Analysis of Management Models of Regional Ports in the Republic of Croatia

Abstract

Seaports play a crucial role in the transportation and logistics chain, and their development and optimization require significant investments in infrastructure, superstructure, human resources, and management. To ensure the efficiency and effectiveness of these investments, it is essential to implement a well-designed port management model. This model should be based on the criteria used to guide the selection process and ensure that the chosen model aligns with the needs and objectives of the port, stakeholders, and community. This study aims to determine the optimal criteria and management model for the regional seaports in the Republic of Croatia. Port management experts’ opinions were obtained through a questionnaire, and data were analyzed using the AHP and fuzzy AHP methods. The results showed that the criterion of functionality is optimal for choosing the appropriate management model, while the most favorable management model is the coordinated decentralized model. The results obtained by both methods were the same. Different criteria and management models, with similarities and differences between the obtained results and the provisions of the National Development Plan of Ports Open to Public Transport of Regional and Local Significance, are discussed and highlighted.

1. Introduction

The choice of the optimal port management model represents one of the fundamental principles for business organization and contributes to the future main purpose and operational range of ports. The port management model can impact the efficiency and effectiveness of port operations and the ability of the port to achieve its key objectives. Therefore, it is important to carefully consider the various management models and select one that meets the needs of the port and the surrounding community. The role of ports has changed and evolved over the years; they are no longer merely trade and shipping centers, but now serve the socioeconomic development of port cities and regions. Adapting the port system and its functionality to the changes observed in the maritime industry is a prerequisite for the competitive position of the port [1]. The contemporary port management model should consider the port’s hinterland and the port as a hub for adding value to goods, as well as the port’s position in the transportation chain [2].

With appropriate programs and legislative measures, the government can strengthen or weaken the development of ports and the systems [3]. In addition, all programs implemented by seaports are often planned in cooperation with central, regional, or local governments. Setting programs and objectives would not be possible without a dialogue with port stakeholders [4]. Therefore, it is necessary to develop viable communication between the ports and their stakeholders, which should also include the residents of the port cities [5]. Port development programs and legislative measures indirectly affect the local population by creating social benefits such as employment opportunities and better shore–island ferry connections. The role of port management and governance in port development programs and legislative actions is to provide a framework for planning, organizing, and implementing these initiatives to maximize their benefits and minimize their negative impacts. A well-designed and appropriately implemented port management model can help ensure that port development programs and legislative actions are coordinated, efficiently implemented, and contribute to the overall goals of the port and its surrounding communities. In the context of the specific impacts mentioned above, a port management model can create employment opportunities and improve shore–island ferry connections by defining the roles and responsibilities of various stakeholders, establishing performance goals and benchmarks, and establishing policies and procedures for resource allocation and decision-making. As such, port management options can be viewed as a multidirectional link between the various port stakeholders at the global, national, and local levels in terms of legal, economic, environmental, and social aspects of management [6].

Various port management models are used worldwide, considering different factors determining the scope of port activity. These models are often classified as follows: (a) by ownership and governance structure, and (b) by type of administrative management [7]. With respect to ownership and governance structure, management models include national (i.e., state-owned) ports, ports managed by cities or regions, autonomous ports, public–private partnership ports, and private ports [7,8,9,10,11]. Administrative management models, on the other hand, include public service ports, tool ports, landlord ports, and fully privatized ports [7,11,12,13].

Croatian legislation divides ports according to their purpose into ports for public traffic and ports for particular purposes, both of which may be open to international or domestic traffic, governed by special regulations. Depending on their size and importance to the Republic of Croatia, ports open for public traffic are divided into ports of special (international) economic interest, ports of regional significance, and ports of local importance [14]. There are 22 regional port authorities [15] and 66 ports of regional significance open to public traffic [16,17] in Croatia. Ports of regional significance are geographically distributed among the regions and fall under the jurisdiction of the port authority of the respective region [16,17].

The port management model provides a starting point for port system functionality and future potential development opportunities, while serving as a tool for solving complex business processes [18]. Several factors determine the optimal type of port organization and management model, including port policy, location, port tradition, and the port’s size and type of traffic [7]. The institutional laws and legislation based on which the regional port management models are formed are the “Law on Maritime Domain and Seaports” and the “Law on Institutions”. Legislators should consider introducing port management models based on the “Law on Maritime Domain and Seaports”. As mentioned above, the law regulates the port authority’s organization, planning, and operation. The “Law on Institutions” is considered auxiliary in this context [19].

This study aims to investigate the effectiveness and efficiency of the management models of regional ports in the Republic of Croatia, and to evaluate the specific criteria for selecting the management model. According to the National Plan [16], regional port authorities in the Republic of Croatia can implement one of four management models: decentralized, coordinated decentralized, centralized port management, or management of one port authority with several subsidiaries. These models offer different approaches to the organization and operation of regional ports, as discussed in more detail in Section 3. By conducting a survey on a group of experts in the field of port management and applying the analytic hierarchy process (AHP) and fuzzy AHP methods, data on the optimal management model and fundamental criteria for deciding on implementing the appropriate model were obtained. The research problem relates to the ways in which the regional seaports are managed. The existing management models in the Republic of Croatia differ mainly according to the criterion of territorial organization, without the previous creation of an analytical framework that would determine the optimal model according to the defined parameters of business performance. The legal framework for port management in Croatian regions may allow for the establishment of multiple port authorities within a single region, which may lead to subjective and autonomous decision-making processes that do not consider development indicators. This can have a negative impact on the efficiency and effectiveness of port operations, the overall purpose and goals of the port, and the wellbeing of its residents. For this reason, it was necessary to conduct primary research considering publicly available parameters and the views of a group of experts directly and indirectly involved in managing regional seaports

This paper consists of five sections, starting with an introduction. The second section contains a literature review divided into two subsections: The first subsection provides an overview of the main features of port management models worldwide. The second subsection provides an overview of the management models applicable to the Croatian regional port system. This is followed by the Materials and Methods section, which briefly explains the criteria and alternatives (models) used in the study and presents the flowchart of the research process. This section also describes the AHP and fuzzy AHP methods. The fourth section presents the results of the research, with each subsection dedicated to the criteria and alternatives (models), as well as the results of the AHP and fuzzy AHP methods. The final section, entitled “Discussion and Conclusions”, outlines the study’s main contributions in the context of existing research and highlights the study’s limitations.

2. Literature Review

Ports play an important role in global trade and logistics, and the management of these facilities significantly impacts the achievement of the main objectives of port strategies [4]. Over the years, various port management models have been developed and implemented in different parts of the world, each with unique characteristics and features. This literature review aims to examine the various port management models proposed and implemented worldwide and in the Croatian regional port system, as well as their strengths and weaknesses. By understanding the different models and their relative advantages and disadvantages, port authorities and decision-makers can make informed decisions about the best management approach for their specific context and needs.

2.1. Predominant Port Management Models Worldwide

Port management solutions consist of several components: government organizations, port organizations, institutional arrangements, port regulatory and management activities, and operational activities. The directional relationships among these components determine who controls and interacts, and the outcomes of these interactions can be measured by metrics such as effectiveness or efficiency [6]. Management models applied to port systems can be classified based on the ownership and governance structure and the type of administrative management [7].

According to the structure of ownership and administration, port management models include the following [7,8,9,10,11]:

• National or state-owned ports represent a management model in which the state controls and manages the port. This type of organization can be characterized by bureaucracy and inflexibility and is usually financed from the state budget. Political interference can also affect the efficiency of management in such ports. However, national or state-owned ports have the advantage of being more closely linked to state institutions and strategic plans, and they may have easier access to state-owned businesses.
• Ports managed by a city or region are overseen directly by the local governing body. This management model is often more flexible than national port management models because it can take into account local considerations, such as the economic impact of the port on the region’s development. Funding for this type of port management is usually provided through the city or region’s budget. In general, this management model can offer the advantage of being more responsive to local needs and priorities. However, it should be noted that similar to national port management structures, this system can be burdened by bureaucratic processes that can hinder efficient port operations.
• Autonomous port management is a management model in which stakeholders monitor the success of the operation. This model is based on the premise that individuals or groups with a vested interest in the success of the port can effectively manage it. This management model may involve the formation of a specialized association by users to manage the operation. These associations are usually autonomous and can adapt quickly to market changes. They can efficiently hire staff, respond to competition, and rely on their revenues to cover costs, leading them to prioritize the needs of their customers. The organizational structure of this type of management can vary depending on the degree of user participation in decision-making.
• Public–private partnerships (PPPs) in port management are collaborations between the public and private sectors to improve operational efficiency, increase service capacity, and reduce port fees. As the economic importance of ports continues to grow, port authorities may struggle to finance necessary investments and compete in the market solely through public funds. PPPs provide a solution by allowing the private sector to contribute resources and expertise to the management and development of the port, aiming to achieve economic benefits for the private sector and social benefits for the public. This management model involves equal participation and decision-making between the public and private sectors.
• Private ports, owned and operated by private legal entities or economic entities, represent a departure from the typical port management system. These ports are often smaller and located in industrial areas. One of the primary reasons for privatizing ports is the government’s desire to reduce the investment costs of developing and operating ports. However, private ownership of ports can also present unique challenges and considerations related to decision-making and financial accountability.

Port management models can be classified based on several factors, including their public, private, or mixed service orientation; their local, regional, or global focus; the ownership structure of their infrastructure and equipment; and the status of their workforce. Consequently, administrative management models can be divided as follows [7,11,12,13]:

• Public service ports, which operate under a port management model where all functions are assigned to the public sector, are typically owned and controlled by government organizations known as port authorities. These port authorities are responsible for regulatory and port-related functions and ownership of all assets. This management model is often found in developing countries where the relevant ministry controls the port. The port authority’s president is often a civil servant, and all port employees are employees of the port authority. However, the absence of private sector involvement and competition can lead to inefficiencies in port operations and business.
• In a tool port management model, the public port authority has the same responsibilities as in a service port model. The difference, however, is in the labor force, as shipping companies hire private companies to load and unload cargo. This can lead to conflicts between private and public companies over liability in the distribution of cargo operations. A weakness of this model is the risk of insufficient investment in terminal equipment. This management model may be attractive in cases where there is a lack of confidence in the private sector to handle port operations effectively.
• The landlord port management model involves a mix of public and private interests in port operations. In this model, the port authority retains ownership of the port’s land and infrastructure, which it leases to private companies. The port authority is also responsible for maintaining the port infrastructure and the roads, berths, and piers, requiring significant investment by private owners. The private companies are responsible for providing and maintaining their superstructure and equipment. This model can be attractive if there is insufficient reliance on the private sector for port operations, but it also carries the risk of insufficient investment in terminal equipment.
• In a fully privatized port, the management of the seaport is entirely in the hands of the private sector. This model is based on market orientation and tariff policy, and the private sector owns all assets and is responsible for all regulatory and port-related tasks. However, there is a risk of monopolistic behavior and loss of public interest in long-term economic development and port strategies. In addition, the private owner of the port can sell or reallocate port land for non-port activities.

2.2. Port Management Models in the Croatian Regional Port System

The basic idea underlying this subsection of the literature review is related to the applicable management models and criteria for the Croatian regional ports. The National Plan defines the applicable management models and criteria [16]. Consequently, the selection of literature for review was necessary to scrutinize the main research variables (i.e., criteria and alternatives (management models)) that are appropriate according to the legislation and plans discussed in the Introduction section. In particular, the authors found few studies that addressed the management models suitable for implementation in the regional ports of Croatia and to which the multi-criteria decision-making method was applied.

Vrus [20] discussed the decentralized system in the ports of the Primorsko-goranska region and concluded that such a management model brings social and economic benefits. However, due to changed legal regulations, parts of this study are not comparable to our research results. The author of [19] discussed the significant economic, theoretical, and legal facts pertaining to the implementation of the management systems in the regional ports. He concluded that all relevant factors affecting port authorities’ development, management, and operation should be considered when deciding on the management model. The author also noted that the models based on a decentralized and regional approach to port management are the most appropriate. Further contributions were provided by Jugović et al. [21], where the authors studied the application of different management models to the port system of the Primorsko-goranska region. Special attention was paid to the following models: decentralized, coordinated decentralized, centralized, and management of one port authority with several subsidiaries. The authors found that the above models can be implemented in the Croatian port system, as they comply with the legal requirements in the Republic of Croatia, have an organizational framework already, and are accepted by the stakeholders. The authors also indicated the quality of the port services criteria preferred in the management model selection through the expert survey method. The authors considered the multi-criteria decision-making (MCDM) research method to be beneficial, allowing the selection of the optimal management model through the validation of different criteria. The National Plan for the Development of Ports Open to Public Traffic of Regional and Local Significance [16] extensively defines the above models and the necessary criteria (i.e., economic-financial, functionality, prioritization/necessity, and success criteria). According to [16], the management model selection should be based on the economic-financial and social criteria, with a preference for the model of one port authority with several subsidiaries. The criteria and management models used in the following study are explained in detail in [16,21].

This literature review highlights the necessity of implementing an effective management model for regional ports and calls for systematic reforms to current governance and legislation. The limitations identified in the existing literature emphasize the need for research utilizing multi-criteria decision-making techniques, such as AHP and fuzzy AHP.

3. Materials and Methods

A flowchart was created to define and select the optimal regional seaport management model using the AHP and fuzzy AHP methods (see Figure 1). According to the National Plan for the Development of Ports Open to Public Traffic of Regional and Local Significance, the necessary criteria crucial for the determination of the optimal regional seaport management model are as follows [16]:

• The economic-financial criterion manifests itself by increasing the intensity of the net financial income of a given management system for the budget of the seaport. In the case of the port system, this refers to the increase in its revenues based on the collection of port fees and other forms of revenue, such as concessions, as well as the reduction in various costs.
• The functionality criterion can be analyzed based on its four most important aspects:
  • The ability to perform the fundamental tasks of port management and the functionality of the port, focusing on technological/technical sub-criteria in the form of investment in port infrastructure, standardization of methods and criteria, quality of port service, achievement of the desired traffic volume, technical conditions, and existing and planned transport infrastructure;
  • Impacts on the social and cultural aspects of the local community refer to the overall positive impact of a particular management system on the local community;
  • Economic development impacts are analyzed in terms of the overall multiplicative effect of the management model on accelerating and increasing the economic development of a particular region;
  • Impacts on entrepreneurship development are reflected in the promotion of the seaport’s focus on businesses and trades in seaport-related activities.
• The prioritization/necessity criterion is reflected in the consistency with basic strategy and policy documents. It refers to the coherence of the selected port management model with the national and European strategic documents, public policy documents, national legal framework, and European legal documents, as swell as the acquis communautaire of the European Union.
• The success criterion represents the possibility of creating benefits for end users and possible negative impacts for existing users. The possibility of creating benefits for end users is reflected in the intensity of the advantages achieved, such as potential cost savings.

When implementing the port management model, the positive impact intensity should undoubtedly exceed that of the negative impacts.

Based on research and legislation, four main port management models can be adopted by regional port authorities in the Republic of Croatia [16,21]:

• A decentralized (i.e., several port authorities) seaport management system implies the establishment of independent port authorities capable of performing all tasks independently. The port authorities are established according to the principle of territorial units. This model has been adopted by the Primorsko-goranska, Dubrovnik-Neretva, and Istria regions. The differences between the regions lie in the number of port authorities. The advantage of the decentralized model over other models is the permanent presence of port authority employees in the ports.
• Coordinated decentralized management (i.e., several port authorities sharing corporate technical services) is based on a legal provision that each region may establish multiple port authorities to manage, construct, and utilize seaports of regional significance that are open to public traffic. This port management model is similar to the current decentralized models in the Istria, Primorsko-goranska, and Dubrovnik-Neretva regions. The difference lies in mutual technical services for all port authorities, aiming to direct all tasks of port authorities to normative and planning activities as a prerequisite for all future port operations.
• Centralized management (i.e., a central port authority) means that operations are concentrated in a central location, while decision-making processes and management authority are based on the organization’s hierarchy. In port management, the centralized model means that a central port authority based in the region’s capital is responsible for all ports of importance.
• The management of one port authority and several subsidiaries represents a model with business units such as branches, institutes, and regional centers, organized according to territorial principles and located on the islands and/or coast. The number of business units would be determined through field research, considering the interests of local governance structures. This model allows for the benefits of a centralized port management system while introducing some of the benefits of decentralization.

When choosing a management model, in addition to valid criteria, a functional approach to port management should be considered based on the multiplicative effects of the port. The principle of the seaport manifests multiplicative effects as a generator of the region’s socioeconomic development [16].

The AHP and fuzzy AHP methods are widely accepted and used in various research areas. It should also be mentioned that these methods are often criticized.

Table 1. Advantages and disadvantages of the methods [22,23].

Method	Advantages	Disadvantages
Analytic hierarchy process (AHP)	Allows the systematic and structured evaluation of complex problems	It may be time-consuming, especially for larger or more complex problems
	Enables the integration of both qualitative and quantitative criteria in the decision-making process	It may be difficult to accurately estimate the relative importance of the criteria being used
	Enables the incorporation of the subjective judgments of decision-makers	It may be difficult to reach consensus among decision-makers on the relative importance of the criteria
	Provides a clear and transparent ranking of the alternatives being considered	It may be sensitive to errors in the data or assumptions used
Fuzzy analytic hierarchy process (fuzzy AHP)	Allows imprecision in the decision-making process	It may be more complex to use than the traditional AHP method
	It can be used to deal with incomplete or uncertain information	It may require the use of specialized software or expertise to implement
	It can handle multiple conflict objectives and criteria	It may be sensitive to errors in the data or assumptions used
	It can be applied to a wide range of problems and decision-making contexts	It may be difficult to validate the analysis results due to the inherent uncertainty in the method

shows the advantages and disadvantages of the methods used. The authors’ decision to use the AHP and fuzzy AHP methods for this research was based on the following facts: The need to fill the literature gap, as the authors discussed in the literature review consider the multi-criteria decision-making method to be beneficial for adopting criteria and models for regional port systems. Arguably, the stakeholders’ subjective assessments can also be considered a strength, given their expertise in regional port management systems. To overcome the obstacle of possible biased judgments, fuzzy set theory (the fuzzy AHP method) was applied in this research to deal with the uncertainty of inaccurate judgments. The methods are explained in detail in the following sections.

3.1. AHP Method

Multi-criteria decision-making (MCDM) is a discipline that analyzes decisions to select the optimal one with respect to different criteria related to a specific goal. This process allows for solving decision-making problems by comparing the alternatives to reach a conclusion about their priorities [24].

The analytic hierarchy process (AHP) is a multi-criteria analysis method that was introduced and developed in the 1970s by Thomas L. Saaty [25]. The AHP method allows for defining the most appropriate decision for the goal, simplifying the complex problem through a system of hierarchies [26]. The hierarchy components are goals, criteria, and alternatives [27], and they are connected in a multilevel model—a hierarchical structure, as shown in Figure 1. The other important feature of the multi-criteria AHP method is the mathematical model used to calculate the priorities of the elements on the same hierarchy level. The fundamental mathematical tool is represented by matrices [27].

The application of the AHP method can be explained by the following steps [28]:

• Develop a hierarchical structure of decision problems with the goal at the top, the criteria in the middle, and the alternatives at the lowest level;
• At each level of the hierarchical structure, the elements of a given level are compared in pairs, with the decision-maker’s choices expressed by Saaty’s scale of relative importance (

  Table 2. Saaty’s nine-point scale of pairwise comparison [24].

  Intensity Importance	Definition
  1	Equally important
  3	Moderately more important
  5	Strongly important
  7	Very strongly important
  9	Extremely important
  2, 4, 6, 8	Intermediate values between adjacent scales

  ), which has five degrees and four intermediate degrees of the described intensities, and corresponding numerical values from 1 to 9;
• From the estimates of the relative importance of the elements at the levels of the hierarchical structure, the local priorities of criteria and alternatives are calculated using a mathematical model—the matrix—synthesizing the results into the overall priorities of alternatives;
• The overall priority of a given alternative is calculated by adding the local priorities, weighted by the higher-level element;
• The analysis is performed.

Saaty introduced the consistency index (CI) and consistency ratio (CR), which are calculated with the following formulae [29]:

$$\mathrm{CI}=\frac{{\mathsf{\lambda }}_{\max }-\mathrm{n}}{\mathrm{n}-1},$$

(1)

where ${\mathsf{\lambda }}_{\max }$ represents a weighting factor, while the number of elements is determined by the n index, and

$$\mathrm{CR}=\frac{\mathrm{CI}}{\mathrm{RI}}.$$

(2)

The consistency ratio (CR) is calculated by dividing the consistency index (CI) by the random index (RI) [26]. As described by Saaty, the value of the random index (RI) was obtained from randomly generated comparison matrices (

Table 3. Random index (RI) [30].

n	1	2	3	4	5
RI	0.00	0.00	0.58	0.90	1.12

) [30].

The value of CR is acceptable if the value is less than 0.1. Otherwise, the choice may be unreliable and needs to be recalculated [31].

3.2. Fuzzy AHP Method

The fuzzy AHP multi-criteria decision-making method is used when there is some uncertainty in the decision-making, e.g., when the decision-maker is unsure of their subjective judgment. Another reason may be that the decision-maker needs more information about the criteria, or that the information is incomplete or unavailable [26]. The fuzzy AHP method is used when the decision-maker’s preference is not explicitly defined due to its unclear nature [32].

In the fuzzy AHP method, the values are expressed as necessary or possible actions. This method is suitable for qualitative modeling criteria and can be used in various areas, such as forecasting, decision-making, evaluation, planning, and development [26].

Figure 2 shows the calculation process of the fuzzy AHP method based on the following six steps [33]:

• Structure the problem—a hierarchical structure of goals, criteria, and alternatives are created;
• Create the fuzzy pairwise comparison matrix;
• Synthesize the judgments—if there are several experts, aggregate their opinions. As shown in the Figure 3, it takes place either before or after calculating the fuzzy weights, i.e., synthesizing the pairwise comparisons (labelled by number 1 in Figure 3) or the fuzzy weights (labeled by number 2);
• Calculate the fuzzy weights of the criteria—in this step, aggregate several fuzzy sets in the matrix into a single fuzzy set;
• Defuzzify the fuzzy weights—this is an additional step compared to the AHP method, which maps a fuzzy set to a crisp value for further comparison;
• Check for consistency.

Lofti A. Zadeh introduced the fuzzy set theory (FST) to determine uncertainty and vagueness. The fuzzy set (FS) represents a class of objects with continuous valuations. The given set is characterized by a membership function that assigns each object with a membership value in the range between zero and one. The triangular fuzzy number (TFN) is denoted by l, m, and u. The above parameters indicate the smallest and largest possible values that describe the fuzzy event. The TFN function is shown in Figure 3 [26].

Saaty’s scale for the fuzzy AHP method looks different from the scale of the AHP method described earlier. Two more numbers are added for each value, representing the smallest and largest values [26] (

Table 4. The scale of fuzzy AHP pairwise comparison [24].

Crisp Importance Value	Triangular Fuzzy Numbers	Definition
1	(1,1,1)	Equally important
2	(1,2,3)	Intermediate value between 1 and 3
3	(2,3,4)	Moderately more important
4	(3,4,5)	Intermediate value between 3 and 5
5	(4,5,6)	Strongly important
6	(5,6,7)	Intermediate value between 5 and 7
7	(6,7,8)	Very strongly important
8	(7,8,9)	Intermediate value between 7 and 9
9	(9,9,9)	Extremely important

).

As in the non-fuzzy AHP method, the consistency index (CI) and consistency ratio (CR) for the matrix $C_m$ are calculated using Formulae (1) and (2). If CR < 0.1 is valid, the analyzed fuzzy elements of the comparison matrix and the obtained eigenvalues and eigenvectors are accepted [29].

4. Results

The questionnaire “Regional seaports model analysis” consists of two parts that were distributed to experts in the port industry: The first part compares and evaluates the fundamental criteria to select the management model for the regional ports. The second part does the same with the management model. In this study, the criteria and parameters of the alternatives were studied separately without comparing them, as shown in Figure 1. The questionnaire included the necessary instructions and explanations, and 10 of the 30 questionnaires sent out were completed (a rate of 33.33%, which is a representative result). The expert group consisted of seven employees of the port authority who were directly involved in the business processes in the port. The remaining three experts were indirectly involved in the operation of the regional ports. It should be emphasized that the arithmetic mean technique was used in synthesizing the judgments of the stakeholders involved in the valorization process of the model and the criteria in the pairwise comparison synthesis phase, as indicated by Liu et al. [33]. The results were obtained and presented using the software tool to calculate the study’s empirical part [34].

4.1. AHP Method—Criteria

In evaluating the research results for the criteria, the weighting factors and indices were established as follows:

$${\mathsf{\lambda }}_{\max }=4.087.$$

(3)

The following result was obtained when the calculated value and the four elements (four criteria) were included in the formula for the consistency index (CI):

$$\mathrm{CI}=\frac{{\mathsf{\lambda }}_{\max }-\mathrm{n}}{\mathrm{n}-1}=0.029.$$

(4)

The result of the calculation of the consistency ratio (CR), considering the obtained value of the consistency index and the random index (RI) (Table 3), was

$$\mathrm{CR}=\frac{\mathrm{CI}}{\mathrm{RI}}=\frac{0.029}{0.90}=3.2\%.$$

(5)

The condition CR < 0.1 was met, because the calculation result of the consistency ratio was CR = 3.2%, i.e., 0.032.

The evaluated results are shown in Figure 4. The experts assessed the criteria according to their subjective judgement using Saaty’s scale (Table 2). As shown in the figure, the functionality criterion had the highest weight, with an overall value of 51.1%. The second-highest criterion in the experts’ selection was the economic-financial one, at 20.1%. The success criterion was rated with a weighting of 16%, while the lowest was the prioritization/necessity criterion, with a weighting of 12.8%. This indicates that the experts selected the functionality criterion as the most important for the selection of the management model.

4.2. AHP Method—Alternatives (Management Models)

When evaluating the research results for the regional port management models, the following weighting factors and indices were determined:

$${\mathsf{\lambda }}_{\max }=4.004.$$

(6)

When the previously determined value and four elements (four management models) were included in the formula to calculate the consistency index (CI), the following result was obtained:

$$\mathrm{CI}=\frac{{\mathsf{\lambda }}_{\max }-\mathrm{n}}{\mathrm{n}-1}=0.0013.$$

(7)

The result of the calculation of the consistency ratio (CR), considering the obtained value of the consistency index (CI) and the random index (RI) (Table 3), was

$$\mathrm{CR}=\frac{\mathrm{CI}}{\mathrm{RI}}=\frac{0.0013}{0.90}=0.15\%.$$

(8)

The condition CR < 0.1 was fulfilled, with CR = 0.15% = 0.0015.

Figure 5 shows the results and the weighting of the compared alternatives. The experts’ evaluation shows that the coordinated decentralized management model was weighted the highest, with an overall weighting of 33.4%. The management model with a port authority and several business units had an overall weighting of 28.9%. According to the results, the decentralized management model had a weighting of 24.3%. The centralized management model had the lowest weighting of 13.5%. From the results presented, the experts select a coordinated decentralized model as the optimal model for managing the seaport.

4.3. Fuzzy AHP Method—Criteria

By applying the fuzzy AHP method in determining the research results for the criteria, the following weighting factors and indices were obtained:

$${\mathsf{\lambda }}_{\max }=4.087.$$

(9)

The determined value and the number of elements (four—the number of defined criteria) in the formula for calculating the consistency index (CI) gave the following result:

$$\mathrm{CI}=\frac{{\mathsf{\lambda }}_{\max }-\mathrm{n}}{\mathrm{n}-1}=0.029.$$

(10)

The consistency ratio (CR) was calculated considering the obtained value of the consistency index (CI) and the random index (RI) (Table 3), according to the following formula:

$$\mathrm{CR}=\frac{\mathrm{CI}}{\mathrm{RI}}=\frac{0.029}{0.90}=3.2\%.$$

(11)

The condition CR < 0.1 was met because the consistency ratio calculation result was 0.032.

Figure 6 shows the overall results of the compared criteria calculated by the fuzzy AHP method and fuzzy triangular numbers. The experts weighted the functionality criterion with the highest value of 41.8%. The economic-financial criterion was weighted at 23.8%, while the success criterion was weighted at 21.1%. The criterion with the lowest weighting was the prioritization criterion, with a value of 13.3%. The experts rated the functionality criterion as the most optimal choice for the regional port management model.

4.4. Fuzzy AHP Method—Alternatives (Management Models)

The following weighting factors and indices were obtained by applying the fuzzy AHP method in calculating the parameters relevant to the alternatives (regional seaport management models):

$${\mathsf{\lambda }}_{\max }=4.004.$$

(12)

When the previously determined value and the number of elements (four elements—four relevant management models) were included in the formula for calculating the consistency index (CI), the result was:

$$\mathrm{CI}=\frac{{\mathsf{\lambda }}_{\max }-\mathrm{n}}{\mathrm{n}-1}=0.0013.$$

(13)

The consistency ratio (CR) was calculated considering the obtained value of the consistency index (CI) and the random index (RI) (Table 3), according to the following formula:

$$\mathrm{CR}=\frac{\mathrm{CI}}{\mathrm{RI}}=\frac{0.0013}{0.90}=0.15\%.$$

(14)

The condition CR < 0.1 was met.

Figure 7 shows the results of the compared management models. When calculating the alternatives evaluated by the experts, it was found that the coordinated decentralized management model received the highest score, with a total weighting of 28.7%. The decentralized model was second, with 28.3%. Management by one port authority and several subsidiaries scored 26.9%. The experts gave the lowest score to the centralized management model, with a weighting of 16%. The experts evaluated the coordinated decentralized model as optimal for managing regional ports.

The following table compares the results of the criteria analyzed with the AHP and fuzzy AHP methods.

Table 5. Comparison of the evaluated criteria.

	AHP Method	Fuzzy AHP Method
Economic-financial criterion	20.1%	23.8%
Functionality criterion	51.1%	41.8%
Prioritization/necessity criterion	12.8%	13.3%
Success criterion	16%	21.1%

shows the comparative results of the evaluated criteria with the AHP and fuzzy AHP methods. The port operation experts gave a weighting of 20.1% to the economic-financial criterion when applying the AHP method. Using the fuzzy AHP method, the same criterion was assigned a weight of 23.8%. The experts gave the best ratings for the functionality criterion when analyzing the presented results using the AHP and fuzzy AHP methods. Thus, the functionality criterion received a rating of 51.1% by the AHP method and 41.8% by the fuzzy AHP method. The functionality criterion received the highest rating according to both methods used in the study. With the AHP method, the prioritization/necessity criterion had a value of 12.8%, while the fuzzy AHP method assigned it a value of 13.3%. It is important to emphasize that the prioritization/necessity criterion was evaluated with the lowest weight, regardless of whether the AHP or fuzzy AHP method was used. The results of the data analysis showed that when the AHP method was applied, the success criterion had a value of 16%, and when the fuzzy AHP method was used, it had a value of 21.1%.

Table 6. Comparison of the evaluated alternatives.

	AHP Method	Fuzzy AHP Method
Decentralized management	24.3%	28.3%
Centralized management	13.5%	16%
Coordinated decentralized management	33.4%	28.7%
Management of one port authority and several subsidiaries	28.9%	26.9%

shows the comparative results of the evaluated alternatives with the AHP and fuzzy AHP methods. The experts weighted the decentralized management model at 24.3% with the AHP method. When applying the fuzzy AHP method, the same model was weighted at 28.3%. The value of the centralized management model with the AHP method was 13.5%, while the same model with the fuzzy AHP method was weighted at 16%. The port industry experts gave the lowest overall score to the centralized management model. In contrast to the centralized management model, the coordinated decentralized management model was rated as the optimal management model, with 33.4% when the AHP method was applied and 28.7% with the fuzzy AHP method. Therefore, coordinated decentralized management was evaluated with the highest weight in analyzing the research results. The model of one port authority management with several business units was assigned a weighting of 28.9% using the AHP method and 26.9% using the fuzzy AHP method. When comparing the results of the AHP and fuzzy AHP methods for management models of regional seaports, applying the fuzzy AHP method led to a change in the order of weighting of the alternatives, as can be seen in the cases of decentralized management and management by one port authority and several business units. In the AHP method, the one port authority management with several business units was ranked second among the best-evaluated alternatives, while the decentralized one was third. With the fuzzy AHP method, this situation was reversed: the model with decentralized management ranked second, while the model with one port authority and several business units ranked third.

5. Discussion and Conclusions

In the Republic of Croatia, there are currently two implemented models for managing regional ports: centralized and decentralized. According to the National Plan for the Development of Ports Open to Public Traffic of Regional and Local Significance, the decentralized management model is the predominant Croatian port management system [16], applied in the Istria, Primorje-Gorski Kotar, Lika-Senj, and Dubrovnik-Neretva regions. The centralized management model is characteristic of the southern regions, except for the Dubrovnik-Neretva region. It is implemented by Zadar, Šibenik-Knin, and Split-Dalmatia regions [16]. The results of our research show that the experts consider a coordinated decentralized model to be optimal for managing the regional ports. The chosen model should enable better and more efficient management of seaports and more efficient operation, considering the following conclusions according to the National Plan [16]: the diversity of entities managing the port, inconsistent collection methods and criteria for the ports’ revenue sources, the risk of unintended use of funds, inadequate prioritization of investments, imbalances in management, and inefficiencies.

As noted in the National Plan’s analysis, the Split-Dalmatia region has the greatest coastal and marine area and the longest coastline. The Split-Dalmatia region applies a centralized system for managing seaports through a single regional port authority. Other regions with a smaller coastal and maritime areas and shorter coastlines, such as the Istria, Primorje-Gorski Kotar, and Lika-Senj regions, have established two or more port authorities for the management of their seaports. Hence, the Istria, Primorje-Gorski Kotar, and Lika-Senj regions, with five, eight, and two regional port authorities, respectively, apply decentralized management models. Regardless of the administrative methods, the Split-Dalmatia, Primorje-Gorski Kotar, and Istria regions generate higher revenues than the other regions. At the same time, the Primorje-Gorski Kotar region achieves the highest total and own income. The way in which the Primorje-Gorski Kotar region conducts its business testifies to a certain independence from regional and state subsidies [16,17].

Regions with a few port authorities also have higher expenditures for salaries and other services, such as accounting, legal services, and travel, which correlate with the number of employees. The costs are higher in the regional port authorities that have implemented centralized management systems—such as the Šibenik-Knin and Split-Dalmatia regions—than in regions with decentralized management models, e.g., Istria, Primorje-Gorski Kotar, and Dubrovnik-Neretva. Port authorities in regions that have opted for decentralized management models have significantly higher operating costs than regions with centralized management systems, which could be related to the number of port authorities in decentralized management systems. Seaports with centralized models have the highest revenue from operations, while the decentralized management models afford lower income [16].

Seaports with centralized management models generate higher revenues from the provision of services but also have higher costs per employee. Port authorities with centralized management models have fewer employees than those with decentralized management models. However, the higher cost per employee results precisely from the need for more staffing to perform the various business processes and procedures of port operations at a high level of quality. For this reason, port authorities with centralized management models are forced to hire external stakeholders—especially service providers [16].

Concerning the facts in the National Plan, it is significant to emphasize that the Split-Dalmatia, Primorje-Gorski Kotar, and Istria regions derive part of their revenues from nautical berths. The Istria region derives more of its revenues from municipal than from nautical berths [16]. This is significant in terms of the functionality criterion—which refers to the tourist season and the increase in tourist supply and demand—and the success criterion concerning the nautical and municipal berths.

According to the National Plan, the choice of the model should be based on economic-financial and social criteria [16]. The authors of [21] preferred the service quality criterion in the selection of the management model. Conversely, the analysis of the results obtained by the AHP and fuzzy AHP methods from the survey of the port industry experts suggests that the model of choice should be based on the functionality criterion. According to the National Plan, the model of one port authority with several business units should be preferred over other models of regional seaport management [16]. However, experts in the port industry opted for a coordinated decentralized management model as optimal. This result coincides to some extent with the authors’ findings in [19]—that a decentralized and regional approach is best for regional port management. Due to the different advantages and disadvantages of each model with respect to the various requirements of the regional port authorities, the choice of a universal model would not be appropriate. The management model unification of the region’s ports should be sought to an acceptable extent, as proposed in the working version of the Law on Maritime Domain and Seaports [35]. A management model of one port authority with several business units is proposed in the working version of the Law on Maritime Domain and Seaports [35] and the National Plan [16].

Considering the arguments and guidelines listed in the working version of the Law on Maritime Domain and Seaports [35] and the National Plan [16], it is important to emphasize the need to implement an efficient management model for the regional seaports based on the management model of a port authority with several business units. Such a model would allow for the benefits of both centralized and decentralized management models [16]. As proposed in the working version of the Law on Maritime Domain and Seaports [35], the port authority could maintain branch offices if needed. In addition, the implemented model should allow for the assignment of responsibilities, and the decision-making of regional seaports’ founders should be coherent and based on financial parameters and metrics related to staff salaries, revenues, various forms of compensation, costs, and the like. Furthermore, a contemporary port management model and port authority should provide incentives for the five functional activities of the port: ship traffic, cargo handling and storage, port expansion, intermodal connections, and port industrial activities [36]. In any case, the implemented model should make it impossible to create a mechanism of political power or social policy in the port authorities of regional seaports. Additionally, the new management model should establish a control mechanism for business processes and activities to enable the seaports’ sustainable development and prevent possible fraud related to concessions, various forms of remuneration, and business strategies. Systematic analysis of all relevant parameters affecting the selection of a management model at the national level enables the selection and implementation of an appropriate unified management model that could be applied to the entire seaport system in the country. The systematic analysis should involve all relevant stakeholders and experts involved in the work of seaports and port authorities of regional significance, to identify the determinants for the approach to developing the management model.

The research presented in this paper makes an important contribution to the field of port management, particularly with respect to regional seaports in the Croatian port system. Through scientific methods and analysis, new empirical knowledge was gained that can improve the efficiency and productivity of port management. In addition, this research enhances and refines the general knowledge of management models and their effectiveness through a science-based approach. These contributions can ultimately increase the overall success of the business and the satisfaction of all stakeholders involved in managing regional seaports. The study of port management models at the global and regional levels in Croatia reveals the existence of various models that port operators can choose. The selection of a particular management model depends on the specific requirements and needs of port users and the market. The possible port management models that can be implemented within the Croatian regional port system are regulated and defined by the National Development Plan of Ports Open to Public Transport of Regional and Local Significance [16]. An analysis of the management models implemented worldwide and those implemented in the Croatian regional port system shows that the current regional port management models in the Republic of Croatia have some similarities with management models where the port is under the administration of the port city or region. It is noteworthy that the management models prevailing at the global level are primarily focused on larger ports, while the management models for smaller ports—such as the regional ports in Croatia—are derived from the port management models prevailing in individual countries.

Limitations were identified in conducting this study, related to the small sample size (10 completed questionnaires compared to 30 sent questionnaires), the criteria and management models adopted from the National Plan, and limited data on port business drivers. It is necessary to investigate the relevance of other possible criteria and/or conduct broader research on the ones used in this research. There is a need to investigate different management models in contemporary seaports worldwide that could possibly be implemented in the Croatian regional port system. Further criteria analysis should involve stakeholders and experts complementing the determinants of the management model and investigating the relevance of other norms or supplementing the existing ones. A potential limitation of using the AHP and fuzzy AHP methods in a study is the subjectivity of the decision-making process. The analysis results may be influenced by the personal preferences and biases of the individuals involved in the decision-making process. It is important to carefully consider the limitations of these methods and use them in conjunction with other techniques to obtain a comprehensive understanding of the decision problem.