Application of Advanced Algorithms in Port State Control for Offshore Vessels Using a Classification Tree and Multi-Criteria Decision-Making

Abstract

This article examines the methods and application of classification trees and multi-criteria decision-making in the process of holding offshore vessels in port (Port State Control—PSC). This work aims to improve the efficiency and precision of the control processes in the detention of offshore vessels by using advanced analytical methods. Methodologically, a classification decision tree was used to identify the most important risk factors, enabling a faster and more accurate assessment of the possibility of detaining offshore vessels in port. Multi-criteria decision-making (MCDM) also enabled the simultaneous assessment of multiple factors, ensuring a balanced, robust, accurate, and objective approach. The research results show that the integration of these methods into the PSC process can significantly increase the safety of shipping and reduce the operating costs of offshore vessels. The application of these analytical tools can lead to a more systematic and transparent inspection process. This paper suggests further research and training of inspectors in the use of these techniques to maximize their applicability and effectiveness. Finally, this paper emphasizes the potential of classification trees and MCDM for safer and more efficient maritime transport by improving PSC procedures.

1. Introduction

Port State Control (PSC) is important to the international maritime safety and pollution prevention strategy. It implements international conventions to ensure the standard operation of vessels regarding safety, security, pollution prevention, and living conditions for the crew.

PSC inspections aim to identify and rectify vessel deficiencies to reduce the risk of accidents, pollution, and other problems at sea. The inspections are carried out by qualified inspectors from national maritime administrations. They have the right to inspect the vessels, talk to the crew, and check the documentation. The inspections can be routine, targeted, or risk-based, with particular attention paid to vessels with a higher risk of defects. PSC is, therefore, a measure used by a port authority or an authorized subject (flag, agent, or recognized organization) to inspect aspects of foreign vessels calling at a country to ensure that they comply with the standards of international conventions.

PSC is carried out by international conventions adopted under the auspices of the International Maritime Organization (IMO), such as SOLAS (International Convention for the Safety of Life at Sea), MARPOL (International Convention for the Prevention of Pollution from Vessels), and MLC (Maritime Labour Convention).

The PSC aims to safeguard the living conditions of seafarers, protect human life and property, and reduce pollution of the sea, coasts, and the environment as a whole. Possible vessel problems can relate to safety, health, and pollution. Typical inspection points are vessel certificates and documentation; safety and rescue equipment; crew working conditions and their health and safety; the structural integrity of the vessel; and environmental protection standards. Suppose a vessel encounters a problem with life or property. In this case, it should not be allowed to continue its voyage unless there is a case of force majeure and there is an urgent need to resolve the situation that poses a threat to human life or the vessel. If deficiencies are found, the vessel may be detained until the problems are resolved. It should remain in position if necessary and remedial action should be taken to bring it into a safe and efficient condition for further voyages. In serious cases, the vessel may be forced to leave port or cease operations or sailing.

To improve vessel performance and crew behavior, PSC popularizes the PSC system to, directly and indirectly, influence the entire maritime industry, including vessel management, seafarer training institutions, vessel management authorities, vessel classification societies, and vessel financiers through inspections, detentions, information on inspections, frequent target lists issued under the PSC MoU, and regional training and cooperation platforms. Any poor performance of the vessel or crew may result in the vessel being detained by the port authority immediately before departure or at the next port of call.

PSC inspections are organized and coordinated at the regional level within the framework of Memorandums of Understanding (MoU), such as the Paris MoU [1], the Tokyo MoU [2], and the Caribbean MoU [3]. These agreements enable the exchange of information and common control standards. The results of PSC inspections are recorded and have an impact on the reputation of the vessel and company owner/operator. Vessels with poor PSC inspection results may have problems obtaining orders and calling at ports. Therefore, PSC is an important tool for improving safety at sea and reducing accidents and pollution in maritime transport, which helps to protect human life and the environment.

Ocean HQ [4] lists the main reasons for detaining a vessel in port. For a vessel owner or operator, port control is not a favorite topic of conversation, because if the port authority detains due to certain deficiencies, it is very likely that additional port charges will be levied. The charter price will increase, and such delays also hurt the vessel’s profitability.

Each port state has the right to independently inspect all vessels calling at its ports, whereby the inspector (PSCO—Port State Control Officer) is authorized to detain the vessel if they think that it has deficiencies until the deficiencies have been rectified. The IMO sees PSC as a means of raising standards in the shipping industry, and many of the key IMO conventions contain provisions requiring governments to inspect foreign vessels calling at their ports to ensure that they comply with IMO standards.

To further promote uniformity in PSC standards, the IMO has encouraged the regionalization of countries so that countries in the same region form a PSC system. Agreements have been signed for Europe and the North Atlantic (Paris Agreement), Asia and the Pacific (Tokyo Agreement), Latin America (Viña del Mar Agreement), the Caribbean (Caribbean Agreement), West and Central Africa (Abuja Agreement), the Black Sea region (Black Sea Agreement), the Mediterranean (Mediterranean Agreement), the Indian Ocean (Indian Ocean Agreement), and the Persian Gulf (Riyadh Agreement).

PSCs often announce their review campaigns in advance and usually focus on new regulations that have recently come into force. However, vessel operators should not only focus on meeting the requirements of the new regulations or only doing what the PSC regime has announced in the campaign. Most detentions of the vessels due to PSC inspections are due to a general lack of maintenance. This means that vessels are not operating under a system of safety organization by the International Safety Management Code (ISM Code) [5], which includes relevant procedures for the vessel’s maintenance and equipment.

Given the complexity and multidimensionality of the criteria used in vessel inspections, there is a need to apply advanced analysis and decision-making methods that can improve the inspection process. Classification decision trees and multi-criteria decision-making (MCDM) methods are powerful tools for analyzing the behavior of complex systems such as PSCs. On the one hand, classification decision trees allow easy decision-making based on available historical data about previous inspections. On the other hand, MCDM integrates different criteria in the process of optimal decision-making.

Therefore, the main assumptions and motivations for the research in this scientific article are as follows:

• Improving the efficiency of PSC inspections through the application of classification trees and MCDM will significantly increase the accuracy in identifying offshore vessels that pose a higher risk or have certain deficiencies, thereby optimizing the allocation of resources and increasing the efficiency of inspections.
• Improving maritime safety through the use of advanced analytical methods will enable more accurate prediction and detection of potential safety risks, more precise prediction of the possibilities of detention of offshore vessels due to the presence of certain irregularities, a reduction in the number of incidents, an increase in safety at sea, and a reduction in the time the vessel spends in port and thus the associated financial costs.
• More effective inspections of offshore vessels contribute to a better understanding of potential risks, marine pollution reduction, and better marine ecosystem protection.

Through the application of modern technologies in the maritime industry, this work contributes to the dissemination of knowledge, the application of modern technologies and methods, and the promotion of innovation and improvement of existing practices. Empirical research with available data on previous PSC inspections of offshore vessels and in real conditions will provide concrete results that prove their effectiveness by suggesting concrete improvements for this complex process. In this way, this article will contribute to the development of PSC practice, enable a better understanding and application of advanced decision-making methods in the maritime industry, and improve safety on a global scale.

This paper is divided into six chapters. After the introduction, the second chapter gives an overview of previous research on PSC and the application of various mathematical, statistical, and other approaches, including machine learning (ML) applications using classification trees and MCDM to optimize the decision-making process in PSC. The third chapter briefly explains the three-stage methodological approach, which consists of 1. the application of the classification tree “rpart”, 2. the MCDM TOPSIS method, and 3. the integration of the results of “rpart” and TOPSIS.

The fourth chapter describes the data source and structure in detail and explains the three-step approach to solving the problem: 1. applying the classification decision tree “rpart”; 2. applying the TOPSIS method; and 3. combining the results of both algorithms. The fifth chapter documents, reviews, and evaluates the results obtained, while the last chapter is dedicated to discussion. At the end, you will find a conclusion, a list of biographies, and a list of abbreviations used.

2. Theoretical Background of the Integration of Machine Learning Algorithms and Methods in PSC

Although the basic international legal framework for PSC was established by various IMO conventions, including SOLAS, MARPOL, and MLC, PSC has evolved over the years into an important instrument for these conventions. As PSC is a key element of global maritime safety and environmental protection, research to date shows considerable scientific interest from researchers contributing in various ways by investigating and demonstrating the positive impact of PSC inspections on vessel safety, seafarers’ working conditions, and environmental protection, all to reduce the number of maritime accidents and incidents, improve overall safety, and reduce pollution.

The Maritime Anti-Corruption Network Report [6] promotes some of the practices that have emerged from the challenges facing the maritime industry. This is because the interactions of PSCOs during inspections are sometimes very complex. The report therefore clarifies the discretionary rights and powers of PSCOs, which on the other hand make it difficult for seafarers to plan the vessel’s sailing in port or to comply with the conditions, as well as obtain a clear interpretation of the rules, which should be harmonized with those applicable internationally.

In dissertation [7], the researcher highlights the challenges associated with ensuring sufficient resources and capacity to carry out PSC inspections. PSC is recognized as an internationally accepted safety enforcement program that detects and corrects deficiencies, promotes best practices, supports compliance, and collects and evaluates safety data. However, the author points out that all interested parties in this process play a key role, namely the shipping companies, the seafarers, and even PSC itself.

Study [8] analyzes the risk factors of vessel detention and identifies the most important factors of maritime safety and environmental protection. Using a dataset collected over six years and comprising a total review of 178,153 records from 2010 to 2015, the authors develop a Bayesian network (BN) model to analyze the influential inspection factors that lead to vessel detention.

The analysis includes data related to flag state, vessel type, recognized organization inspection body, and the vessel’s age. The results of this study guide PSC officials and vessel owners in identifying critical areas to improve maritime safety. The results promote environmental sustainability and help to create a cleaner environment by suggesting a similar methodological approach for future PSC inspections.

Recognizing that PSC is an important measure to improve maritime safety and reduce the number of shipping accidents, study [9] points out that some MoUs have started to implement a new inspection regime (NIR), but its effectiveness has yet to be investigated. Therefore, the study reviews the NIR effectiveness and the degree of improvement in vessel safety. As in the previously cited study, the authors use the BN model to determine the relationship between the NIR, vessel defects, detentions, and marine casualties and to examine the impact of the NIR on maritime safety. Study [10] analyzes the factors responsible for detaining vessels under PSC using the Grey Rational Analysis (GRA) model with increased entropy weighting to understand how different factors influence the decision to detain a vessel. Entropy-weighted GRA is an advanced technique for solving multi-criteria decision problems combining elements of GRA and entropy weighting. GRA is a part of the grey system theory, which Julong Deng developed [11]. The empirical analysis conducted is based on data on vessel detention in the Asia–Pacific region collected under the Tokyo MoU over the past ten years. Study [12] uses derived data from the vessel arrival reporting system to identify a specific type of inspection vessel using a combination of the GRA model and the entropy weight method (EWM). In this case study, different types of arriving vessels at five selected ports in Malaysia were analyzed to determine the possible outcome of vessel inspections. Based on 100,623 records of vessel arrivals collected over five years (2015–2019), the arriving vessels were identified, analyzed, evaluated, and assessed.

In study [13], the authors use a concentrated inspection campaign (CIC) derived from the PSC Addendum, i.e., a defined individual series of inspections of vessels for non-compliance carried out in three consecutive months at the end of each calendar year. The study uses GRA, TOPSIS (Technique for Order Preference by Similarity to Ideal Solution), and the MCDM method to analyze 71,376 records with 496 possible deficiency codes for 21 vessel types according to the Paris MoU, to improve the inspection pattern. This study combines the three-sigma rule to identify elements of vessel inspection that are unlikely to be met, based on the decisions of Member States’ Port Facility Security Officers (PFSOs). In study [14], the authors analyze PSC implemented by the port authority, i.e., the system for inspecting foreign vessels that enter the port and are detained because they do not meet the expected standards. The study analyzes the detection of critical deficiencies that influence the decision to detain the vessel by combining the cloud model, Criteria Interaction through the Inter-Criteria Correlation (CRITIC) method, and perspective theory. The cloud model is used to solve problems related to the possible uncertainties of the PSC inspection results, while the CRITIC method is used to determine the weighting values of defects and to describe the dependencies between different defects. In study [15], the authors use a variant of the Deck of Cards Method (DCM), which enables a subjective evaluation of decision-making by building an MCDA (multi-criteria decision analysis) model. The elements presented in the paper, from the criteria framework to the criteria scales, from the criteria value functions to the criteria weights, reflect the subjective judgment. Although the DCM was proposed by Simos [16], later improved by Figueira and Roy [17] and extended to other contexts by Corrente et al. [18], to determine the weighting of criteria in the originally conceived downloaded MCDA methods ELECTRE (Elimination and Choice Expressing Reality) and PROMETHEE (Preference Ranking Organization Method for Enrichment Evaluation), the DCM is used in this study to formalize the construction of the system MCDA model. However, the proposed model shows that the values lead to classifications that require additional input of data and resources by the PSC authorities, which is not always applicable.

Therefore, the authors of study [19] used data obtained through vessel inspections in the national ports of PSC to assess their compliance with radio traffic safety regulations by applying binary logistic regression. This study analyses the relationship between the severity of maritime communication deficiencies and some characteristics of the inspected vessels. To this end, the study uses 23,725 PSC inspection data and proposes several classification criteria to better assess the risk associated with maritime distress communication. This study uses regression to analyze inspection deficiencies associated with skill deficiencies among Global Maritime Distress and Safety System (GMDSS) operators.

Other studies [20] used and proposed other machine learning algorithms applicable in the shipping industry to evaluate the effectiveness of different machine learning algorithms, but did not analyze the details of each algorithm. The results of the cited study show that different machine learning algorithms can predict the braking performance of a 9500 TEU container vessel better than deviations based on a specific formula, resulting in a lower mean square error (MSE).

The implementation and evaluation of the classification tree model in PSC have been carried out in a series of case studies with empirical data that have been successfully implemented in different ports.

Paper [21] analyzes the spatio-temporal distribution of pollution caused by ships using large datasets from the Automatic Identification System (AIS). The authors analyze pollution patterns in the vicinity of ports and their impact on the marine environment. Using sophisticated analytical methods, the study emphasizes the importance of understanding these patterns to make informed decisions about the management of marine resources and the protection of the environment. The study also emphasizes the need for better monitoring and regulation of shipping traffic to reduce the negative impact on the ecosystem of ports.

Study [22] covers various machine learning methods, including classification decision trees, in the context of PSC. The research applies machine learning techniques, decision trees, and connectivity analyses to investigate the relationship between vessel selection in the pre-inspection phase and vessel defects in the inspection phase.

Research [23] incorporates unknown variables into a practical decision problem by predicting unknown variables using auxiliary data. The authors use the classical approach of model development by machine learning to generate point estimates in a deterministic decision technique. ML regression models are used for the prediction. The authors note that the quantitative objective is discrete and that the properties are analogous to the categorical objectives in the classification problems. Considering that it is much easier to describe and estimate the distribution of categorical variables than that of quantitative variables, this study innovatively proposes the use of random forest (RF) models in combination with regression and classification features to generate distributions of discrete quantitative targets. A review of previous research found that numerous studies have investigated the factors that influence the detention of vessels to suggest improvements to the effectiveness of PSC inspections. However, most investigations and studies rarely consider the three following aspects simultaneously: 1. the conditions under which offshore vessels are detained; 2. the application of mathematical methods and machine learning techniques, such as classification decision trees in combination with MCDM methods, to simplify the process of making decisions about the possibility of detaining the vessel; and 3. the application of methods that can predict whether or not a vessel with certain defects will be detained on the values of variables and the results of previous inspections. The aim of this study is therefore to create a systematic, robust, and accurate framework that combines classification trees and MCDM methods to identify the most important deficiencies in the inspection of offshore vessels and to predict whether a vessel will be detained based on these deficiencies and other variable factors.

The theoretical framework for analyzing the detention of vessels in ports comprises the theoretical knowledge of the importance of this process for the efficient management of maritime traffic. Vessel detention in ports directly impacts the business and economic performance of both vessels and ports. Additionally, detention can result in economic losses, logistical delays, and customer dissatisfaction. Therefore, it is crucial to identify the key factors for vessel detention to improve the overall efficiency of maritime transport.

The detention times of vessels have a direct impact on the utilization of port capacity, the optimal flow of cargo, and the speed of cargo handling. Understanding the importance of vessel detention in ports is crucial for the competitiveness of ports and the overall efficiency of maritime transport. Detention of vessels can be related to various deficiencies, such as technical problems, lack of human resources, administrative difficulties, or legal inadequacies. Technical deficiencies include inadequacies in equipment or infrastructure, while operational deficiencies may result from a lack of coordination of logistics processes. Legal and regulatory gaps can make it difficult to complete administrative procedures and customs formalities quickly.

Technical deficiency identification [24] is key to understanding the problem of vessel detention in ports. Operational deficiencies [25] refer to deficiencies in logistical processes or operational procedures that can slow down the detention of vessels in ports. Legal and regulatory deficiencies [26] refer to deficiencies in regulations, laws, or standards that may affect the detention of vessels in ports. The identification of these deficits is crucial for the development of strategies and measures to improve maritime transport as a whole.

Offshore vessels play an important role in various sectors, particularly in the oil and gas industry, and in other areas such as renewable energy, underwater research, rescue operations, and transport. The category of offshore vessels includes 1. drilling rigs; 2. support vessels, i.e., platform supply vessels (PSVs) and anchor handling supply vessels (AHTS); 4. construction and maintenance vessels; 5. tankers that can be used as floating production, storage, and offloading (FPSO) vessels; 6. research vessels; 7. renewable energy vessels; and 8. rescue vessels [27].

In this article, the deficiencies of offshore vessels are categorized by the practice and available provisions of SOLAS-ISM. Paris/Tokyo MoU [28] is only one of the determinants for classifying the “seriousness” of offshore vessel detention. The main determinants of the Tokyo MoU “deficiency” findings used in this paper are listed in

Table 1. Primary items of deficiency codes in Tokyo MoU.

Code	Description	Code	Description
01000	Certificates and Documentation	10000	Safety of Navigation
02000	Structural Conditions	11000	Life-Saving Appliances
03000	Water/Weathertight Conditions	12000	Dangerous Goods
04000	Emergency Systems	13000	Propulsion and Auxiliary Machinery
05000	Radio Communications	14000	Pollution Prevention
06000	Cargo Operations Including Equipment	15000	ISM (International Safety Management)
07000	Fire Safety	16000	ISPS (International Safety for Port and Vessels)
08000	Alarms	99000	Other
09000	Working and Living Conditions	18000	Labor Conditions

[29].

Classification decision trees are popular machine learning algorithms used for classification and prediction. There are several types of classification and regression decision tree algorithms, but some of the best-known and most commonly used are as follows:

• “rpart” (Recursive Partitioning and Regression Trees) [30] is used for classification and regression. CART (Classification and Regression Trees) [31] is a method for creating classification and regression trees for forecasting and modeling. CHAIN (Classification Hierarchy Analysis) [32,33] is not a standard method like “rpart” or CART.

In this study, the authors opted for a combination of the “rpart” classification decision tree and the TOPSIS multi-criteria decision method.

MCDM is a decision-making process in which several factors or criteria must be considered. The characteristics of this approach include analyzing several alternatives, quantifying the criteria, ranking the options, and finding the optimal solution. This process can be complex, as several parameters need to be simultaneously evaluated, and various methods are used to facilitate decision-making in such situations. The review of previous research presented in the second chapter of this article has shown that MCDM is increasingly present in the nautical industry, especially in the processes related to keeping vessels in port. Many studies have focused on method development and techniques that can improve the efficiency of decision-making in this context.

The benefits of applying MCDM to the detention of offshore vessels in port include the possibility of better decision-making, more efficient use of resources, and optimization of performance. However, challenges include the complexity of the criteria analysis process, the need for model validation, and adaptation to changing conditions. It is important to carefully balance the benefits and challenges to achieve optimal management of this process.

Some of the best-known methods of MCDM are as follows:

• AHP [34] is a method for structuring complex decisions in a hierarchical form. Criteria and alternatives are compared in pairs, and the result is a weighting of the criteria and alternatives that enables a decision to be made.
• TOPSIS [35] is a method based on the concept that the best alternative is the one that is closest to the ideal solution and furthest from the worst solution. The distance of each alternative to the ideal and anti-ideal solution is calculated.
• ELECTRE [36] is a method that uses the concept of dominance to compare alternatives. It considers the weighting of the criteria and the dominant relationships between the alternatives. PROMETHEE [37] is a method based on the comparison of pairs of alternatives and the expression of preferences for each alternative. The result represents the ranking of alternatives according to overall preferences. SAW (Simple Additive Weighting) [38] is a method in which each alternative is assigned an overall value resulting from the sum of the weighted scores for each criterion. The alternatives are ranked based on these totals.

3. Methodological Approach of Integration of Classification Trees and MCDM Methods in PSC

By integrating classification models and MCDM into the port management process of offshore vessels, it is possible to combine the advantages of both approaches for more efficient decision-making. Classification models provide a structure for data analysis, while MCDM incorporates different parameters and priorities into the decision-making process. This integration improves the quality of decisions and optimizes processes to keep vessels in port.

There are various methods for integrating classification models and MCDM into the port laytime process. The combination of methods aims to combine the advantages of classification models and MCDM for a more efficient and accurate decision-making process.

The “rpart” classification tree algorithm and the TOPSIS MCDM method are used in this study.

The algorithm “rpart” (Revised Partitioning Algorithm) [39] uses a decision tree approach for classification and regression. The steps of the procedure are as follows:

• Selection of the best partitioning:
  • The algorithm starts with the entire data training set as the root.
  • For each variable, the best partitioning is calculated, i.e., the point that divides the data into two parts with the largest difference in target values. Criteria such as the Gini index or entropy (information gain) are used for classification [40].
• Division of the data: The data are divided into two parts according to the best split. This process is repeated recursively for each new node.
• Creating leaves: The splitting process continues until each node fulfills a stop criterion (e.g., minimum number of samples in a leaf, maximum tree depth, or if further splitting does not bring any significant improvement).
• Assignment of classes to nodes: The leaves are classified according to the majority class of the data or according to the mean for regression tasks.
• Pruning of neighborhoods: To reduce the complexity of the tree and avoid overfitting, pruning can be performed. This is carried out using methods such as “cost-complexity pruning” [41].

TOPSIS is a method for organizing alternatives according to several criteria. The steps of the TOPSIS method include the following:

• Creating a decision matrix—creating a matrix that contains the scores for all alternatives according to all criteria.
• Normalizing the matrix “$r_{ij}$” (total dataset: number of alternatives ($i)$ × number of variables $\left(j\right)$) by eliminating the unit of measurement, e.g., by vector normalization:

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

  (1)

  where $x_{ij}$ is the value of alternative $i$ according to criterion $j$.
• Creation of a weighted, normalized matrix and use of weighting criteria:

  $${\vartheta }_{ij}={\omega }_j·d_{ij}$$

  (2)

  where ${\omega }_j$ is the weight of criterion j.
• Identification of ideal and anti-ideal points: The ideal solution $A^{*}$ (best possible) and the anti-ideal solution $A^{-}$ (worst possible) are determined as follows:

  $$A^{*}=\vartheta 1\ast , \vartheta 2\ast ,\dots ,\vartheta n\ast$$

  (3)

  and

  $$A^{-}=\left\{{\vartheta }_1^{-},{\vartheta }_2^{-},\dots ,{\vartheta }_n^{-}\right\}$$

  (4)

  where ${\vartheta }_1^{*}$ and ${\vartheta }_1^{-}$ are the maximum and minimum values for criterion $j$.
• Calculating the distance from the ideal Equation (5) and anti-ideal Equation (6) point: The distance of each alternative from the ideal and anti-ideal solution is calculated using the Euclidean distance:

  $$D_i^{*}=\sqrt{{{\displaystyle \sum }}_{j=0}^n{\left({\vartheta }_{ij}-{\vartheta }_j^{*}\right)}^2}$$

  (5)

  $$D_i^{-}=\sqrt{{\displaystyle \sum }_{j=0}^n{\left({\vartheta }_{ij}-{\vartheta }_j^{-}\right)}^2}$$

  (6)
• Calculation of the relative approximation to the ideal solution Equation (7): The relative proximity of the individual alternatives to the ideal solution is calculated as follows:

  $$C_i^{*}={\displaystyle \frac{D_i^{-}}{D_i^{*}+D_i^{-}}}$$

  (7)

  where $C_i^{*}$ is between 0 and 1. Higher values indicate a better alternative.
• The alternatives are categorized by ranking the values of $C_i^{*}$ from the highest to the lowest.

4. Research Methodology

The methodological approach pursued in this paper comprises several steps shown by a block diagram (Figure 1).

• Collect vessel data:

  -

  Input: vessel data (e.g., vessel type, inspection history, equipment condition, and regulatory compliance);

  -

  Description: Collect all relevant information about the vessel to be used for the analysis.

• Preparation of the data

  -

  Input: Raw data about the vessel;

  -

  Processes: Data cleansing, normalization, and transformation;

  -

  Output: Clear and formatted data, ready for analysis.

• Application of the “rpart” classification model:

  -

  Input: Prepared data;

  -

  Processes:

  Training: use the data to train the “rpart” model.

  Prediction: Use the trained model to predict whether the vessel needs to be detained.

  -

  Output: Predict whether the vessel should be detained or not (e.g., “Yes” or “No”).

• Combination with the TOPSIS method:

  -

  Input: Predictions from the “rpart” model as well as additional criteria (e.g., safety and environmental impact).

  -

  Operations:

  Normalization and weighting of criteria;

  Calculation of ideal and anti-ideal solutions;

  Calculation of the distance to the ideal and anti-ideal solution;

  Ranking of alternatives.

  -

  Output: Ranking of the alternatives and final result (e.g., recommendation to keep or not to keep the ship).

• Making the decision:

  -

  Input: Ranking results of the TOPSIS method;

  -

  Work steps: Analyze the results and make a decision on whether to keep the vessel;

  -

  Output: Decision (e.g., “Detain the vessel” or “‘Don’t detain the vessel”).

• Report:

  -

  Input: The decision made based on the analysis;

  -

  Processes: Creation of reports for PSC (Port State Control) with an explanation of the decision;

  -

  Output: Report for PSC.

4.1. Dataset Description

The input dataset is represented by the matrix $X=\left[x_{ij}\right], i=1,\dots m;j=1,2\dots ,n,$ where $m$ is the number of observed instances (alternative or inspection of offshore vessels) and $n$ is the number of observed variables.

The source of the data used in this empirical study on the detention and control of offshore vessels is EQUASIS [42]. The input dataset consists of data on 405 inspections and 27 variable values. Since one of the variables is the name of the vessel, this variable is ignored in the following to avoid possible legal issues.

The target variable in the formation of the decision tree is “Detention” and it takes the values “Yes” or “No”. If the offshore vessel is detained, this specification has the value “Yes” for a specific dataset describing the inspection, otherwise “No”. The total number of recorded inspections that make up the input dataset is 405, of which 40 offshore vessels were detained and 365 were not.

Table 2. Variable number (Var No), variable name, representation and description, type, and possible values or range.

Var No	Variable_Name	Representation and Description	Type	Possible Values/ Range
1	Detention	Vessel Detention	Character	Yes/No
2	InitialInspection	Initial Inspection	Integer	[0, 1]
3	MoreDetailedInspection	More Detailed Inspection	Integer	[0, 1]
4	FollowUpInspection	Follow-Up Inspection	Integer	[0, 1]
5	StandardInspection	Standard Inspection	Integer	[0, 1]
6	NumberOfInspections	Number Of Inspections	Integer	[0, 1]
7	NumberOfDeficiency	Number Of Deficiency	Integer	[0, 38]
8	ISM	ISM Deficiency	Integer	[0, 31]
9	MARPOL	MARPOL Deficiency	Integer	[0, 3]
10	CertificateDocumentation	Certificate and Documentation Deficiency	Integer	[0, 4]
11	PropulsionAuxiliaryMachinery	Propulsion Auxiliary Machinery Deficiency	Integer	[0, 10]
12	SafetyOfNavigation	Safety Of Navigation Deficiency	Integer	[0, 2]
13	RadioCommunications	Radio Communications Deficiency	Integer	[0, 5]
14	EmergencySystems	Emergency Systems Deficiency	Integer	[0, 3]
15	FireSafety	Fire Safety Deficiency	Integer	[0, 4]
16	MLC	MLC Deficiency	Integer	[0, 5]
17	Alarms	Alarms Deficiency	Integer	[0, 1]
18	ISPS	ISPS Deficiency	Integer	[0, 5]
19	OtherTypeofDeficiencies	Other Types of Deficiencies	Integer	[0, 1]
20	WaterWeatherTightConditions	Water/Weathertight Condition Deficiency	Integer	[0, 6]
21	LifeSavingAppliances	Life-Saving Appliances Deficiency	Integer	[0, 2]
22	GT	GT—Gross tonnage of the offshore vessel	Integer	[2012, 80106]
23	CountryOfInspection (COI)	Country Of Inspection of the offshore vessel	Character	1 of 36 Countries
24	Flag	Offshore vessel’s flag	Character	1 of 30 Flags
25	MoU	Memorandum of Understanding	Character	1 of 10 MoUs
26	YOB	Year of offshore vessel built	Character	1 of 26 YOBs

,

Table 3. Variable name and count of instances grouped by the variable Detention = “No” and Detention = “ Yes”.

Variable Name	All Dataset			Detention No			Detention Yes
	Total	=0	=1	Total	=0	=1	Total	=0	=1
InitialInspection	405	192	213	365	172	193	40	20	20
FollowUpInspection	405	399	6	365	359	6	40	40	0
StandardInspection	405	399	6	365	362	3	40	37	3
ISPS	405	398	7	365	360	5	40	38	2

,

Table 4. Variable name, and count of instances grouped by the variable Detention = “No” and Detention = “ Yes”.

No	Variable_Name	All Dataset				Detention No				Detention Yes
		Total	=0	=1	>1	Total	=0	=1	>1	Total	=0	=1	>1
1	MoreDetailedInspection	405	238	165	2	363	214	149	2	40	24	16	0
2	NumberOfInspections	405	0	16	389	365	0	15	350	40	0	1	39
3	NumberOfDeficiency	405	6	84	315	365	6	80	279	40	0	4	36
4	ISM	405	319	68	18	365	290	64	11	40	29	4	7
5	MARPOL	405	319	68	18	365	290	64	11	40	29	4	7
6	CertificateDocumentation	405	189	114	102	365	177	105	83	40	12	9	19
7	PropulsionAuxiliaryMachinery	405	381	19	5	365	346	18	1	40	35	1	4
8	SafetyOfNavigation	405	267	100	38	365	253	87	25	40	14	13	13
9	RadioCommunications	405	349	47	9	365	322	37	6	40	27	10	3
10	EmergencySystems	405	354	43	8	365	323	38	4	40	31	5	4
11	FireSafety	405	251	109	45	365	235	98	32	40	16	11	13
12	MLC	405	328	50	27	365	305	42	18	40	23	8	9
13	Alarms	405	391	11	3	365	357	7	1	40	34	4	2
14	OtherTypeofDeficiencies	405	306	79	20	365	282	65	18	40	24	14	2
15	WaterWeatherTightConditions	405	375	25	5	365	342	20	3	40	33	5	2
16	LifeSavingAppliances	405	306	67	32	365	280	60	25	40	26	7	7

,

Table 5. “GT”—gross tonnage of the offshore vessel; its minimum, mean, and maximum values are grouped by Detention = “No” and Detention = “ Yes”.

	Dataset			Detention No			Detention Yes
GT	Min	Mean	Max	Min	Mean	Max	Min	Mean	Max
	2012	4939.3	80106	2012	5032.8	80106	2012	4086.6	6776

,

Table 6. Country Of Inspection (COI) (36 different occurrences), count of instances grouped by the variable Detention = “No” and Detention = “ Yes”.

No	COI	All Dataset			Detention No			Detention Yes
		Total	=0	=1	Total	=0	=1	Total	=0	=1
1	Australia	405	360	45	365	328	37	40	32	8
2	Brazil	405	404	1	365	364	1	40	40	0
3	Bulgaria	405	402	3	365	362	3	40	40	0
4	China	405	393	12	365	355	10	40	38	2
5	Colombia	405	403	2	365	363	2	40	40	0
6	Cyprus	405	372	33	365	333	32	40	39	1
7	Denmark	405	387	18	365	347	18	40	40	0
8	Egypt	405	399	6	365	360	5	40	39	1
9	France	405	403	2	365	363	2	40	40	0
10	Germany	405	400	5	365	361	4	40	39	1
11	Ghana	405	402	3	365	362	3	40	40	0
12	Greece	405	399	6	365	361	4	40	38	2
13	Hong Kong	405	403	2	365	363	2	40	40	0
14	India	405	403	2	365	363	2	40	40	0
15	Israel	405	398	7	365	360	5	40	38	2
16	Italy	405	402	3	365	362	3	40	40	0
17	Japan	405	403	2	365	363	2	40	40	0
18	Malaysia	405	403	2	365	363	2	40	40	0
19	Malta	405	387	18	365	347	18	40	40	0
20	Morocco	405	404	1	365	364	1	40	40	0
21	Netherlands	405	389	16	365	350	15	40	39	1
22	New Zealand	405	403	2	365	365	0	40	38	2
23	Nigeria	405	399	6	365	363	2	40	36	4
24	Norway	405	387	18	365	352	13	40	35	5
25	Poland	405	404	1	365	364	1	40	40	0
26	Romania	405	403	2	365	363	2	40	40	0
27	Russia	405	399	6	365	359	6	40	40	0
28	Singapore	405	381	24	365	344	21	40	37	3
29	South Africa	405	403	2	365	363	2	40	40	0
30	Spain	405	389	16	365	349	16	40	40	0
31	Sweden	405	403	2	365	363	2	40	40	0
32	Thailand	405	403	2	365	363	2	40	40	0
33	Trinidad and Tobago	405	404	1	365	364	1	40	40	0
34	Tunisia	405	398	7	365	359	6	40	39	1
35	United Kingdom	405	286	119	365	249	116	40	37	3
36	United States of America	405	397	8	365	361	4	40	36	4

,

Table 7. Flag—offshore vessel’s flag (30 different appearances); count of instances grouped by the variable Detention = “No” and Detention = “ Yes”.

No	Flag	All Dataset			Detention No			Detention Yes
		Total	=0	=1	Total	=0	=1	Total	=0	=1
1	Azerbaijan	405	401	4	365	361	4	40	40	0
2	Bahamas	405	385	20	365	347	18	40	38	2
3	Belgium	405	394	11	365	355	10	40	39	1
4	Belize	405	403	2	365	365	0	40	38	2
5	Brazil	405	375	30	365	337	28	40	38	2
6	Canada	405	384	21	365	346	19	40	38	2
7	Cyprus	405	393	12	365	353	12	40	40	0
8	Denmark	405	387	18	365	347	18	40	40	0
9	Egypt	405	404	1	365	364	1	40	40	0
10	France	405	392	13	365	352	13	40	40	0
11	Germany	405	404	1	365	365	0	40	39	1
12	Gibraltar	405	385	20	365	345	20	40	40	0
13	Greece	405	384	21	365	344	21	40	40	0
14	Liberia	405	395	10	365	360	5	40	35	5
15	Luxembourg	405	375	30	365	336	29	40	39	1
16	Malaysia	405	400	5	365	362	3	40	38	2
17	Malta	405	386	19	365	346	19	40	40	0
18	Marshall Islands	405	401	4	365	363	2	40	38	2
19	Mexico	405	392	13	365	354	11	40	38	2
20	Nigeria	405	402	3	365	363	2	40	39	1
21	Norway	405	358	47	365	319	46	40	39	1
22	Panama	405	401	4	365	362	3	40	39	1
23	Russia	405	397	8	365	358	7	40	39	1
24	Singapore	405	400	5	365	361	4	40	39	1
25	St Vincent and Grenadines	405	396	9	365	359	6	40	37	3
26	Tuvalu	405	398	7	365	358	7	40	40	0
27	United Arab Emirates	405	402	3	365	362	3	40	40	0
28	United Kingdom	405	399	6	365	361	4	40	38	2
29	United States of America	405	403	2	365	364	1	40	39	1
30	Vanuatu	405	349	56	365	316	49	40	33	7

,

Table 8. Memorandum (MoU) variable (10 different appearances), count of instances grouped by the variable Detention = “No” and Detention = “ Yes”.

No	MoU	All Dataset			Detention No			Detention Yes
		Total	=0	=1	Total	=0	=1	Total	=0	=1
1	Abuja	405	395	10	365	359	6	40	36	4
2	Black	405	404	1	365	364	1	40	40	0
3	Black Sea	405	402	3	365	362	3	40	40	0
4	Caribbean	405	404	1	365	364	1	40	40	0
5	Indian Ocean	405	379	26	365	343	22	40	36	4
6	Mediterranean	405	358	47	365	323	42	40	35	5
7	Paris	405	171	234	365	343	22	40	31	9
8	Tokyo	405	333	72	365	304	61	40	29	11
9	US Coastguard	405	397	8	365	361	4	40	36	4
10	Vina Del Mar	405	402	3	365	362	3	40	40	0

and

Table 9. YOB—Year of offshore vessel built (26 different appearances), count of instances grouped by the variable Detention = “No” and Detention = “ Yes”.

No	YOB	All Dataset			Detention No			Detention Yes
		Total	=0	=1	Total	=0	=1	Total	=0	=1
1	1992	405	404	1	365	364	1	40	40	0
2	1997	405	404	1	365	364	1	40	40	0
3	1998	405	396	9	365	356	9	40	40	0
4	1999	405	387	18	365	347	18	40	40	0
5	2001	405	401	4	365	361	4	40	40	0
6	2002	405	388	17	365	351	14	40	37	3
7	2003	405	398	7	365	360	5	40	38	2
8	2005	405	389	16	365	349	16	40	40	0
9	2006	405	380	25	365	343	22	40	37	3
10	2007	405	388	17	365	348	17	40	40	0
11	2008	405	395	10	365	356	9	40	39	1
12	2009	405	389	16	365	349	16	40	40	0
13	2010	405	372	33	365	335	30	40	37	3
14	2011	405	366	39	365	330	35	40	36	4
15	2012	405	348	57	365	320	45	40	28	12
16	2013	405	366	39	365	332	33	40	34	6
17	2014	405	377	28	365	337	28	40	40	0
18	2015	405	383	22	365	346	19	40	37	3
19	2016	405	380	25	365	341	24	40	39	1
20	2017	405	399	6	365	359	6	40	40	0
21	2018	405	402	3	365	362	3	40	40	0
22	2019	405	403	2	365	363	2	40	40	0
23	2020	405	403	2	365	365	0	40	38	2
24	2021	405	404	1	365	364	1	40	40	0
25	2022	405	400	5	365	360	5	40	40	0
26	2023	405	403	2	365	363	2	40	40	0

describe all variables that define their type, range, or mean value, and the number of occurrences grouped according to the values of the variable “Detention”.

Standardization or normalization of data is not required when most of the data are on the same scale (the case in this research). The criteria are in the same range, so no additional scaling is required. Furthermore, algorithms such as decision trees, random forests, or Naive Bayes do not rely on distances between the data and therefore do not require standardization or normalization. These algorithms work on the principle of decision rules, so differences in the scaling do not affect their accuracy. The TOPSIS method, on the other hand, requires normalization of the data in the first step of the approach.

4.2. Implementation Methodology

For the application of the decision tree algorithm “rpart” and the MCDM TOPSIS method (which only uses numerical values of the letter variables “Detention”, “Country of detention”, “Flag”, and “MoU” and the numerical value “YOB”), these are converted into so-called “dummy” variables [43]. In this way, both algorithms can use the same data structure and group the occurrence of each value by the variable “Detention”, which can have the value “Yes” or “No”. Dummy variables are a useful tool to translate categorical data into a form that can be used by machine learning algorithms. This is necessary because most machine learning algorithms are designed for numerical inputs. Furthermore, the use of dummy variables avoids the problem of introducing a wrong order or ordinality between the categories, which could happen if the categories were converted directly to integers. Each new variable can have the values 0 or 1, with 1 indicating the presence of a particular category.

When applying the TOPSIS method, the data from all 405 alternatives and 125 variables were used. Based on the frequency of occurrence for the entire set of input data, grouped by the variable “Detention”, the criteria and the target (impact) of each criterion are defined. When using the TOPSIS method, the text variable “Detention” is also converted into a numerical value, as the TOPSIS method can only process numerical values. For this reason, there is one more variable (125) in the TOPSIS method than in the creation of a classified decision tree.

The list of all variables (125) used in the TOPSIS method with the assigned weighting values and “impact” can be found in

Table 10. The list of all variables, assigned weight (W), and impact (I) in the TOPSIS method.

Variable Name	W	I	Variable Name	W	I	Variable Name	W	I	Variable Name	W	I
InitialInspection	20	-	COI_Greece	5	+	Flag Denmark	1	+	MoU Vina Del Mar	1	+
MoreDetailedInspection	16	-	COI_HongKong	1	+	Flag Egypt	1	+	YOB_1992	1	+
Follow-UpInspection	1	-	COI_India	1	+	Flag France	1	+	YOB_1997	1	+
StandardInspection	3	-	COI_Israel	5	+	Flag Germany	2	+	YOB_1998	1	+
NumberOfinspections	39	-	COI_Italy	1	+	Flag Gibraltar	1	+	YOB_1999	1	+
NumberOfDeficiency	36	-	COI_Japan	1	+	Flag Greece	1	+	YOB_2001	1	+
ISM	7	-	COI_Malaysia	1	+	Flag Liberia	10	+	YOB_2002	2	+
MARPOL	7	-	COI_Malta	1	+	Flag Luxembourg	2	+	YOB_2003	3	+
CertificateDocumentation	19	-	COI_Morocco	1	+	Flag Malaysia	3	+	YOB_2005	4	+
PropulsionAuxiliaryMachinery	4	-	COI_Netherlands	3	+	Flag Malta	1	+	YOB_2006	5	+
SafetyOfNavigation	13	-	COI_NewZealand	5	+	Flag Marshall Islands	3	+	YOB_2007	6	+
RadioCommunications	3	-	COI_Nigeria	10	+	Flag Mexico	3	+	YOB_2008	7	+
EmergencySystems	4	-	COI_Norway	1	+	Flag Nigeria	2	+	YOB_2009	8	+
FireSafety	13	-	COI_Poland	1	+	Flag Norway	2	+	YOB_2010	9	+
MLC	9	-	COI_Romania	1	+	Flag Panama	1	+	YOB_2011	11	+
Alarms	2	-	COI_Russia	1	+	Flag Russia	1	+	YOB_2012	12	+
ISPS	2	-	COI_Singapore	1	+	Flag Singapore	1	+	YOB_2013	6	+
OtherTypeOfDeficiencies	2	-	COI_SouthAfrica	1	+	Flag_St Vincent and Grenadines	1	+	YOB_2014	1	+
WaterWeatherTightConditions	2	-	COI_Spain	1	+	Flag Tuvalu	1	+	YOB_2015	3	+
LifeSavingAppliances	7	-	COI_Sweden	1	+	Flag_United Arab Emirates	0.1	+	YOB_2016	1	+
GT	3	-	COI_Thailand	1	+	Flag_UnitedKingdom	1	+	YOB_2017	1	+
COI_Australia	25	+	COI_TrinidadandTobago	1	+	Flag_UnitedStatesofAmerica	1	+	YOB_2018	1	+
COI_Brazil	1	+	COI_Tunisia	3	+	Flag Vanuatu	1	+	YOB_2019	1	+
COI_Bulgaria	1	+	COI_UnitedKingdom	5	+	MoU Abuja	4	+	YOB_2020	5	+
COI_ChinaPeoplessRepublic	5	+	COI_UnitedStatesofAmerica	10	+	MoU_Black	1	+	YOB_2021	1	+
COI_Colombia	1	+	Flag_Azerbaijan	1	+	MoU_Black Sea	1	+	YOB_2022	1	+
COI_Cyprus	3	+	Flag_Bahamas	3	+	MoU_Caribbean	1	+	YOB_2023	1	+
COI_Denmark	1	+	Flag_Belgium	2	+	MoU_Indian Ocean	4	+	Detention_0	10	-
COI_Egypt	3	+	Flag_Belize	3	+	MoU_Mediterranean	1	+	Detention_1	100	+
COI_France	1	+	Flag_Brazil	3	+	MoU_Paris	12	+
COI_Germany	3	+	Flag_Canada	3	+	MoU_Tokyo	11	+
COI_Ghana	1	+	Flag_Cyprus	1	+	MoU_US CoastGuard	4	+

. The weighting values of each criterion and the “target” effect (min = “-”; max = “+”) of each of the 125 variables in the TOPSIS method are determined based on the number of occurrences in the input dataset. Larger values are assigned to variables that appear more than once in the input dataset when the vessel is detained, i.e., when “Detention” = Yes.

The implementation of the classification tree and MCDM TOPSIS methods in this work was carried out using several R packages [44,45].

The complexity of algorithms that combine “rpart” and the TOPSIS method can be analyzed separately for each algorithm and then integrated to obtain the overall complexity of the combined approach.

“rpart” is an implementation of the classification decision tree algorithm. The complexity of this algorithm depends on several factors: Number of instances (N): total number of samples in the training set. Number of attributes (M): number of attributes or features in the data. Tree depth (D): the depth of the final tree.

For most implementations, the complexity of the “rpart” algorithm can be roughly estimated as O(N * M * log N), where 1. the algorithm traverses all data instances (N) and all attributes (M) to compute the optimal splitting points; 2. the logarithmic factor results from the process of building the tree, where the splitting of the data on each branch can be considered as a binary search.

The TOPSIS method involves several steps, each of which has its complexity: 1. normalization of the data matrix: if there are m alternatives and n criteria, the normalization has a complexity of O(m * n). 2. The weighting of the normalized matrix: this is also O(m * n), since each element of the matrix is multiplied by the corresponding weight. 3. Calculating the distance to the ideal and anti-ideal solution: this involves summing the differences for each alternative, which has a complexity of O(m * n). 4. Ranking the alternatives: the complexity of the ranking is O(m * log m).

The overall complexity of the TOPSIS method can be approximated as O(m * n), since all steps are linear concerning the number of alternatives and criteria.

The combined complexity depends on the order in which these methods are applied and on their mutual interactions. If “rpart” is first applied to identify relevant alternatives and then TOPSIS to rank them, the overall complexity can be a combination of the individual complexities: “rpart” complexity: O(N * M * log N). TOPSIS complexity: O(m * n), where m is the number of alternatives that come from the “rpart” analysis.

Assuming that m is approximately N (the number of alternatives remaining after the “rpart” analysis), the combined complexity can be O(N\*M\*logN) + O(N\*n).

In practice, this combined complexity can be higher, especially if M and n are large or if multiple iterations are required between these steps. Ultimately, the importance of these factors depends on the specific implementation and data size, but this provides a framework for considering the overall complexity of combining “rpart” and TOPSIS methods.

5. Results

In this case study, the input dataset (405 instances of inspection of the offshore vessels × 125 variables) is randomly divided into a training and testing dataset in a ratio of 70:30. The test dataset accounts for 30% of the total data and is used to evaluate the model after it has been trained. This joint step is performed for several important reasons:

• It makes it possible to evaluate the model’s performance using data that the model did not see during training. This gives a better picture of how the model generalizes to new, unknown data.
• Avoidance of overfitting. Since the model is only trained on one dataset, there is a risk that it will overfit the specifics of that dataset. The test dataset is used to check whether the model generalizes well or whether it has only learned the specific features of the training dataset.
• Validation of model selection, as different models and their parameters can be compared using a test dataset. This way, the best model can be selected and its hyperparameters optimized. Hyperparameters are parameters that are used to control the process of machine learning models. They are preset and do not change during model training. In contrast to model parameters that are learned from the data, hyperparameters are usually set before training and influence model performance.
• Data partitioning enables the evaluation of various model performance metrics (such as Accuracy, Precision, Recall, etc.) against the test dataset. These metrics help to understand how effective the model is in real-life situations.

Sometimes a third dataset, called the validation dataset, is also used to tune the model’s hyperparameters and select a better model during training. The dataset is used for the final evaluation. The training dataset for the “rpart” classification decision tree therefore consists of 283 instances and the test dataset of 122 (possible alternatives). Both datasets have 123 independent variables, while the variable “Detention” is a target variable that can have a value of 0 (no) and 1 (yes).

The textual and graphical (Figure 2) expression of the “rpart” decision tree model in R is interpreted as follows.

Textual representation of the model result:

The expression presented in

Table 11. Decision tree results interpretation.

n = 283 node), split, n, loss, yval, (yprob) * denotes terminal node 1) root 283 31 0 (0.89045936 0.10954064) 2) NumberOfDeficiency < 6.5 233 10 0 (0.95708155 0.04291845) * 3) NumberOfDeficiency >= 6.5 50 21 0 (0.58000000 0.42000000) 6) NumberOfinspections >= 6.5 35 10 0 (0.71428571 0.28571429) * 7) NumberOfinspections < 6.5 15 4 1 (0.26666667 0.73333333) *	1): Identification of the node (root node). root: The root node of the tree. 283: Number of instances in the root node (entire training dataset). 31: Number of incorrectly classified examples if all examples are classified as class 0. 0: Class prediction (highest probability) at the root node. (0.89045936 0.10954064): Probabilities for each class (class 0: 89.05%, class 1: 10.95%).	2): Identification of the node. Number of Deficiency < 6.5: Rule for division (if the Number of Deficiency is less than 6.5, go to this node). 233: Number of instances in this node. 10: Number of misclassified examples if all are classified as class 0. 0: Class prediction (class 0). (0.95708155 0.04291845): Probabilities for each class (class 0: 95.71%, class 1: 4.29%). *: Marking that the node is terminal (leaves).
3): Node identification. Number Of Deficiency >= 6.5: Rule for the subdivision (if the Number Of Deficiency is greater than or equal to 6.5, go to this node). 50: Number of instances in this node. 21: Number of misclassified examples if all are classified as class 0. 0: Class prediction (class 0). (0.58000000 0.42000000): Probabilities for each class (class 0: 58%, class 1: 42%).	6): Identification of the node. Number of Inspections >= 6.5: Splitting rule (if Number Of Deficiency is greater than or equal to 6.5, go to this node). 35: Number of instances in this node. 10: Number of misclassified examples if all are classified as class 0. 0: Class prediction (class 0). (0.71428571 0.28571429): Probabilities for each class (class 0: 71.43%, class 1: 28.57%). *: Marking that the node is terminal (leaves).	7): Identification of the node. Number of Inspections < 6.5: Splitting rule (if the Number of Inspections is less than 6.5, go to this node). 15: Number of instances in this node. 4: Number of misclassified examples if all are classified as class 1. 1: Class prediction (class 1). (0.26666667 0.73333333): Probabilities for each class (class 0: 26.67%, class 1: 73.33%). *: Marking that the node is an end node (leaves).

describes how the decision tree uses the Number of Deficiency and the Number of Inspections to classify data into two classes (Detention) (0—No; 1—Yes), and how decisions are made based on these attributes.

node: Identification of the node in the tree.

split: The rule used to split the data in this node.

n: Number of instances in this node.

loss: The number of instances that would be misclassified if all instances in a node were classified according to the majority class.

yval: Class prediction in this node.

(yprob): Probability for each class in this node.

indicates an end node: Indication that the node is an end node (leaf) and does not subdivide further.

The reason for using a threshold of 7 for the “Number Of Deficiency” and the “Number of Inspections” is to round off and simplify the interpretation of the results. In practice, the threshold value of 7 is used as an integer value, which is intuitive and easier to interpret when making decisions. However, in the analyses, the threshold of 6.5 is used as a more precise, numerical threshold derived from statistical models and data analyses.

The difference between the thresholds in these parts of the text reflects different aspects of data interpretation—one is more a function of rounding to simplify interpretation, the other for the precision of analysis.

The model created this way with the training dataset was tested with the test dataset. The result of the prediction of a possible outcome is shown in a confusion matrix.

A confusion matrix [46] is an instrument for evaluating the performance of a classification model. It helps to understand how the model categorizes the examples and makes it possible to identify the types of errors that the model makes.

-

Actual 0: Actual examples of class 0.

-

Actual 1: Actual examples of class 1.

-

Predicted 0: Examples predicted by the model as class 0.

-

Predicted 1: Examples predicted by the model as class 1.

Elements of the confusion matrix interpretation (

Table 12. Confusion matrix.

	Predicted 0	Predicted 1
Actual 0	110	3
Actual 1	5	4

):

• True positives (TPs): number of true positive examples correctly categorized as positive by the model (4 (Actual 1, Predicted 1));
• True negatives (TNs): Number of true negative examples correctly categorized as negative by the model (110 (Actual 0, Predicted 0));
• False positives (FPs): The number of true negative examples the model incorrectly categorized as positive (3 (Actual 0, Predicted 1));
• False negative (FN): The number of true positive examples the model incorrectly categorized as negative (5 (Actual 1, Predicted 0)).

This means the following: for 110: out of 113 real negative examples (class 0), the model correctly categorized 110 as negative; 3: out of 113 real negative examples (class 0), the model categorized 3 as positive; out of 9 real positive examples (class 1), the model correctly categorized 4 as positive; 5: out of 9 real positive examples (class 1), model 5 incorrectly categorized as negative.

The metric derived from the confusion matrix is the proportion of correctly classified examples from the classification decision tree (“rpart”) for the test dataset, which is calculated according to Equation (8)

$$Accuracy={\displaystyle \frac{TP+TN}{TP+TN+FP+FN}}={\displaystyle \frac{110+4}{110+4+3+5}}\approx 0.934$$

(8)

Precision is defined by Equation (9) and has a value of 0.57143, Specificity is defined by Equation (10) and has a value of 0.97345, while Recall is defined by Equation (11) and has a value of 0.4444. F1 Score is defined by Equation (12) and has a value of 0.5.

$$Precision={\displaystyle \frac{TP}{TP+FP}}={\displaystyle \frac{4}{4+3}}\approx 0.571$$

(9)

$$Specificity={\displaystyle \frac{TN}{TN+FP}}={\displaystyle \frac{110}{110+3}}\approx 0.973$$

(10)

$$Recall={\displaystyle \frac{TP}{TP+FN}}={\displaystyle \frac{4}{5+5}}\approx 0.444$$

(11)

$$F1 Score=2·{\displaystyle \frac{Precision\times Recall}{Precision+Recall}}=0.5$$

(12)

The F1 Score—Equation (12)—is a performance measure of the classification model that represents the harmonic mean between Precision and Recall. It is used when there is an imbalance between the classes and when both Precision and Recall are important. The F1 Score is useful to achieve a balance between Precision and Recall and not just optimize one of these parameters. So, an F1 Score with a value of 0.5 indicates a trade-off between Precision and Recall. Since the Precision has a value of 57.14%, the predictions labeled as positive by the model are positive. The model correctly identified 44.44% of the actual positive instances. If the F1 Score is low (as in this case), this indicates a significant number of false positive or false negative predictions or even both. Depending on the application context, such performance can sometimes be unacceptable, especially if the consequences of prediction errors are severe.

The reason for this may be that only 10% of the total dataset contains truly positive values, namely 40 (for Detention = 1) and 365 (for Detention = 0).

The F1 Score, which has a value of 0.5, shows that both the Precision and the Recall are quite low and that the “rpart” model is not particularly efficient. For this reason, the MCDM method TOPSIS is used in the next phase.

Of course, these metrics allow a comprehensive analysis of the performance of the “rpart” classification model and help to evaluate how effective the model is in solving a given classification problem with a classification decision tree.

Based on the assigned weights (W) and impact (I) for each of the variables in the total set of alternatives (with 405 instances × 125 variables) (Table 10), the TOPSIS method ranked all 40 in the top 40 with distance = 1 in the order shown in

Table 13. The first 40 best classification alternatives (No Alt) of the TOPSIS method.

No Alt	Detention_1	Score	Rank	No Alt	Detention_1	Score	Rank
404	1	0.64004	1	390	1	0.60817	21
403	1	0.63895	2	405	1	0.60740	22
397	1	0.63747	3	388	1	0.60662	23
396	1	0.63503	4	283	1	0.60567	24
152	1	0.63494	5	387	1	0.60561	25
51	1	0.63361	6	348	1	0.60485	26
381	1	0.63266	7	347	1	0.60379	27
395	1	0.62939	8	391	1	0.60315	28
380	1	0.62630	9	402	1	0.60272	29
394	1	0.62623	10	171	1	0.60120	30
125	1	0.62549	11	384	1	0.60103	31
93	1	0.62532	12	393	1	0.59639	32
130	1	0.62456	13	382	1	0.58679	33
321	1	0.62314	14	355	1	0.57963	34
271	1	0.62196	15	383	1	0.57542	35
401	1	0.62081	16	400	1	0.56435	36
389	1	0.61294	17	324	1	0.56393	37
385	1	0.61245	18	323	1	0.56292	38
398	1	0.61153	19	392	1	0.54063	39
399	1	0.60908	20	386	1	0.50631	40

. This shows that the weighting of the criteria and the values of the impact vector of the input dataset considerations are correct. Table 13 thus shows the 40 best alternatives identified using the TOPSIS method. The columns are No Alt (alternatives); Detention_1; and Score and Rank, sorted from best to worst.

Note: In the TOPSIS method, the best-rated alternative is the one with the highest score, but in this empirical study the one with the highest probability of detention, i.e., Detention = 1, was rated as such.

For the trained classification decision tree model “rpart”, a prediction of the probability of detention (Detention Probability) is also created for all examples (405) of the input dataset. The probability values are then added as a new column to the original dataset (column Detention Probability “rpart”,

Table 14. The first 40 best classification alternatives by combining the “rpart” algorithm and the TOPSIS method.

No	No Alt	D = 1	Detention Probability (rpart)	TOPSIS Score	Combined Score	No	No Alt	D = 1	Detention Probability (rpart)	TOPSIS Score	Combined Score
1	A397	1	0.733	0.637	0.685	21	A343	0	0.733	0.358	0.545
2	A396	1	0.733	0.635	0.684	22	A248	0	0.733	0.349	0.541
3	A93	1	0.733	0.625	0.679	23	A385	1	0.286	0.612	0.449
4	A271	1	0.733	0.622	0.678	24	A399	1	0.286	0.609	0.447
5	A389	1	0.733	0.613	0.673	25	A388	1	0.286	0.607	0.446
6	A398	1	0.733	0.612	0.672	26	A387	1	0.286	0.606	0.446
7	A390	1	0.733	0.608	0.671	27	A402	1	0.286	0.603	0.444
8	A405	1	0.733	0.607	0.670	28	A171	1	0.286	0.601	0.443
9	A348	1	0.733	0.605	0.669	29	A384	1	0.286	0.601	0.443
10	A347	1	0.733	0.604	0.669	30	A393	1	0.286	0.596	0.441
11	A391	1	0.733	0.603	0.668	31	A355	1	0.286	0.580	0.433
12	A382	1	0.733	0.587	0.660	32	A324	1	0.286	0.564	0.425
13	A383	1	0.733	0.575	0.654	33	A323	1	0.286	0.563	0.424
14	A400	1	0.733	0.564	0.649	34	A386	1	0.286	0.506	0.396
15	A392	1	0.733	0.541	0.637	35	A404	1	0.043	0.640	0.341
16	A49	0	0.733	0.391	0.562	36	A403	1	0.043	0.639	0.341
17	A139	0	0.733	0.387	0.560	37	A152	1	0.043	0.635	0.339
18	A260	0	0.733	0.377	0.555	38	A51	1	0.043	0.634	0.338
19	A94	0	0.733	0.377	0.555	39	A381	1	0.043	0.633	0.338
20	A346	0	0.733	0.375	0.554	40	A395	1	0.043	0.629	0.336

). In this way, information on the probability of the offshore vessel being detained is obtained (Column D = 1, Table 14) for each example in the dataset. These data are useful and are used in the further analysis.

The combination of the “rpart” (Detention Probability) and TOPSIS (TOPSIS Score) results is carried out by calculating the weighted sum of the Combined Score (columns 6 and 12—Table 14) for each example in the dataset.

The new column “Combined Score” in the dataset thus represents the weighted sum of “Detention Probability” (probability of detention from “rpart”) of and “TOPSIS Score” (the result of the TOPSIS method) and is calculated according to Equation (13), where and represents the $i$-th alternative of the entire dataset. Neither of these two values (“Detention Probability” and “TOPSIS Score”) is favored, as each component is assigned a weight of 0.5 (50%).

$$CombinedScore\left[\mathrm{i}\right]=0.5 \ast DetentionProbability\left[\mathrm{i}\right]+0.5\ast TopsisScore\left[\mathrm{i}\right]$$

(13)

The final results (Table 14) show that of the 40 alternatives (Alt) with the highest adherence probability, 33 (or 82.5%) belong to the group in which the variable Detention has the value (D = 1 or Yes), while 7 have the value (D = 0 or No), or 17.5%. This means that the results of the 40 most likely detention vessels identified by the combination of “rpart” and TOPSIS match 82.5% of cases. (See Table 14)

This means that although “rpart” is used in the entire dataset (as can be seen in Figure 3, which shows that there are 45 checked vessels in the entire dataset, of which 40 are Not-detained vessels (N) and 5 are Detained vessels (D)) it is possible that one of the 5 detained vessels is not identified as “Detained” by the “rpart” algorithm.

The TOPSIS method, on the other hand, individualizes all 4 detained vessels in the total set of 45 vessels (of which 41are Non-detained vessels (N) and 4 are Detained vessels (D)).

However, by combining these two methods, it is possible to determine with greater certainty which vessels are more likely to be detained.

6. Discussion

A total of 405 instances (alternatives) and 125 variables were used for the empirical study in this article. When applying the “rpart” classification decision tree, the data were randomly divided into a training dataset (283 × 124) and a test dataset (122 × 124) in a ratio of 70:30. The number of independent variables is 123, while the dependent variable is “Detention”, which can be classified as “Yes” and “No”. For both the training and test datasets, when applying the “rpart” classification tree, all categorical variables (“Country of Inspection”, “Flag”, “Memorandum”, and “YOB”) were converted into numerical variables to show the number of occurrences of each variable in the input dataset for the entire dataset, but also grouped by the variable “Detention”.

When applying the MCDM method TOPSIS, data from all 405 alternatives and 125 variables were used. Based on the frequency of occurrence for the entire set of input data, the criteria and the target (impact) of each criterion were defined. When using the TOPSIS method, the text variable “Detention” was also converted to a numeric value, as the TOPSIS method can only process numeric values. For this reason, there is an additional variable (125) in the TOPSIS method.

Data validation can be crucial when using the TOPSIS method to ensure the accuracy and reliability of the results. Several methods were used to validate the data in the TOPSIS method as follows:

• All data were checked. The input dataset does not contain any missing values and outliers (data outside the possible ranges that can significantly affect the results). If this were the case, the data would be deleted before application.
• Data consistency was checked, i.e., all values of the variables are in the same format and make sense in the context of the problem to be analyzed. The data were normalized so that all values were in the same range (i.e., between 0 and 1). This is an important element of validation as the TOPSIS method works with distances between points, so different ranges can distort the results. The weighting values were checked for all variables and all reflect the actual priorities.
• A basic sensitivity analysis was performed by changing the weighting values of the criteria and analyzing how this change affected the ranking of the solutions.
• A stability check was performed by analyzing how small changes in the input data affected the results of large changes in the ranking.

Additionally, the TOPSIS method yielded all 40 vessels detained. This essentially confirms that partial (minor) changes to the input dataset do not significantly alter the results, which is also a cross-validation step. Cross-validation was applied to reduce the risk of over-learning the model and improve its robustness, especially in real-world applications with high data variability.

The classification decision tree model “rpart” correctly identified 44.44% of the true positive cases (actually detained vessels). This is justified by the small number of actual vessels detained (Detention = 1 is 40 or 10%) in the total number of alternatives (405).

However, the MCDM TOPSIS method, which is based on the fixed weight values of the criteria and the impact (min or max) of each criterion, provided excellent results and ranked all positive instances (Detention = 1) among the 40 most trustworthy, i.e., the best.

The combined results of “rpart” with TOPSIS MCDM show that of the 40 most likely alternatives (Alt) for retaining offshore vessels, 33 (or 82.5%) belong to the group that would likely be detained.

The results confirmed that by applying a combination of classification decision trees and MCDM, it is possible to improve the decision-making process when offshore vessels are detained in port.

Finally, analyzing the complexity of algorithms [47] helps to understand the performance and resource requirements, which is crucial for efficient application in different scenarios and with different data sizes. The overall complexity of the algorithm includes the calculation of the temporal complexity, i.e., how much time is required to execute the algorithm, and the spatial complexity, i.e., how much computer memory and other relevant resources are required to execute the algorithm. Both are listed in

Table 15. The complexity of algorithms.

	rpart	TOPSIS
Time complexity	$O\left(n\times m\right)\log m$	$O\left(n\times m\right)$
Spatial complexity	$O\left(m\times n\right)$	$O\left(m\times n\right)$

.

In the “rpart” algorithm, $m$ stands for the number of instances and $n$ for the number of variables, and in TOPSIS, $m$ stands for the number of instances and $n$ for the number of criteria.

The analysis revealed several important advantages and challenges in implementing this approach. By implementing classification trees in software tools, it is possible to automate part of the PSC process for keeping offshore vessels in port, ensure greater consistency in decision-making, and reduce the possibility of human error.

The classification trees enabled the identification of key factors that influence the decision to detain offshore vessels. This helps inspectors to focus on critical aspects during the inspection, increasing efficiency and reducing the time needed for decision-making. The decision tree generated in the R package provided a visually understandable representation of the decisions, facilitating their interpretation and application in practice, so that inspectors (but also vessels and other interested parties) can quickly, easily, and clearly understand the logic behind the decision and adapt their inspection procedures accordingly.

On the other hand, MCDM has proven to be a comprehensive, flexible approach and a powerful decision support tool. Based on historical data (qualitative and quantitative) on the detention of offshore vessels, MCDM enabled an assessment and prediction of the possibility of future detention of vessels, resulting in a more balanced and objective approach. The proposed approach has also been shown to apply to the specific needs and priorities of different ports and inspection teams, allowing for minor and/or major changes in the assignment of weighting values to variables and their targets according to the respective safety and operational requirements. Therefore, the tools of the MCDM methodology provide structural support in the decision-making process and help inspectors make informed and transparent decisions, reduce subjectivity, and increase confidence in the PSC process.

The main drawbacks of this approach relate to the following important elements. It is necessary to focus on the potential challenges in practical application, including 1. training of inspectors should consider the resources and time required to train inspectors in the application of machine learning and MCDM methods and the strategies to overcome these challenges; 2. technical requirements should be analyzed through an analysis of technical barriers and 3. organizational barriers point to the importance of changing the management and culture within organizations to enable the successful adoption of new technologies. Furthermore, recommendations should be made for future research related to analyzing all these aspects and developing practical guidelines and case studies that would facilitate implementation in different contexts.

Although classification trees and MCDM offer significant benefits, their implementation requires initial investment in software tools and training of inspectors. Ensuring adequate training and support is critical to the success of these methods. On the other hand, the success of these analytical methods depends on the quality and reliability of the data. Therefore, deficiencies in data collection or irregularities in recording can hurt the accuracy and usefulness of the results. In addition, changes to existing PSC procedures may be met with resistance from inspectors and other involved parties. It is important to communicate the benefits appropriately and ensure the involvement of all relevant stakeholders in the change process.

7. Conclusions

In this article, the application of a combination of machine learning algorithms, i.e., classification trees and MCDM, in the process of holding offshore vessels in port, better known as PSC, was investigated. The analysis showed that these methods can significantly improve the efficiency and accuracy of the inspection process and detention of vessels. Classification trees are a powerful tool for identifying key risk factors, enabling inspectors to make faster and more accurate detention decisions.

The use of MCDM has further improved the decision-making process as multiple factors can be considered simultaneously, ensuring a balanced approach that minimizes subjectivity. The combination of these methods has enabled the creation of a more systematic, transparent, reliable, and robust PSC framework that can lead to increased safety of navigation and reduced operational costs.

Based on the results presented, further exploration and integration of machine learning techniques into existing PSC procedures is recommended. The use of advanced analytical tools can significantly contribute to improving safety standards and operational efficiency in the maritime sector. In addition, training inspectors on these tools and methods can further increase their applicability and effectiveness.

Finally, this paper points to the significant potential of improving the PSC process of modern analytical machine learning methods, which can contribute to safer and more efficient maritime transport.

The research conducted has several potential limitations related to the quality and scope of the data, the complexity and robustness of the model, methodological limitations, practical implementation, validation and generalization, and technical performance. If the data used to train and test the model are not sufficiently representative or contain errors, the results may be unreliable. If the data come from a limited number of sources or geographical areas, the models may not be generalizable to all situations or regions. Classification trees can be prone to overfitting, where the model responds too accurately to the specifics of the training rather than to general patterns. Algorithms such as “rpart” can reach their limits in terms of the complexity of the data and the interpretability of the results. If the research is still in the development phase, there may not be sufficient evidence of the stability and reliability of the results. The weighting of the criteria can be subjective and depends on the accuracy of the weightings. The implementation of advanced algorithms may require significant technical resources and staff training, which can be a barrier for organizations with limited budgets. There is a possibility that inspectors and other users may be unwilling to accept new methods due to resistance to change or lack of training. If a model is not tested on independent datasets, one does not always have insight into its ability to generalize the results across different scenarios. The results may relate to a specific context or period and may not apply to all types of offshore vessels or different regions.

Understanding and recognizing these limitations will certainly help to formulate more realistic conclusions and recommendations for this work and identify areas for future research and improvement.