Evaluation of Supply–Demand Relationship of the Yangtze River Freight Market

Abstract

In order to effectively predict the supply–demand status of the inland waterway freight market of the Yangtze River, this study takes the inland waterway transportation of the Yangtze River as the research object, selects the supply–demand balance index model as the basic model, combines the characteristics of the Yangtze River Freight Market (YRFM), establishes the supply–demand balance index model of the inland waterway freight market of the Yangtze River, and uses the early warning light method in the early warning theory for reference, combined with mathematical statistics and expert analysis. The state interval and critical value are divided for the calculated supply–demand balance index of the inland waterway freight transport system of the Yangtze River. Through empirical analysis, the change in trend of the supply–demand balance index is basically consistent with that of the Yangtze River’s dry bulk cargo comprehensive freight index. Since the Yangtze River’s dry bulk cargo comprehensive freight index can be used as a barometer to reflect the trend of the YRFM. The model calculation results can truly reflect the supply–demand status of the YRFM and help operators to optimize transportation capacity and the government to adjust policies in a targeted manner.

1. Introduction

Different countries have waterways for cargo transportation, such as the Yangtze River in China, the Mississippi River in the United States, and the Rhine in Europe [1]. The Mississippi River plays a crucial role in the transportation efficiency of bulk goods, such as American agricultural products [2]. Petroleum products, chemical products, and sand, stones, and gravel are the most important cargo types for Rhine River transportation [3]. In the Yangtze River shipping market (YRSM), dry bulk cargo, liquid dangerous goods, and containers are the main transportation segments, among which the bulk cargo transportation segment accounts for nearly 80% [4]. It can be seen from this that the attributes of the main cargo types in major Inland Waterway Transport (IWT) are similar. The transport scale of the Yangtze River has ranked first among the world’s inland rivers since 2005 [5]. From 2016 to 2023, with the in-depth implementation of major national strategies, such as the Yangtze River Economic Belt, the economy of the Yangtze River Basin maintained sustained and rapid development, and the average annual growth rate of the cargo volume of the Yangtze River was nearly 4.2% [4].

As the cargo volume of the Yangtze River increases, the corresponding demand for ship capacity gradually rose through the supply–demand relationship between ships and cargo [6]. The level of large-scale, specialized, and standardized development of ships on the Yangtze River has been continuously improved. The average deadweight tonnage of ships has increased from 1490 to 2200, and the standardization rate of ships passing through locks has reached 98% [4].

Since the reform and opening-up policy was implemented, the YRSM has gradually developed into a market close to perfect competition [7]. The cyclical characteristics of the YRSM can be described as follows: When there is insufficient shipping capacity, the demand of the shipping market cannot be met, freight rates rise, and shipping companies generally make profits; after new capacity is put into operation, the tight demand in the shipping market is alleviated, and freight rates fall; when new capacity is continuously added, the demand in the shipping market cannot absorb the existing capacity, freight rates plummet, and shipping companies generally suffer losses; when the market supply of shipping capacity continues to exceed market demand, shipping companies consider suspending operations or gradually scrapping old ships [8]. Therefore, the imbalance between market supply and demand is the core issue plaguing the healthy development of the shipping industry, which is specifically manifested in the disorderly expansion of ship capacity in the YRSM and leads to intensified internal market competition and a significant expansion of the scale of corporate losses [9]. These issues highlight the urgent need for more intuitive indicators or methods to measure the supply and demand dynamics of the YRSM. These indicators or methods are crucial for providing a decision-making basis for shipowners, improving the service efficiency of government departments, and optimizing the effectiveness of macro-control policies.

Against this background, our study mainly addresses the issue of excess ship capacity in the Yangtze River, and the core contributions of this study are reflected in three aspects:

• It fills the gap in specialized research on the balance between supply and demand of shipping capacity in the YRSM, and addresses the lack of targeted analytical tools in the existing literature;
• It establishes a quantitative evaluation framework for supply and demand dynamics, enabling systematic analysis of the capacity matching level, which represents a breakthrough compared with previous qualitative or generalized research methods;
• It provides practical state classification standards for the evaluation of supply and demand in the shipping market, and offers actionable insights for shipowners to optimize shipbuilding decisions and for the government to improve the effectiveness of macro-control.

In the rest of the paper, Section 2 presents the literature review. Section 3 elaborates on the methodology. Section 4 illustrates the data analysis. Section 5 is the conclusion.

2. Literature Review

2.1. Supply and Demand of the Shipping Market

At the level of the relationship between freight rates and supply–-demand, Yin and Shi [10] examined the connection between the volatility of the China Containerized Freight Index (CCFI) and supply–demand conditions; Fan et al. [11] took the tanker freight index as the research object, analyzed relevant influencing factors, and used a gray model to explore its mechanism, finding that crude oil production, crude oil seaborne volume, and tanker capacity scale are key factors affecting the volatility of the freight index; Efes et al. [12] discovered that freight rates respond to changes on both the demand and supply sides of dry bulk cargo, with a stronger response to changes in the dry bulk fleet on the supply side.

At the level of market decision-making and system dynamics, Fernández L et al. [13] used classic demand models and network models within an equilibrium framework to characterize the decision-making behaviors of shippers and carriers; Han et al. [14] constructed a system dynamics model representing the shipping market based on marine economic theory, and evaluated the impact of changes in cargo transportation demand, shipyard supply capacity, and carbon emission standards on shipbuilding demand through scenario analysis. Nomikos and Tsouknidis [8] adopted a Structural Vector Autoregression (SVAR) model to distinguish between demand and supply shocks driving the shipping freight market, constructed a new shipping transportation index, and quantified the impact of shipping service demand.

In terms of inland waterway transportation, Deng et al. [15] constructed a gravity model using AIS data to study the relationship between ship tonnage and cargo transportation distance. This study deeply revealed the cargo transportation characteristics of inland waterways and provided decision support for ship capacity organization in the context of market supply and demand.

In summary, existing studies cover multiple market segments, such as air transportation, shipping, and inland waterway transportation, and explore the topics from perspectives including supply–demand interaction, freight rate volatility, and subject decision-making. They provide rich theoretical support for analyzing the operational laws of various transportation markets and making practical decisions.

2.2. Evaluation Methods for Supply–Demand Relationships

From the perspective of core evaluation methods, the academic community has currently developed a variety of mature analytical frameworks, providing direct tools for assessing supply–demand relationships. The excess capacity method [16] measures the gap between the actual market capacity and reasonable demand to intuitively determine the degree of imbalance between capacity supply and demand. It is suitable for quickly identifying whether the market is in a state of excess or shortage. The production function method [17], by contrast, uses a production function to construct a correlation model between inputs (e.g., transportation capacity, labor) and outputs (e.g., cargo volume, ton-kilometers). It infers the supply–demand matching level from the perspective of production efficiency, providing a basis for optimizing the structure of resource inputs. The supply–demand equilibrium index method [18], another important approach, quantifies the matching degree between the supply and demand sides by building a comprehensive index. This enables the quantitative description of the market’s equilibrium state and provides a unified standard for cross-period and cross-regional comparative analysis of supply and demand.

In the research on supply–demand relationships in specific transportation market segments, scholars have combined the characteristics of different markets and used models to deepen the exploration of supply–demand interaction mechanisms. Ferrari et al. [19] proposed a nonlinear econometric model to determine the relationship between the shipbuilding industry (supply side) and economic cycles (demand side) over the past 30 years. This model revealed the asymmetric impact of demand-side variables on supply-side development and the cyclical characteristics of such impact. Charemza and Gronicki [20] considered both equilibrium and disequilibrium aspects simultaneously and constructed an equilibrium model for the shipping market and the ship market. Chen et al. [21] studied the current status of capacity supply and balance issues in the international dry bulk cargo transportation market. Jia et al. [18] and Liu [22], respectively, conducted research on the capacity–cargo volume balance parameters and balance methods for coastal transportation. Zhang [23] combined multiple forecasting models, established a supply–demand balance model, and introduced the capacity index as a parameter, which scientifically reflects the supply–demand balance of the international dry bulk shipping market.

Among the studies by the aforementioned scholars, the basic evaluation methods in the transportation field and the research findings on segmented transportation markets have, respectively, provided methodological references and scenario-specific references for the supply–demand evaluation of the Yangtze River shipping cargo market. However, most existing research on inland waterway transportation focuses on exploring cargo transportation characteristics (e.g., Deng et al.’s [15] study of constructing a gravity model using AIS data), while specialized supply–demand evaluation research targeting inland waterway shipping remains relatively insufficient. As a core scenario of inland waterway transportation, the Yangtze River dry bulk transportation market can draw on existing basic methods (e.g., optimizing the excess capacity method to adapt to inland waterway capacity statistical standards) and segmented market models (e.g., referencing the supply–demand balance model framework of the international dry bulk market [18,21]). It can provide references from two dimensions—the attributes of dry bulk transportation and the logic of capacity balance—and build an evaluation system suitable for the Yangtze River dry bulk transportation scenario. This will further enrich the theoretical research landscape in the transportation field and offer a paradigm reference for supply–demand research in the inland dry bulk transportation markets of other regions.

3. Methodology

3.1. The YRFM Supply and Demand Balance Index Model

The purpose of this study is to quantitatively analyze the supply–demand relationship in the YRSM and lay a foundation for analyzing the supply–demand status by constructing a comprehensive function related to supply and demand. Therefore, it is most appropriate to adopt the supply–demand equilibrium index as the model form for studying the supply–demand relationship in the YRSM.

The supply–demand equilibrium index method [18] evaluates the supply–demand relationship by constructing a function related to supply and demand. However, the parameters associated with traditional supply–demand functions are difficult to collection data and different from YRSM. If relevant parameters are adjusted by optimizing parameter settings to make them applicable to the YRSM and reducing the difficulty of data collection, the supply–demand equilibrium index can conduct a quantitative analysis of the supply–demand relationship in the YRSM.

This study will take the freight market of the YRSM as the research object and conduct an analysis of the market’s supply–demand equilibrium index. This study defines “supply–demand balance” in the YRSM as a state where the supply of ship capacity in the Yangtze River system moderately exceeds the demand for the YRFM within a certain period of time. According to the characteristics of market operation and the difficulty of obtaining data, “a certain period of time” can be one year, half a year, one quarter, or one month.

Transport demand refers to effective transport demand, i.e., the actual cargo volume completed by the YRFM, excluding potential transport demand, which for calculating the “equivalent capacity” of the transport supply refers to the total capacity of the ships on the Yangtze River, i.e., the total deadweight tonnage. The parameters and their definitions that will appear later are shown in

Table 1. Description of parameter and variable symbols.

Parameter	Description
$I$	The supply–demand equilibrium index of a transport market.
$D$	The equivalent capacity required to meet the transport demand of a transport market under ideal conditions of transport organization. The main purpose of introducing the variable D is to convert the transport demand into a corresponding transport supply, thus enabling a comparison with the actual supply of capacity in the freight market.
$S$	The capacity of the transport supply, which is the total deadweight tonnage of ships of the YRFM.
$D_{it}$	The equivalent capacity required to complete the cargo volume of route i in period t (i = 1, 2, …, n).
$Q_{it}$	The cargo volume completed on the i-th route within period t.
$S_{it}$	The total capacity (rated deadweight tonnes) of ships operating on route i in period t.
$N_{it}$	The maximum number of voyages of operating ships to complete route i in period t under the ideal conditions of transport organization.
$\alpha$	The directional imbalance coefficient of transport demand reflects the spatial imbalance of transport demand in the YRFM. It is defined as the ratio of the cargo volume in the main direction (between upstream and downstream cargo volumes to the average upstream and downstream cargo volume). $\alpha$∈ [0, 1].
$\beta$	The temporal imbalance coefficient of transport demand reflects the law of seasonal fluctuations in transport demand of the YRFM to varying degrees. It is the ratio of the cargo volume in the peak month (for the main transport direction between upstream and downstream) to the monthly average cargo volume. $\beta$∈ [0.9, 1].
${\mathsf{\theta }}_{\mathrm{t}}$	The operating rate of ships in period t under ideal transport organization conditions.
$\overline{t_{it}}$	The average voyage time of a voyage on route i in period t under ideal transport organization conditions. $\overline{t_{it}}$= $W_{it}+P_{it}+C_{it}$.
$W_{it}$	The average waiting time for lockage of the i-th route within period t.
$P_{it}$	The average berthing time per voyage for the i-th route during period t (including productive stay and non-productive stay) under ideal transport organization conditions.
$C_{it}$	The average sailing time of the i-th route within period t under ideal transport organization conditions.
${\mathrm{R}}_{\mathrm{i}\mathrm{t}}$	The cargo turnover of the i-th route within period t.
${\mathrm{V}}_{\mathrm{i}\mathrm{t}}$	The economic speed of ships on the i-th route within period t.
$\overline{l_t}$	The average carrying distance in this freight market in period t.

.

The equilibrium state of the market is described by establishing a composite index related to the supply of capacity and the demand for transport, as shown in Equation (1):

$$I={\displaystyle \frac{D}{S}}$$

(1)

The equivalent transport capacity $D_{it}$ required to fulfill the cargo volume of the i-th route in period t is related to the directional imbalance coefficient α, temporal imbalance coefficient β of transport demand in this market, and the maximum number of voyages $N_{it}$ that operating ships can complete in period t. This is shown in Equation (2):

$${\displaystyle \frac{D_{it}}{\alpha ·\beta }}={\displaystyle \frac{Q_{it}}{N_{it}}}$$

(2)

By substituting Equation (2) into Equation (1), the expression for the supply–demand balance index in period t is shown in Equation (3):

$$I_t=\sum _{i=1}^n{\displaystyle \frac{\alpha \beta ·Q_{it}}{N_{it}}}/\sum _{i=1}^n{S}_{it}$$

(3)

For the YRFM with a relatively fixed route pattern, the maximum number of voyages that can be completed by the operating ships on the i-th route in period t can be obtained based on the ship’s working hours and the average voyage time of one voyage on this route, as shown in Equation (4):

$$N_{it}={\displaystyle \frac{T\cdot {\theta }_t}{\overline{t_{it}}}}$$

(4)

Substituting Equation (4) into Equation (3), the expression of the supply and demand balance index of the YRFM can be obtained as shown in Equation (5):

$$I_t=\sum _{i=1}^n{\displaystyle \frac{\alpha \beta ·Q_{it}·\overline{t_{it}}}{T·{\theta }_t}}/\sum _{i=1}^n{S}_{it}$$

(5)

For cargo types such as dry bulk cargo, due to the complex and variable route pattern of the YRFM, the average voyage time of a single voyage is not easy to obtain. The voyage time required to complete a voyage usually includes sailing time and berthing time, and the waiting time for lockage of ships also needs to be considered. Based on this, the maximum number of voyages can be transformed into the form shown in Equation (6):

$$N_{it}={\displaystyle \frac{T\cdot {\theta }_t}{W_{it}+P_{it}+C_{it}}}$$

(6)

Considering the operability of the model application and the principle of green development of the Yangtze River shipping, the equivalent capacity D required by the YRFM is adopted as the capacity required when the ship operates at the economic speed $V_{it}$, and then the average sailing time can be derived from the product of the cargo turnover $R_{it}$ and the cargo volume and the economic speed. Substituting Equation (6) into Equation (3), the expression of the supply–demand balance index of the YRFM is deformed into the form of Equation (7):

$$I_t={\sum }_{i=1}^n{\displaystyle \frac{\alpha \beta ·\left[Q_{it}·\left(W_{it}+P_{it}\right)+\frac{R_{it}}{V_{it}}\right]}{T·{\theta }_t}}/{\sum }_{i=1}^n{S}_{it}$$

(7)

where the average distance is more readily available, the average sailing time can be replaced by the ratio of the average distance $\overline{l_t}$ of the route to the economic speed, and the expression for the supply–demand balance index is deformed into the form of Equation (8):

$$I_t=\sum _{i=1}^n{\displaystyle \frac{\alpha \beta ·\left[Q_{it}·\left(W_{it}+P_{it}\right)+Q_{it}\frac{\overline{l_t}}{V_{it}}\right]}{T·{\theta }_t}}/\sum _{i=1}^n{S}_{it}$$

(8)

3.2. Division of Supply and Demand Index Warning Intervals

Based on the operational patterns of the YRFM, this study draws on the shipping prosperity signal light method [24] and adopts a set of red, yellow, green, pale blue, and blue light indicators from the field of traffic control to issue early warning signals for the supply–demand relationship status of the market. The state of the market’s supply–demand relationship is evaluated and judged by observing changes in the early warning signals.

Currently, the primary methods for determining the warning threshold values for supply–demand balance states are the expert method and the mathematical statistics method. Since the YRFM can be considered a fully open market, the supply and demand of the transportation system generally fluctuate around the long-term trend (supply–demand equilibrium state). Therefore, the supply–demand balance index calculated based on the supply–demand relationship of the transportation system should follow a normal distribution. The basic steps for using the mathematical statistics method to solve for the threshold values of the state interval are as follows:

① Select a set of time series data for the supply–demand balance index of the transportation market. Based on the actual data points from historical records, determine the central line of fluctuations and use this as the center of the normal range for the supply–demand balance index. When the sample data volume is limited, it is important to exclude time periods that deviate significantly from the average level.

② Based on the probability requirements for the index appearing in different state regions, use probability statistical methods to calculate the critical values.

When dividing the proportions of different state intervals, a symmetrical method should first be used to classify the state intervals into three major categories. The first category is the “supply–demand balance” interval, which belongs to the normal region, and most data points should be assigned to this region, with a probability of 50%. The second category includes the “severe supply shortage” and “severe supply surplus” intervals, which belong to the extreme regions and should have relatively lower proportions, with probabilities generally set at around 10%; the third category is the “supply shortage” and “supply surplus” intervals, which are relatively stable zones, i.e., transitional zones, with point probabilities higher than those of extreme zones, set at 15%, as shown in Figure 1.

The meanings of the five supply–demand state intervals in the YRFM are as follows:

(i)

“Severe supply shortage” is represented by a red light, which indicates a severe shortage of supply in the market. Specifically, it means that the market demand is growing rapidly, while the supply of transportation capacity is far from meeting the transportation demand. This situation will lead to phenomena such as a sharp rise in freight rates, a large number of cargoes being stranded at ports, and ships being detained;

(ii)

“Supply shortage” is represented by a yellow light, which indicates insufficient supply in the market. Specifically, the growth rate of transportation demand is higher than that of transportation capacity supply, resulting in a situation where demand exceeds supply;

(iii)

“Supply–demand balance” is represented by a green light, which indicates that the market is in a state of supply–demand balance, where the supply of transportation capacity and transportation demand generally maintain a basic balance on the whole;

(iv)

“Supply surplus” is represented by a pale blue light, which indicates an oversupply in the freight market. Specifically, the growth of transportation capacity supply is faster than that of transportation demand, resulting in a situation where supply exceeds demand;

(v)

“Severe supply surplus” is represented by a blue light, which indicates a severe oversupply in the market. Specifically, the market demand has weakened significantly, the contradiction between supply and demand has become more prominent, and this will lead to a sharp drop in freight rates and a general decline in the profits of shipping enterprises.

According to probability theory and statistics, for small sample time series data of supply and demand balance indices, the t-distribution should be used to estimate the population mean. First, calculate the mean $\overline{X}$ and standard deviation S of the supply and demand balance index; then, the confidence interval with a confidence level of $1-\alpha$ is

$$\left[\overline{X}-t_{\alpha /2}\left(n-1\right){\displaystyle \frac{S}{\sqrt{n}}},\overline{X}+t_{\alpha /2}\left(n-1\right){\displaystyle \frac{S}{\sqrt{n}}}\right]$$

(9)

In Equation (9), n represents the degrees of freedom. By calculating the confidence intervals with confidence levels of 50% and 80%, the critical values for the state intervals can be determined, as shown in

Table 2. Formula for calculating the critical values of each state interval.

Intervals	Upper Limits	Lower Limits
red light	$+\mathrm{\infty }$	$\overline{X}+t_{0.1}\left(n-1\right){\displaystyle \frac{S}{\sqrt{n}}}$
yellow light	$\overline{X}+t_{0.1}\left(n-1\right){\displaystyle \frac{S}{\sqrt{n}}}$	$\overline{X}+t_{0.25}\left(n-1\right){\displaystyle \frac{S}{\sqrt{n}}}$
green light	$\overline{X}+t_{0.25}\left(n-1\right){\displaystyle \frac{S}{\sqrt{n}}}$	$\overline{X}-t_{0.25}\left(n-1\right){\displaystyle \frac{S}{\sqrt{n}}}$
pale blue light	$\overline{X}-t_{0.25}\left(n-1\right){\displaystyle \frac{S}{\sqrt{n}}}$	$\overline{X}-t_{0.1}\left(n-1\right){\displaystyle \frac{S}{\sqrt{n}}}$
blue light	$\overline{X}-t_{0.1}\left(n-1\right){\displaystyle \frac{S}{\sqrt{n}}}$	$0$

. Once the critical values for the state intervals are calculated, the corresponding warning signal conditions for each sample data point can be obtained.

4. Results

This section applies the theories and methods described in the previous sections to carry out an empirical study of the supply and demand relationship in the YRFM. This study adopts the statistics related to the Yangtze River Shipping Development Report 2009–2024 to measure the supply and demand relationship of the YRFM.

From the Yangtze River Shipping Development Report 2009–2024, it is easy to obtain the cargo volume, cargo turnover, and the total deadweight tonnage of ships in the YRFM, which are showed in

Table 3. Cargo volume, cargo turnover, and ship transportation capacity in the YRFM.

Year	Cargo Volume (Million Tonnes)	Cargo Turnover (Gigatonne Kilometers)	Total Deadweight Tonnage (10,000 Tons)
2024	4145.2	1879.7	126.3
2023	3970.0	1835.7	127.4
2022	3650.0	1688.2	118.4
2021	3390.0	1579.9	116.9
2020	3120.0	1423.7	118.0
2019	3176.2	1466.5	118.0
2018	3059.8	1395.5	115.5
2017	3038.6	1362.8	117.7
2016	2919.4	1281.4	121.3
2015	2864.8	1218.5	113.5
2014	2736.1	1148.3	101.3
2013	2534.6	909.3	92.0
2012	2302.7	774.9	83.9
2011	2131.8	676.5	79.0
2010	1906.8	615.9	67.4
2009	1576.4	547.4	53.3

. From the Yangtze River Shipping Development Report 2009–2024, the average berthing time of in the YRFM is 72 h (including waiting time for loading and unloading and operation time), and the annual operation rate is 90%; according to the statistical data of water cargo flow in the YRFM, the directional imbalance coefficient of transport demand between upstream and downstream cargo volumes to the average cargo volumes of the YRFM is calculated to be 1.25, and the ratio of throughput of the Yangtze River ports in the peak month to the monthly average throughput is calculated to be 1.09. In addition, due to the poor objective environment of ship navigation at night, if the driving personnel are not vigilant and the measures are not effective, it is very easy to induce all kinds of accidents; according to the relevant statistics, in the past ten years, the proportion of serious and big waterborne accidents which occurred at night is up to 70% or more on the Yangtze River, and they are concentrated in the time period from 23:00 to 03:00; in order to guarantee the safety of ship navigation at night, it is necessary to adopt safe navigation speeds to ensure the safety of ship navigation at night. In order to ensure the safety of ship navigation at night, it is necessary to adopt safe speed to ensure that the ship can be stopped within an appropriate distance to avoid collision when necessary, which will result in a reduction in capacity. Therefore, taking into account the need for safe navigation of the ship, the daily sailing time of the ship is taken as 16 h when calculating the capacity supply.

Since the above parameters are applicable to Equation (7), this study selects Equation (7) for empirical calculation, and the calculated results of the supply–demand balance index are shown in

Table 4. Supply–demand balance indexes of the YRFM.

Year	Supply–Demand Balance Index	Year	Supply–Demand Balance Index
2024	100.21	2016	69.00
2023	94.64	2015	71.53
2022	91.05	2014	76.17
2021	88.36	2013	74.03
2020	80.40	2012	71.65
2019	82.08	2011	69.41
2018	80.46	2010	73.11
2017	76.50	2009	77.96

.

As the statistical data from 2009 to 2024 measure the state interval of the supply–demand balance index of the YRFM, the calculation results may deviate from the actual equilibrium level due to the market being in a deep depression for a long period of time. Therefore, this paper adopts a combination of expert method and mathematical statistics method to calculate the critical value of the state interval of the supply–demand balance index. Based on the calculation results of the mathematical statistical method, this paper comprehensively considers the growth trend of the transport demand of the YRFM and the elasticity of the transportation capacity supply. In accordance with the principle of being moderately forward-looking, and after consulting with the relevant experts, the range of the supply–demand balance index state intervals is determined. Specifically, taking into account the time period from the approval, design, and construction to the operation of new transportation capacity, the transportation capacity supply that can meet the total demand in the next two years is set as the center of the fluctuation of supply and demand. Opinions from relevant experts are solicited regarding parameters, such as the growth rate of transportation demand, and the proportion of transportation capacity shortage or surplus corresponding to the critical values of extreme zones (i.e., the “severe supply shortage” and “severe supply surplus” zones) and transition zones (i.e., the “supply shortage” and “supply surplus” zones). The numerical range of the state intervals is calculated by synthesizing the experts’ opinions. The range of status intervals calculated by the mathematical statistics method and the expert method were weighted according to the weight of 3:7, and the final comprehensive results were obtained, as shown in

Table 5. The numerical range of the state intervals.

Status Interval	Early Warning Signal	Numerical Range
severe supply shortage	red light	(100.3, +∞)
supply shortage	yellow light	(95.6, 100.3)
supply–demand balance	green light	(78.3, 95.6)
supply surplus	pale blue light	(73.5, 78.3)
severe supply surplus	blue light	(0, 73.5)

.

Therefore, the warning signals corresponding to the supply–demand balance state of the YRFM from 2009 to 2024 are shown in

Table 6. Status interval for supply–demand balance of inland river freight market in the Yangtze River.

Year	Supply–Demand Balance Index	Early Warning Signal	Status Interval
2024	100.21	yellow light	supply shortage
2023	94.64	green light	supply–demand balance
2022	91.05	green light	supply–demand balance
2021	88.36	green light	supply–demand balance
2020	80.40	green light	supply–demand balance
2019	82.08	green light	supply–demand balance
2018	80.46	green light	supply–demand balance
2017	76.50	pale blue light	supply surplus
2016	69.00	blue light	severe supply surplus
2015	71.53	blue light	severe supply surplus
2014	76.17	pale blue light	supply surplus
2013	74.03	pale blue light	supply surplus
2012	71.65	blue light	severe supply surplus
2011	69.41	blue light	severe supply surplus
2010	73.11	blue light	severe supply surplus
2009	77.96	pale blue light	supply surplus

.

The following can be seen from Table 6:

• The supply–demand balance index of the YRFM in 2024 is 100.21, which falls into the red light interval, indicating that the market was in a state of supply shortage in 2024. In 2024, the Ministry of Transport of the People’s Republic of China implemented the subsidy policy for the scrapping and renewal of old operational ships, promoting a new round of replacement of old operational ships and the adjustment of the ship transportation capacity structure [25]. Driven by this incentive policy, shipowners showed high enthusiasm for phasing out old operational ships on the Yangtze River, resulting in a decrease in market transportation capacity. Therefore, the calculated 2024 index is consistent with the actual supply–demand situation of the YRFM.
• From 2009 to 2017, the YRFM is in the blue or pale blue light interval in general, with short-lived signs of recovery only appearing in 2009, 2013 to 2014, and 2017. According to the meaning of the state interval, it can be seen that during the period of 2009–2017, the capacity growth rate of the Yangtze River inland freight market was faster than the growth rate of transportation demand, which led to the overall market capacity supply to varying degrees of excess, and the supply–demand balance index fell into the oversupply or even severe oversupply interval.
• In the early part of 2018, the YRFM saw transportation supply exceed demand due to the excessively rapid growth of transportation capacity in the earlier stage; after 2018, the growth rate of transportation capacity slowed down, and, combined with the slow growth of market transportation volume, the supply–demand relationship tended to balance. Meanwhile, after 2018, with the expiration of the ship standardization subsidy policy, the willingness of transportation capacity suppliers to build ships has decreased, and the transportation capacity and transportation demand have reached a state of supply–demand balance.

Since dry bulk cargo constitutes the main cargo type in the YRFM, accounting for about 80% of the cargo volume, the Yangtze River’s dry bulk cargo comprehensive freight index can be used as a barometer reflecting the trend of the Yangtze River inland freight market. In order to verify the reasonableness of the model calculation results, the supply and demand balance index is compared and analyzed with the Yangtze River’s dry bulk cargo comprehensive freight index, as shown in Figure 2. In Figure 2, the trend of the supply–demand balance index is basically consistent with that of the Yangtze River’s dry bulk cargo comprehensive freight index, indicating that the model calculation results can truly reflect the supply–demand status of the YRFM.

5. Discussion and Conclusions

In this study, the supply–demand balance index model is selected. By integrating the supply–demand characteristics of the YRFM system and the market’s feature of organizing transportation mainly through round-trip voyages, a method for calculating the equivalent capacity required to meet the transportation demand of the YRFM is proposed. Meanwhile, based on relevant data foundation conditions, the basic formula is derived, and further derivation is conducted to obtain the deformed form of the basic formula, ultimately establishing a supply–demand evaluation model for the YRFM. However, this method has limitations: As waterway conditions continue to improve, some seagoing ships also engage in transportation activities in the lower reaches of the Yangtze River, and there are differences in parameter selection between seagoing ships and inland waterway transportation. To simplify calculations, this study does not include the transportation volume and capacity of seagoing ships in the statistics. The model uses annual input data (e.g., annual cargo volume, annual average load rate) to calculate overcapacity via Equation (7). This resolution cannot capture short-term market fluctuations. All simplifications are made to balance model complexity and practical applicability, with each justified by industry data or research feasibility, avoiding arbitrary assumptions. By comparing the trend of the supply–demand balance index and the Yangtze River dry bulk freight index, the trends of the two are basically consistent, indicating that the model calculation results can truly reflect the supply–demand status of the YRFM.

The validity of the model is verified through empirical research. The results show that the change in trend of the supply–demand balance index of the YRFM is basically consistent with that of the Yangtze River’s dry bulk cargo composite freight index; the model results can intuitively reflect the state of the market’s supply–demand relationship and are highly consistent with the actual market operation. This evaluation model can truly and objectively reflect the supply–demand relationship of the YRFM, realize the quantitative analysis of the adaptability of the supply to the demand in the YRFM, and fill the gap in the theoretical basis for capacity adjustment in the YRFM.

This evaluation method and its results hold practical significance for shipping operators and government management authorities. The combination of the annual index calculation results and the conclusions of relevant market demand forecasts can be used to predict the upper and lower limits of future market capacity supply regulation targets, providing a decision-making basis for management authorities to formulate macro-control policies. The monthly calculation results, on the other hand, can be used to assess the capacity supply guarantee capability—specifically, the capacity guarantee level in peak months and the relative idleness of capacity in low months—providing a decision-making basis for operators to formulate capacity adjustment plans.

In the future, with the continuous accumulation of operation data of the YRFM, the value of the equilibrium point of the supply–demand balance index will continue to converge to the equilibrium level of market operation. When conditions are ripe, based on the value range of the supply–demand balance index state interval, research and construction of capacity supply response mechanisms under different supply–demand states can be carried out, so as to prevent excessive decline in transportation prices and ensure the sustainable and healthy development of the YRFM. At the same time, during the trial operation of the YRFM supply–demand balance index, through the adjustment and optimization of the index compilation scheme, supply–demand balance indices for micro-segmented markets, such as specific routes, specific ship types, and specific cargo types, can be gradually developed. In addition, based on the similarities of the characteristics of transported cargo types, this model can also be explored and applied in the inland waterway shipping markets of other countries.