–Chongqing line currently mainly focus on e-commerce express items as the primary cargo category. They undertake e-commerce express packages from downstream partners such as SF Express, JD Logistics, and ZTO Express, which gather goods from various e-commerce platforms, enabling the express items to travel from Zhengzhou to Chongqing via the Zhengzhou–Chongqing line. Meanwhile, the types of goods served are being planned to expand to biomedical products, fresh cold chain products, high-end manufacturing, and high-value-added logistics products. The maximum loading capacity reaches 15 tons. The railway operator dispatches two round-trip high-speed rail verification trains daily between Zhengzhou Airport Station and Chongqing North Railway Station, covering a transportation mileage of 1028 km. Transit time is controlled within 5 h. And the timeliness is equivalent to aviation transport, which is 1 day faster than highway transport.

5.2. Result Analysis

The main cargo transported by high-speed rail are high-value and time-sensitive products, such as fresh food, urgent business items, biopharmaceutical products, electronic products, etc. So this study mainly considers high-value goods. Assume that the total freight volume across all transportation modes in the Zhengzhou–Chongqing corridor is 5000 tons within half a year. In this case, the characteristic values of each factor are shown in

Table 2. Eigenvalues of each influencing factor.

Transportation Methods	Economy	Rapidity	Convenience	Stability	Environment
High-speed rail	1000×$x$ 1	200	0.7	1	1
Highway	450	600	1	0.9	0.085
Civil aviation	2800	75	0.7	0.6	0.014

¹ The actual distance of the Zhengzhou–Chongqing high-speed railway line is 1028 km, which is approximately calculated as 1000 km.

. The description of the values of each factor refers to the existing literature [36] and the results of field research. The freight transport price of highway transport is 0.45 RMB per ton·kilometer (RMB/t·km), the price of aviation transportation is 2.8 RMB/t·km, and the transportation cost of high-speed rail freight is 2.04 RMB/t·km. (The relevant person in charge of the Zhengzhou–Chongqing high-speed rail freight we consulted stated that the average cost of the Zhengzhou–Chongqing high-speed rail freight is approximately 2.1 RMB/kg. With the length of the Zhengzhou–Chongqing high-speed rail line being 1028 km, the unit cost is approximately 2.04 RMB/t·km.) According to the transportation volume and distance, we set the subsidy to high-speed rail freight to 50% of the transportation cost, which is 1.02 RMB/t·km. The design speed of the Zhengzhou–Chongqing high-speed railway is 350 km/h and we let the speed of high-speed rail transportation be 300 km/h. The speed limit on highways is generally 100 or 120 km/h and we let the speed of road transport be 100 km/h. The speed of civil aviation transport is 800 km/h and we let the time value $t$ be 60. The transportation capacity of high-speed rail, based on daily one-way verification train, is 15 tons, resulting in the transportation capacity of half a year being 2700 tons. Using the Delphi method, the other indicators are as follows: the convenience index of road transport is 1, the convenience index of high-speed rail transport and civil aviation transport is 0.7, the stability index of high-speed rail transport is 1, the stability index of road transport is 0.9, and the stability index of civil aviation transport is 0.6. For the carbon emission per unit of each transportation mode [37], the carbon emission data of each transportation mode is 32.7 g CO² per ton·kilometer (g/t·km) for highway transport, 2.8 g/t·km for high-speed rail transport, and 196.1 g/t·km for aviation transport. Therefore, the green and low-carbon index are 1 for high-speed rail, 0.085 for highway, and 0.014 for aviation transport.

Substituting various indicators into the optimization model, the calculated optimal price is 1.75 RMB/t·km. The high-speed rail carries 422 t of freight. The revenue of the high-speed rail operator is RMB 300,343.

5.3. Result Discussion

In Section 5.2, we calculated the result when the average cost of high-speed rail freight transportation was 2.04 RMB/t·km. But this cost was obtained through our investigation. The average freight cost of high-speed rail varies in different stages of development, routes, and backgrounds. This section discusses the pricing outcomes under the change in average cost of high-speed rail freight transportation.

When discussing the results under different costs (using a step size of 0.1), high-speed rail pricing, freight volume, and high-speed rail operator revenue with different average costs of high-speed rail freight transportation are shown in

Table 3. The results with different average costs of high-speed rail freight.

Freight Costs (RMB)	High-Speed Rail Pricing (RMB)	High-Speed Rail Freight Volume (t)	High-Speed Rail Operator Revenue (RMB)	Logistics Companies’ Cost (RMB)
1.64	1.588	612	471,073	2,598,326
1.74	1.669	509	407,761	2,541,891
1.84	1.669	509	382,269	2,541,891
1.94	1.669	509	356,778	2,541,891
2.04	1.751	422	308,791	2,494,034
2.14	1.832	348	265,884	2,453,745
2.24	1.913	287	227,916	2,420,035
2.34	1.913	101	213,554	2,420,035

. The trends in high-speed rail pricing, freight volume, and high-speed rail operator revenue with changes in costs are shown in Figure 2. Through observation, it is not difficult to find that as costs increase, the optimal pricing also increases, but the freight volume and revenue gradually decrease with the increase in costs. The above rules are consistent with our understanding and prove that the model has a certain reliability.

Furthermore, we discuss the results with different total freight demands. We have calculated the results for a total freight volume from 3000 tons to 6000 tons with a step size of 500. After calculation, high-speed rail pricing, freight volume, and high-speed rail operator revenue with different total freight volumes are shown in

Table 4. The results with different total freight volumes.

Total Freight Volume (t)	High-Speed Rail Pricing (RMB)	High-Speed Rail Freight Volume (t)	High-Speed Rail Operator Revenue (RMB)	Logistics Companies’ Cost (RMB)
3000	1.75	253	185,275	1,495,420
3500	1.75	295	216,154	1,745,823
4000	1.75	337	247,033	1,995,227
4500	1.75	380	277,912	2,244,630
5000	1.75	422	308,791	2,494,034
5500	1.75	464	339,670	2,743,437
6000	1.75	506	370,550	2,992,841

. We observed that the pricing of high-speed rail freight was 1.75 RMB/t·km and did not change with the overall demand for freight. But as the total freight volume increased, it also led to an increase in high-speed rail freight volume, thereby increasing the revenue of high-speed rail operators.

6. Sensitivity Analysis

The market competition of various transportation modes is not the same under different transportation distances. High-speed rail freight should refine the transportation distance, find its favorable range, and formulate a reasonable freight rate. We divide the transportation distance of high-speed rail freight transportation into three categories: short distance, medium distance, and long distance. Short-distance transportation is 0~500 km, medium-distance transportation is 500~1000 km, and long-distance transportation is more than 1000 km. The study was conducted in 1700 km steps from 200 km to 100 km.

Table 5. The results with different haul distances.

Haul Distance (km)	High-Speed Rail Pricing (RMB)	High-Speed Rail Freight Volume (t)	High-Speed Rail Operator Revenue (RMB)	Logistics Companies’ Cost (RMB)
100	1.02	4235	0	466,825
300	1.02	3916	0	1,345,865
500	2.8	922	820,641	2,213,646
700	2.47	442	450,042	2,209,742
900	2.03	347	318,420	2,532,570
1100	1.78	256	214,826	2,863,689
1300	1.60	190	144,181	3,226,567
1500	1.49	129	91,736	3,596,148
1700	1.38	97	60,295	4,001,221

shows the results for different transport distances. Figure 3 shows the trend in high-speed rail freight volume and the changes in the revenue of high-speed rail operators under different transportation distances.

The results indicate that high-speed rail freight has a significant competitive advantage in medium-distance transportation.

High-speed rail freight is in an extremely disadvantaged position when operating over shorter distances. The model proposed in this article suggests that when the distance is below 500 km, high-speed rail freight should only charge transportation prices that can make up for the cost. Although high-speed rail operators are currently in a non-profit state, they can further reduce the total cost of logistics companies. The benefits brought to logistics companies by lowering freight rates far outweigh the benefits brought to high-speed rail operators by increasing freight rates. But these are only theoretical optimal results. In practice, it is difficult for high-speed rail operators to choose to sacrifice all personal interests to bring about social benefit growth.

For medium distance and long distance, the advantage of high-speed rail freight transportation decreases with the increase in transportation distance. High-speed rail operators can only enhance their competitive advantage by reducing freight pricing. But the total revenue will also decrease with the decrease in freight pricing. During this process, the total cost of the logistics company also increases, as the increase in transportation distance would naturally lead to an increase in costs.

As a necessary means to regulate the high-speed rail freight market, government subsidies can effectively reduce operating costs and incentivize freight rate optimization. The results are shown in

Table 6. The results with different government subsidies.

Government Subsidies	High-Speed Rail Pricing (RMB)	High-Speed Rail Freight Volume (t)	High-Speed Rail Operator Revenue (RMB)	Logistics Companies’ Cost (RMB)
50%	1.75	422	308,791	2,494,034
45%	1.91	287	227,341	2,420,035
40%	1.99	235	181,869	2,391,974
35%	2.15	158	131,655	2,349,504
30%	2.31	105	94,296	2,320,686

. Figure 4 shows the trend of optimal pricing of high-speed rail freight under different government subsidies.

With the decline in government subsidies for high-speed rail freight, the freight volume of high-speed rail is gradually declining, the share of high-speed rail in the market competition is slowly decreasing, the optimal pricing is also rising progressively, and the revenue of high-speed rail operators is gradually decreasing. By reducing net costs, subsidies have prompted high-speed rail pricing to fall and become more attractive to logistics companies. The subsidy not only optimizes the competitive position of high-speed rail but also promotes the development of green logistics, which is in line with the “dual carbon” goal orientation.

7. Conclusions

Focusing on the perspectives of high-speed rail operators and logistics companies, this paper constructs a bi-objective optimization pricing model and a freight mode split model, integrated with the TOPSIS method. We systematically analyze the pricing strategy of high-speed rail freight under different haul distances and different government subsidies. The main conclusions are as follows. The case study of China’s Zhengzhou–Chongqing high-speed railway verifies the effectiveness of the pricing strategy. Further analysis of different haul distances shows that high-speed rail occupies a significant advantage in medium-distance transport. However, as the transport distance increases, the competitiveness of high-speed rail freight gradually declines, and the total revenue of the high-speed rail operator decreases with the haul distance. When the transport distance is short, it is difficult for high-speed rail operators to make profits. This indicates that high-speed rail freight needs to focus on the medium-distance freight markets and consolidate the advantageous range through optimal pricing strategies. In addition, government subsidies have a significant effect on the improvement in the competitiveness of high-speed rail freight. Our study shows that subsidies can optimize pricing flexibility and attract logistics companies by reducing the net cost of high-speed rail operations. At the same time, the subsidy policy could help increase the share of high-speed rail in the freight market, which has significant social benefits and environmental value. The government can promote the healthy and rapid development of high-speed rail freight by formulating reasonable subsidy policies.

The bi-objective optimization pricing model studied in this paper provides theoretical support for the pricing of high-speed rail freight. The sensitivity analysis of high-speed rail freight pricing has contributed to promoting coordinated development of multimodal transport and improving logistics efficiency. However, the model has some limitations in practical application. For example, the model assumes sufficient transportation capacity and does not fully consider the impact of the price strategy adjustments by other transportation modes such as roads and aviation, which may be improved in the future. When the total volume of goods exceeds the total capacity of all transportation modes, this model is no longer applicable. In fact, when the pricing of high-speed rail freight changes, highways and civil aviation may also adjust their pricing strategies accordingly. These three are in a state of game equilibrium. But this model did not take into account this change. That may be one of the reasons for possible deviations in real-world conditions. In the future, game theory can be introduced into models to more accurately depict the relationships between different transportation modes.