Research on Ship Type Decision-Making for General Cargo Ship Owners Under Capacity Iteration: A TOPSIS Method Based on Agent Scoring

Abstract

This study quantifies ship-type performance indicators by training intelligent agents to evaluate and score vessels. The Analytic Hierarchy Process (AHP) is then applied to assess the internal consistency of the collected data, ensuring its authenticity and validity. Subsequently, the entropy weight method is employed to objectively determine the significance of each indicator in ship-type decision-making. Finally, COSCO (China COSCO Shipping Corporation Limited) Shipping’s capacity gap reflects the results of the methodology: the TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) technique ranks all feasible ship-type combinations, presenting their relative merits through quantitative results. A standardized grading system is further proposed to evaluate these combinations systematically. Ultimately, the 10 most suitable solutions are identified—none achieving the theoretical maximum rating of Grade 10—demonstrating room for improvement in vessel performance.

1. Introduction

Economic globalization has driven sustained growth in maritime shipping demand [1]. As core assets of this industry, vessel operational efficiency, cost-effectiveness, and environmental impact remain critical concerns for shipping companies. However, in recent years, the increasing trade friction between China and the United States has introduced significant volatility in global shipping markets [2].

As one of the most influential international economic events of the 21st century [3], the Sino-US trade dispute has profoundly impacted tariff barriers in both countries and the world. This conflict has notably triggered significant trade diversion effects. From 2018 to 2022, China’s exports to the United States decreased by 90 billion USD (16.2%), while U.S. exports to China declined by 23 billion USD (11.4%) during the same period [4].

Beyond the tariff war, unforeseen events around the world have also significantly impacted global maritime trade. The Russia–Ukraine conflict remains one of the most direct and severe disruptions to global shipping [5]. As the “breadbasket of Europe,” Ukraine’s obstructed grain exports have severely disrupted global food supply chains and shipping routes for bulk carriers. Furthermore, extreme weather events, such as the drought-induced crisis at the Panama Canal, have led to strict restrictions on the number of vessels allowed to transit daily and their maximum draft depth [6].

Chinese shipping companies have also felt the impact [7]. For instance, COSCO Shipping, one of China’s leading shipping companies, highlighted that U.S. tariffs on several countries have raised import costs to the U.S. This has led to a more cautious approach among U.S. customers, and it is anticipated that, in the short term, this will negatively affect the vessel load factor on trans-Pacific routes.

Furthermore, according to the latest Shanghai Export Containerized Freight Index released by the Shanghai Shipping Exchange [8], on 11 April 2025, the shipping rates (inclusive of sea freight and additional charges) from the Shanghai Port to major ports of the West and East Coast were USD (the U.S. dollor) 2202 per FEU and USD 3226 per FEU, respectively. This represents a decrease of 4.8% and 2.4% compared to the previous period.

In contrast, during the same period [9], the shipping rate from Shanghai port to the Mediterranean reached USD 2144 per TEU, representing an increase of 5.7% compared to the previous period. The rate for Australia and New Zealand was USD 890 per TEU, reflecting a 6.1% increase, while the rate for South America was USD 1566 per TEU, showing a 9.1% increase over the prior period.

In the face of the complexities of the global trade environment, shipping companies require more flexible and efficient vessel deployment strategies to remain competitive in a fluctuating market.

Traditional capacity allocation is highly dependent on individual experience, which makes it challenging to address the multifaceted nature of multi-objective and multi-constraint situations [10]. With the advancement of computer technology and optimization algorithms, shipping optimization methods based on mathematical models and intelligent algorithms have emerged as a key area of research [11]. Researchers use modeling techniques to comprehensively account for factors such as load factor, route length, sailing speed, and carbon emissions [12,13,14], offering systematic and scientifically grounded solutions to the shipping industry.

In the field of vessel optimization, scholars both domestically and internationally have carried out extensive research [15,16]. Early studies primarily focused on single-objective optimization techniques, such as minimizing ship resistance or maximizing cargo capacity. However, these single-objective methods have practical limitations, as they do not take into account other critical factors, such as construction costs, operational efficiency, and carbon emissions, resulting in optimization outcomes that are not fully applicable in real-world scenarios.

This paper tackles the following two issues:

➀ Fleet performance encompasses various dimensions, including transport efficiency, cost effectiveness, seaworthiness, cargo handling efficiency, and market adaptability. This paper develops a scientific evaluation framework by systematically quantifying the different performance metrics of vessels.

➁ Rational capacity allocation involves several conflicting goals, such as balancing transport efficiency with operational costs and environmental performance with economic gains. This paper proposes an efficient optimization algorithm to identify the optimal balance between these multiple objectives, helping shipping companies make informed decisions about capacity allocation.

The structure of this paper is as follows. Section 2 provides a literature review of the research methods relevant to this study. Section 3 proposes a model to assess the decision-making process of the type of vessels. Section 4 presents a case study to validate the proposed model, while Section 5 concludes this paper.

2. Literature Review

2.1. Agent Scoring

This paper seeks to address two key issues. The first is the development of a scientific evaluation framework and the quantification of various performance indicators. Holm et al. [17] gathered insights from 384 experts and applied the Common Vulnerability Scoring System (CVSS) to quantify the severity of security vulnerabilities. The results showed that the average discrepancy between the experts’ assessments and the CVSS base score was 0.38. Wendt et al. [18] constructed a reliable dataset on sleep spindle scoring, which could quantify abstract metrics, and measured the inter-expert and intra-expert agreement for sleep spindle scoring. However, manual scoring is prone to the drawbacks of incorporating subjective opinions [19]. Hier et al. [20] developed a mental state expert to assist in scoring and reporting test results. Carvalho et al. [21] proposed an agent-based model to evaluate prediction markets.

Therefore, we have decided to leverage the shipping company’s vessel information database to train a scoring agent, aiming to develop a more scientifically grounded scoring method. To assess the reliability of the agent’s scores, this paper will perform an internal consistency test. The Analytic Hierarchy Process (AHP) enables the derivation of a priority vector based on pairwise comparisons of a set of objects, thus reflecting the decision maker’s preferences. By applying AHP, this article effectively validates the agent’s scoring system [22].

2.2. Entropy Weight Method

Since each indicator has a different level of impact on the ship type, we need to determine the importance of each indicator to obtain a comprehensive score for each type of vessel.

Wu and Zhang [23] proposed the concept of intuitionistic fuzzy weighted entropy and validated the method developed based on the entropy weight approach for multi-criteria decision making. Liborio et al. [24], considering the uncertainty of experts regarding the importance of sub-indicators in multi-dimensional phenomena, introduced a new hybrid weighting method.

The entropy weight method is entirely objective when assigning weights to key indicators, which leads to its inability to account for experts’ preferences or the actual importance of certain key indicators [25,26]. Furthermore, outliers and extreme values can have a significant impact on the entropy value and weights [27], which has not been considered in previous studies. However, since the scores we obtain are based on the agent’s evaluation and have been verified through AHP, this avoids the drawbacks of the entropy weight method, such as its failure to consider subjective preferences, as well as the impact of outliers and extreme values on the entropy value and weights.

2.3. TOPSIS

In practical shipping scenarios, different types of vessels often need to work together to complete the transportation [28]. Therefore, we need to obtain comprehensive scores for various combinations.

The evaluation and optimization of multiple alternatives with multiple criteria has always been a key activity in the decision-making process. TOPSIS, which stands for Technique for Order Preference by Similarity to Ideal Solution, is a classic multi-criteria decision-making method. It is used for comprehensive evaluation and ranking of a finite set of alternatives. The core concept of TOPSIS is based on a simple idea: the optimal solution should be closest to the ideal solution and farthest from the negative-ideal solution. It has been used in research and decision-making [29]. Raval and Sarkar [30] used the TOPSIS method to identify key performance indicators (KPIs) related to Building Information Modeling (BIM) and blockchain in the Indian high-speed rail project. Karzan [31] integrated the Multi-Objective Particle Swarm Optimization (MOPSO) algorithm with TOPSIS within a multi-criteria decision-making framework to tackle inventory planning issues, producing solutions tailored to the preferences of different decision makers. These examples highlight the effectiveness of TOPSIS in addressing multi-criteria decision-making challenges. Accordingly, this paper applies the TOPSIS method to evaluate all the alternatives.

3. Ship Type Decision Model

By reviewing and analyzing relevant literature, this study reveals an inherent transformable relationship between traditional qualitative and quantitative indicators in the ship type decision-making process. Specifically, fuzzy and abstract concepts can be converted into quantifiable parameters through scientific methods, while existing quantitative indicators (such as capacity gaps) serve as effective constraints for ship type analysis. Based on this insight, this study develops a decision-making model, as shown in Figure 1.

3.1. Quantitative Indicators

This stage involves the following steps:

➀ Confirm evaluation indicators based on actual conditions and collect ship information and other data from shipping companies as the underlying database.

➁ Train the agent to function as an expert avatar using the database, enabling it to generate a scoring matrix for each type of ship across various indicators.

3.2. Data Processing

The steps in this stage are as follows:

➀ Based on the agent scoring matrix obtained in Section 3.1, this study applies the Analytic Hierarchy Process (AHP) to test internal consistency. If the consistency ratio ($CR$) is less than 0.1, we consider the scoring matrix to have acceptable internal consistency and retain it; otherwise, we discard it. Specifically, for matrices with a dimension of 1 (n = 1), which contain only a single element, the consistency ratio is assumed to be 0. For matrices with a dimension of 2 (n = 2), which have only one comparison relationship, the consistency ratio is also 0. These two cases do not require a consistency check. As the matrix dimension increases, the number of pairwise comparisons grows exponentially, increasing the complexity of the judgements. The random consistency index ($RI$) follows this pattern: when 3 ⩽ n ⩽ 10, the $RI$ value increases monotonically with dimension; when n > 10, the $RI$ value rises gradually and converges to 1.49. Therefore, for practical applications, we recommend using 1.49 as the $RI$ benchmark for matrices with n > 10. This approach takes into account the practical use of the AHP method, as most decision-making problems involve judgement matrices with dimensions not exceeding 10, ensuring both reliable judgements and method operability. We conduct the AHP test as follows:

First, calculate the maximum eigenvalue $\lambda max$ for each judgement matrix using matrix multiplication and eigenvalue calculation.

Next, we calculate the consistency index $CI$:

$$CI={\displaystyle \frac{{\lambda }_{\max }-n}{n-1}}$$

(1)

Here, n represents the dimension of the matrix (i.e., the number of criteria).

Next, we calculate the $CR$:

$$CR={\displaystyle \frac{CI}{RI}}$$

(2)

Here, $RI$ refers to the random consistency index, which is a predefined value based on the matrix dimension n. The corresponding $RI$ value for a given n can be found in a reference table.

Ultimately, if $CR<0.1$, the scoring matrix is considered valid and retained; if $CR>0.1$, the matrix requires adjustment [32].

In the end, we obtain a comprehensive agent scoring matrix.

➁ Given that the influence of each evaluation indicator on the overall score varies, this study employs the entropy weight method to quantify the weight of each indicator, thereby accurately assessing their contribution to the overall evaluation. The formula is as follows:

Normalize the data using Formulas (3)–(8):

$$X_{ij}^{\prime }={\displaystyle \frac{Min{X}_i}{X_i}}$$

(3)

$$Y_{ij}={\displaystyle \frac{X_{ij}^{\prime }}{{\sum }_{i=1}^m{X}_{ij}^{\prime }}}$$

(4)

$$h_i={\displaystyle \frac{-{\sum }_{j=1}^n{Y}_{ij}ln{Y}_{ij}}{lnn}}$$

(5)

Then, compute the indicator weights $Y_{ij}$ and subsequently the weights based on $h_i$.

The calculation formula for weight $G{L}_i$ is as follows:

$$G{L}_i={\displaystyle \frac{1-h_i}{{\sum }_{i=1}^m(1-h_i)}}$$

(6)

And

$$0\le G{L}_i\le 1$$

(7)

$$\sum _{i=1}^{m}G{L}_i=1$$

(8)

Data normalization plays a crucial role in ensuring the stability and accuracy of the entropy weight method. We standardize the data to eliminate the influence of different units and scales, preventing potential distortions in weight calculation caused by these differences. Normalization minimizes the impact of extreme values or outliers, resulting in more reliable outcomes. This approach enhances the reproducibility of the research method by reducing sensitivity to changes in the scale of the original data. It ensures that all variables contribute equally to the entropy calculation, leading to a more balanced evaluation. Moreover, it strengthens the scientific rigor of the method, as it can be consistently applied to various datasets without introducing bias due to differing data ranges.

➂Based on the weight coefficients of each evaluation indicator and the corresponding scores, this study uses a weighted comprehensive evaluation method to calculate the final score for each type of ship. The calculation process is as follows: First, the agent scores are preprocessed to calculate the arithmetic average score for each ship type under each evaluation indicator. Next, the average score for each indicator is multiplied by its corresponding weight coefficient to obtain the weighted score. Finally, the weighted scores of all indicators are summed using linear weighting to derive the comprehensive evaluation value for each type of vessel. This calculation method can be expressed as follows:

$$TotalScore=\sum _{i=1}Scor{e}_{i}G{L}_i$$

(9)

where $G{L}_i$ is obtained from Equation (6).

3.3. Ship Type Decision

This stage mainly involves the following steps:

➀ Identify the required capacity range and calculate all possible combinations using an iterative algorithm.

➁Calculate the score of each combination for each indicator, as shown in the following formula:

$$CombinationScor{e}_{ij}=\sum _{n=1}^N{\displaystyle \frac{TotalScor{e}_i{C}_{n}G{L}_j}{TotalBoats}}$$

(10)

Here, N represents the total number of ship types. $CombinationScor{e}_{ij}$ refers to the score of combination i under indicator j, while $TotalScor{e}_i$ represents the overall score of each ship type, which is already calculated in Equation (9). $C_n$ denotes the number of times a specific ship appears in the combination, and $TotalBoats$ indicates the total number of ships in the combination. $G{L}_j$ represents the weight of a specific indicator. Finally, we sum the contribution scores of each ship type in the combination for a particular indicator to obtain the total score of the combination under that indicator.

➂ We construct a matrix of scores for all combinations under each indicator and analyze it using the TOPSIS method, as outlined in Equations (11) to (20), to ultimately derive the overall score for each combination. TOPSIS relies on the shortest distance to the ideal solution and the longest distance to the negative ideal solution. The TOPSIS method will be explained in the following stages.

The original matrix is obtained, where we have already computed the score for each value in the matrix using Equation (10). Here, $x_{ij}$ represents the data of combination i under indicator j (where $i=1,2,\dots ,I$ and $j=1,2,\dots ,J$).

$$X=\left[\begin{array}{c}CombinnationScor{e}_{ij}\end{array}\right]=\left[\begin{array}{cccc}{x}_{11}& x_{12}& \dots & x_{1J}\\ x_{21}& x_{22}& \dots & x_{2J}\\ \dots & \dots & \dots & \dots \\ x_{I1}& x_{I2}& \dots & x_{IJ}\end{array}\right]$$

(11)

We normalize the original decision matrix by calculating the normalized value $y_{ij}$ for each element. This value is obtained by dividing $x_{ij}$ from matrix X by its norm, as shown below:

$$y_{ij}={\displaystyle \frac{x_{ij}}{\sqrt{{\sum }_{i=1}^I{x}_{ij}^2}}}$$

(12)

We present the normalized value $y_{ij}$ as the matrix Y, as shown below:

$$Y=\left[\begin{array}{cccc}{y}_{11}& y_{12}& \dots & y_{1J}\\ y_{21}& y_{22}& \dots & y_{2J}\\ \dots & \dots & \dots & \dots \\ y_{I1}& y_{I2}& \dots & y_{IJ}\end{array}\right]$$

(13)

Determine the ideal solutions: Define $P^{+}$ and $P^{-}$ as the positive and negative ideal solutions, respectively. These can be obtained from the above normalized values.

$$P^{+}=[y_1^{+},y_2^{+},\dots ,y_J^{+}]$$

(14)

$$P^{-}=[y_1^{-},y_2^{-},\dots ,y_J^{-}]$$

(15)

where for benefit-type attributes:

$$y_j^{+}=max{y}_{ij}{y}_j^{-}=min{y}_{ij}$$

(16)

And for cost-type attributes:

$$y_j^{+}=min{y}_{ij}{y}_j^{-}=max{y}_{ij}$$

(17)

Next, we calculate the weighted Euclidean distance.

$$D_i^{+}=\sqrt{\sum _{j=1}^J{w_j(y_{ij}-y_J^{+})}^2}$$

(18)

$$D_i^{-}=\sqrt{\sum _{j=1}^J{w_j(y_{ij}-y_J^{-})}^2}$$

(19)

Finally, we calculate the total score for each combination.

$$V_i={\displaystyle \frac{D_i^{-}}{D_i^{-}+D_i^{+}}}$$

(20)

In this paper, the combinations are rated on a scale of 10 levels. The final results are categorized as follows: [0, 0.1] as Level 1, [0.1, 0.2] as Level 2, etc.

4. Case Analysis

Assuming that the owner of a general cargo ship has a capacity gap of 20,000–25,000 Deadweight Tonnage (DWT), this study uses the fleet structure of China COSCO Shipping Specialized Carriers Co., Ltd., the owner of the world’s largest general cargo fleet, as a case study to ensure the universality of the research. The types of ships planned for construction, along with their respective capacities, are shown in the

Table 1. Ship Types and Their Capacities.

	Information	DWT	Name
Number
1		9100	HAI WANG ZHI XING
2		22,000	LESHENG
3		28,000	DA QING
4		38,000	TIAN EN
5		62,000	ZHONG YUAN HAI YUN KAI TUO
6		68,000	GREEN KEMI
7		77,000	GREEN ITAQUI

below:

In Section 4.1, Section 4.2 and Section 4.3, we presented partial data, while the complete dataset is provided in the Appendix A, along with corresponding explanations.

4.1. Quantitative Indicators

Due to the multidimensional impacts different ship types have in actual operations, this study focuses on five key evaluation indicators: transport efficiency, economy, seaworthiness, loading and unloading efficiency, and market adaptability. Detailed explanations are presented in

Table 2. Key Indicators and Explanations.

Transport Efficiency	Cargo capacity per voyage
Economy	Net profit generated from completing a voyage
Seaworthiness	Safety performance of vessels
Loading and Unloading Efficiency	Port operating time of vessels
Market Adaptability	Ability of ship types to adapt to new cargo types when market demand changes

.

This study uses the domestic AI software ChatOS with model GPT-4O as an entry point for training the intelligent agent. The GPT-4o model is integrated through the model interface to simulate expert scoring. The specific training process explains as below.

➀ Collecting and cleaning data related to types of COSCO Ships, followed by data pre-processing.

➁ Using the ChatOS platform, we input the preprocessed data into the GPT4o model and train it using supervised learning. During the training process, the model gradually learns how to score various indicators of different types of vessels based on the experience and rules of experts.

➂ We invited five experts from the COSCO Shipping field to repeatedly compare and calibrate the intelligent agent’s scoring results to ensure that the agent’s scoring was as close as possible to the expert evaluation method.

While training the intelligent agent, we simulated different expert avatars to score each indicator of each type of ship. The advantage of this method is that it minimizes human subjective bias to the greatest extent and ensures the reliability and accuracy of the evaluation results. Finally, we collected five intelligent agent scoring matrices. One of the intelligent agent evaluation matrices is shown in

Table 3. One of The Agent Evaluation Matrices.

	Indicator	Transportation Efficiency	Cost- Effectiveness	Seaworthiness	Loading and Unloading Efficiency	Market Adaptability
Number
A		1	10	7	10	10
B		4	9	8	8	9
C		4	8	8	7	9
D		5	7	8	6	9
E		9	6	10	5	7
F		9	5	10	4	7
G		9	5	10	4	7

. Here, we assign ship types numbered 1 to 7 as A–G.

4.2. Data Processing

4.2.1. AHP Verification

Based on Section 4.1, we performed AHP testing on each agent scoring matrix to assess the consistency of their evaluations. This process helped ensure the reliability and consistency of the experts’ ratings. An example of the test results for one evaluation matrix is shown in

Table 4. The Test Results for One of The Evaluation Matrices.

Indicator	CR
Transportation efficiency	0j
Cost-effectiveness	(2.2428747972225386 × ${10}^{-16}$ + 0j)
Seaworthiness	(−1.1214373986112693 × ${10}^{-16}$ + 0j)
Loading and unloading efficiency	(−3.3643121958338077 × ${10}^{-16}$ + 0j)
Market adaptability	(1.1214373986112693 × ${10}^{-16}$ + 0j)

below.

The results show that all agent ratings are highly consistent. Therefore, we retained the ratings of all agents. After performing the calculations, we present the final composite scores, derived using the arithmetic mean method, in

Table 5. Composite Agent Scoring Matrix.

	Indicator	Transportation Efficiency	Cost- Effectiveness	Seaworthiness	Loading and Unloading Efficiency	Market Adaptability
Number
A		1.4	9.2	7	9.6	10
B		3.8	9.2	8.2	8	8.8
C		4.4	8.2	7.8	7.6	9.2
D		5.2	6.8	8	6.4	9.6
E		9.4	6	9.6	5.6	6.6
F		9.2	5	9.2	4.6	7.2
G		9.4	4.6	9.2	4	7.2

below.

4.2.2. Calculate the Indicator Weights

Based on the composite agent scoring matrix in Section 4.2.1 and applying Formulas (3) to (8), we calculated the weights for each indicator. The results are presented in

Table 6. The Weight of Each Indicator.

Indicator	Weight
Transportation efficiency	0.735974
Cost-effectiveness	0.096926
Seaworthiness	0.015518
Loading and unloading efficiency	0.118484
Market adaptability	0.033098

.

The analysis reveals that transportation efficiency carries the highest weight. According to the entropy weight method, the weight value reflects the extent to which this indicator impacts the overall decision. Therefore, it can be concluded that, when selecting the ship type, the company should prioritize transportation efficiency.

4.2.3. Calculate the Comprehensive Score of Each Ship Type

Based on Formula (9), we calculated the comprehensive score for each ship type. The specific results are shown in

Table 7. The Comprehensive Score of Each Ship Type.

Ship Type	Comprehensive Score
A	3.499136
B	5.054803
C	5.359100
D	5.686344
E	8.530641
F	8.181688
G	8.219022

.

From this, it is clear that the scores of E, F, and G are significantly higher than those of A, B, C, and D, with the transportation efficiency scores of E, F, and G also noticeably surpassing those of A–D. This further validates the findings presented in Section 4.2.2.

4.3. Ship Type Decision

4.3.1. Calculating the Number of Combinations

We used the recursive function find-combinations to calculate the total number of possible combinations. When selecting ship types, the function first chooses one ship type from the available list and adds its cargo capacity to the total capacity of the current combination. The recursion builds all possible combinations by adding one ship type at a time until the total cargo capacity exceeds the maximum limit or reaches the minimum limit.

To improve efficiency, we implemented a pruning strategy during recursion. If the total cargo capacity of the current combination exceeds the preset maximum value (250,000), the recursion immediately backtracks to the previous level, avoiding unnecessary calculations. Similarly, if the current combination’s cargo capacity approaches the lower bound of the target range (200,000) and a valid range cannot be obtained by adding more ship types, the recursion terminates early for that branch. Additionally, the recursion ensures that combinations that have already been processed are not recalculated, significantly reducing the computational load.

These optimization strategies enhanced the execution efficiency while maintaining the correctness of the algorithm. They avoided redundant calculations and ensured that the final output combinations met the given cargo capacity range. Some of them are shown in

Table 8. A portion of all the combinations.

Combination 1	Combination 2	Combination 3	…	Combination 2530	Combination 2531	Combination 2532
A	A	A		F	F	G
A	A	A		F	G	G
A	A	A		G	G	G
A	A	A
A	A	A
A	A	A
A	A	A
A	A	A
A	A	A
A	A	A
A	A	A	…
A	A	A
A	A	A
A	A	A
A	A	A
A	A	A
A	A	A
A	A	A
A	A	A
A	A	A
A	A	A
A	A	A
	A	A
		A

.

4.3.2. Calculating the Comprehensive Score of the Combinations

Based on Section 4.3.1, we calculated the score for each combination across various indicators using Formula (10), with some of the results presented in

Table 9. The scores of some combinations under each indicator.

	Indicator	Transportation Efficiency	Cost- Effectiveness	Seaworthiness	Loading and Unloading Efficiency	Market Adaptability
Combination
Combination 1		1.030364	0.891722	0.108623	1.137444	0.330983
Combination 2		1.030364	0.891722	0.108623	1.137444	0.330983
Combination 3		1.030364	0.891722	0.108623	1.137444	0.330983
...		…	…	…	…	…
Combination 2530		6.820026	0.471708	0.142762	0.521329	0.238308
Combination 2531		6.869091	0.458784	0.142762	0.497632	0.238308
Combination 2532		6.918156	0.445861	0.142762	0.473935	0.238308

. The purpose of this is to obtain a matrix related to the indicators and combinations.

Based on these scores, we constructed the matrix and calculated the overall scores for all combinations using Formulas (11) through (20). The top 10 combinations are listed in

Table 10. The Top 10 Scoring Combinations.

Combination	Sore	Level
Combination 2525	0.885493	9
Combination 2526	0.873347	9
Combination 2527	0.864413	9
Combination 2528	0.861313	9
Combination 2529	0.857514	9
Combination 2530	0.855113	9
Combination 2531	0.852416	9
Combination 2532	0.849468	9
Combination 2519	0.830050	9
Combination 2521	0.823408	9

.

Based on the table above, it is clear that combination 2525, which involves producing four YUN KAI TUO vessels, is the optimal choice under various conditions. Additionally, combinations 2526, 2527, 2528, 2529, 2530, 2531, 2532, 2519, and 2521 can be considered in sequence, as all of these combinations achieved Level 9.

Smaller and larger vessels each offer distinct advantages and disadvantages across various dimensions, with each vessel type tailored to specific operational scenarios.

First, as highlighted in Section 4.2.2, transportation efficiency is a critical performance indicator for evaluating vessels. Smaller vessels typically have lower cargo capacities per trip, making them ideal for transporting small quantities of goods with diverse varieties. These vessels excel in markets with frequently changing demand or on routes with lower cargo volumes. Their primary advantage lies in their flexibility and adaptability, allowing them to meet dynamic market demands. In contrast, larger vessels offer higher cargo capacities per trip, making them well-suited for bulk cargo transportation, especially on long-distance routes or in areas with concentrated demand for bulk goods. Their economies of scale are substantial, as they reduce per-trip transportation costs, thus enhancing overall economic efficiency. Consequently, larger vessels dominate the bulk cargo transport sector, particularly in the shipping of commodities such as oil, coal, and iron ore.

From an economic standpoint, smaller vessels generally incur higher unit transportation costs due to their limited capacity and the need for frequent voyages. However, their purchase and maintenance costs are relatively lower, making them more suitable for short-distance transportation and routes requiring frequent, flexible adjustments. This makes smaller vessels more cost-effective for markets where transportation volumes are not large but where high-frequency transport is essential. In comparison, larger vessels benefit from significant cost advantages in terms of unit transportation costs, particularly for long-distance shipping. Their ability to carry large volumes per trip allows them to spread operational costs across a larger cargo base, lowering per-unit costs. However, they come with higher acquisition and maintenance costs, and their routes tend to be more fixed, making them ideal for long-distance routes with stable demand for bulk cargo.

Regarding seaworthiness, smaller vessels are more vulnerable to adverse sea conditions due to their weaker resistance to wind and waves, which makes them unsuitable for deep-sea or complex maritime routes. They are better suited for nearshore operations or calmer waters, such as inland rivers, coastal areas, or inter-island transport. Larger vessels, on the other hand, possess superior resistance to harsh weather, allowing them to navigate deep-sea routes and handle challenging sea conditions. In particular, during storms or rough seas, larger vessels maintain greater stability, ensuring safe transport. This makes them particularly suitable for long-distance voyages and international trade routes.

When it comes to loading and unloading efficiency, smaller vessels typically exhibit faster loading and unloading times, enabling them to complete these operations quickly and minimize port stay durations, thereby improving overall transportation efficiency. This advantage makes smaller vessels particularly well-suited for high-frequency operations, as they can swiftly adjust capacity and routes to accommodate shifting market demands. Larger vessels, due to their size, face more complex loading and unloading procedures, leading to longer port stay times and, consequently, reduced transportation efficiency. This disadvantage becomes more pronounced in ports with inadequate facilities or when vessels frequently dock and depart.

In terms of market adaptability, smaller vessels are more flexible and capable of quickly adjusting routes and transport plans in response to changes in market demand. They are particularly effective for short-distance transport and diversified shipping needs. In volatile markets, smaller vessels mitigate operational risks and maintain a high level of adaptability. In contrast, larger vessels typically rely on stable cargo flows. When their load factor drops, operational costs increase significantly, heightening market risk. Larger vessels are more sensitive to market fluctuations, as they experience greater losses when traveling empty, and their reliance on stable cargo sources makes them more vulnerable to disruptions.

The comparative analysis above validates the accuracy of the decision-making results derived from this research.

5. Conclusions

This paper proposes a TOPSIS method based on agent scoring for ship type decision-making. The goal is to scientifically and reasonably construct an evaluation indicator system, effectively quantify and allocate each performance indicator, and design an efficient optimization algorithm to support decision-making.

This paper presents a model suitable for cargo ship capacity configuration. First, a ship type evaluation system is constructed through reasonable analysis. Then, the intelligent agent is trained to simulate the scores of experts in relevant fields for each ship type under various indicators, creating a score matrix and using AHP to test its internal consistency. Next, after calculating the average score matrix, the entropy weight method is used to calculate the weights of the indicators, thereby obtaining the score for each ship type. Based on this, the weights of each possible combination under various indicators are calculated. Finally, the TOPSIS method is used to calculate the overall score for each combination to facilitate decision-making. This paper takes the fleet of China COSCO Shipping Specialized Transport Co., Ltd. as an example, analyzing a specific case and verifying the model.

The innovations and contributions of this paper are as follows: Firstly, an intelligent agent is used to replace experts in scoring ships. Additionally, a novel algorithm different from traditional decision-making methods is proposed, which avoids potential errors and subjective biases inherent in conventional decision-making processes. Finally, a transport capacity rating system is introduced, enabling a more intuitive comparison of capacity differences among various combinations.

The limitations of this paper are as follows: First, the process of collecting agent scores requires substantial human resources to evaluate multiple participants, such as cargo owners, ship owners, and charterers. However, this paper only explores the internal consistency of ship owners’ ratings. Future research could consider introducing consensus mechanisms to further improve the accuracy and reliability of decision results. Second, the grading method proposed in this paper sets a theoretical maximum of 10 levels. However, in practical application, this theoretical maximum was not reached, indicating that there is still room for improvement in ship performance. Therefore, the industry should focus on enhancing ship performance in the future. In the case study presented in this paper, we found that the weight of a ship’s transport efficiency significantly impacts the overall score. This indicates that the future shipbuilding industry should focus its main efforts on improving ship transport efficiency; for example, modifying hull shapes to reduce resistance and increase speed, lowering fuel consumption or adopting new energy sources to enhance endurance, using new materials to reduce the weight of empty ships, etc.