Port selection has been a hot topic for many last decades because of the great influence seaports have on the maritime transport industry. In particular, the sea container shipping industry plays an important role in global trade because of its strong development and the values and benefits it brings.

Due to the complex multi-criteria decision-making problems in container terminal selection, researchers are increasingly paying attention to this topic. Studies related to container terminal selection from shipping companies’ perspective are implemented in many countries and regions, such as European ports (Nazemzadeh & Vanelslander, 2015), Australia (Ng et al., 2013), Taiwan (Nir et al, 2003; Chou, 2010; Hsu et al., 2021), Korea (Yeo et al., 2008; Ha et al., 2017), Africa (Gohomene et al., 2016), and China (Yuen, 2012). However, lack of research on container terminal selection in Vietnam. In general, port studies in Vietnam often only point out effectiveness or ineffectiveness, they do not rank alternatives (Nguyen & Kim., 2015; Nguyen et al., 2016; Pham et al., 2018; Kuo et al., 2020; Nguyen et al., 2021). As a coastal country with the advantage of a long coastline and close to international maritime routes, Vietnam’s seaport system is attracting major international shipping lines to operate. Southern seaports develop more dynamically than other regions and play an important role in Vietnam’s shipping industry (Nguyen et al., 2021). Therefore, this paper investigate the performance of top four container terminals in the Southern seaport system including Cat Lai terminal in Hochiminh city seaport, Tan Cang-Cai Mep international terminal (TCIT), Cai Mep international terminal (CMIT) and SP-SSA international terminal (SSIT) in Cai Mep Thi Vai seaport system.

One of the popular methods introduced to solve decision-making in port choice problem is AHP method (Song & Yeo, 2004; Chou, 2010; Lam & Dai, 2012; Yuen et al., 2012; Ng et al., 2013). This method is simple to apply and quickly to identify the optimal alternative. Pairwise comparison matrices in the AHP imply the consistency of a rational decision and are strongly aligned with human judgment. However, in the complexity of the real world, assumption that decision making is a rational process are flawed (Pham et al., 2024). Another famous method to solve MCDM problem is TOPSIS. Personal judgments in TOPSIS are shown with crips value is considered not always possible. The fuzzy method is used under a fuzzy environment to handle this reason. However, information is not only characterized by fuzziness. Port choice involves resolving complex problems that are inherently ambiguous and uncertain (Park & Yeo, 2012). To eliminate the uncertainty, ambiguity, and subjectivity, this paper proposes a systematic method by integrating a AHP and TOPSIS based on rough set theory to address the evaluation bias problem in AHP and TOPSIS to improve the judgment consistency and choose the best alternative.

The rest of the paper is organized as follows: Section 2 briefly reviews the literature reviews on port selection studies. Section 3 discusses the proposed methodology to support the container terminal selection procedure. Section 4 provides a real case study of Vietnam. The conclusion is presented in Section 5.

Container terminal selection is a complex problem and is considered as a multi-criteria decision-making. A container terminal selection problem can enhance terminal’s efficiency by investigating its performance and the importance of crucial factors that have a role in selection decision of shipping lines. Numerous studies have been conducted to assess container terminals from shipping companies perspective based on vastly developed methods. These methods provide a numerical approach to determine the optimal alternative among a broad set of criteria. Applications of different MCDM methods in container terminal selection normally evaluate a system based on economic, environmental, and technical factors. AHP method is one of the most popular methods used in the past decades. Chou (2010) performed a study to evaluate the behaviour of carriers’ port choice and investigated the importance weight of factors influencing their port selection in the multiple-ports region. In this research, the main factors included port charge, port operation efficiency, and load/discharge efficiency. Nazemzadeh & Vanelslander, 2015 presented a study using the AHP method for evaluating five dimensions of container terminals, including port capacity, port costs, port productivity, quality of hinterland connection, and geographical location. Hsu et al. (2020) adopted the exploratory factors analysis (EFA) method to evaluate the port choice factors for ship calls of liner carriers. Yeo (2008) proposed an assessment structure for identifying and assessing the competitiveness of major ports in Korea and China. Notthamon Kananika et al. (2019) developed a model for investigating the port sustainability performance of container ports in Thailand, considering economic, environmental, and social criteria using the best-worst method. In Vietnam, scholars pay attention to port research, but is has some limitations. Most of port studies use the data envelopment analysis (DEA) method to evaluate the efficiency of container terminals (Nguyen & Kim., 2015; Nguyen et al., 2016; Pham et al., 2018; Nguyen et al., 2019; Kuo et al., 2020; Nguyen et al., 2021). However, by using DEA, the authors ignored the consideration of decision-makers’ preferences and the uncertainty of the overriding decision-making environment (Pham et al., 2024). Moreover, this method has limitations because it is very hard to provide suggestions to decision-makers on how to improve efficiency. Nguyen et al. (2016) proposed AHP method to classify 11 container terminals in Northern Vietnam, considering quantitative factors including throughput, number of berths, berth maximum draft, container yard square, medium vessel size, and average handling productivity. Nguyen et al. (2019) performed an analysis of container terminals with input data consisting of container throughput and the number of vessel call. It can be argued that previous studies have not only overlooked the complexity involved in the selection and evaluation process of container terminals, but also neglected to account the diversity of criteria that influence their competition, efficiency, and effectiveness. In addition, these studies have not clearly indicated which subject group’s viewpoint the assessment is based on. Pham & Yeo (2019) evaluated transshipment container terminals’ service quality from shipping companies’ perspective, identifying four main factors: function, accessibility, management and convenience. Authors believed that their study help shipping companies to make decisionn about choosing a transhipment container terminal that will allow them to cut cost. However, it lacks the inclusion of economics factor that should be used to assess container terminals. Therefore, in this study a more diverse and comprehensive set of criteria, including infrastructure, economic, and technical are selected from research history and expert survey, which are proposed to rank top container terminal in Southern Vietnam.

Fuzzy set theory has been extensively used to address ambiguity and uncertainty. Celik et al. (2008) proposed competitive strategies for Turkish container ports using fuzzy axiomatic design and fuzzy TOPSIS. Chou et al., (2010) introduced fuzzy MCDM based on fuzzy numbers to solve the container transportation demand split demand. Wang et al. (2014), while considering some factors, like port service, hinterland condition, availability, logistics cost, regional center, and connectivity, adopted a hybrid fuzzy - Delphi - TOPSIS approach to choosing the optimal bunkering ports for liner shipping companies. Briefly, these methods are reasonable, easy to implement, flexible, and logically consistent. Although fuzzy set methods demonstrate strong capability in representing uncertainty through the use of membership functions, this advantage primarily applies to individual assessment information (Zhu et al., 2020). Within the decision-making group, the aggregation of discrete evaluation values is still challenging problem.

A new approach with more advantages than fuzzy set in dealing with vagueness and uncertainty is rough set theory, which was first introduced by Pawlak (1982). This method was utilized popular in different fields such as failure mode and effects analysis (Hong Fang et al., 2019), risk evaluation and effect analysis (Musavarah Sarwar et al., 2021), sustainable supplier selection (Arprit Singh et al., 2023), and supplier selection (Stevic et al., 2017). In our best understanding, there are no publications in literature utilize MCDM methods based on rough numbers in container terminal selection.

This paper proposes a decision model for container terminal selection is depicted in Figure 1. We adopted the input data that presented in Pham et al. (2024). This framework can be divided into two main phases. In the first phase, the rough AHP method (Song et al., 2013) is utilized to calculate the rough weight of each criterion, and de-roughness of interval rough weight is also investigated to determine which criterion has play a crucial role in the shipping lines’ port choice. In second phase, a novel TOPSIS method based on the rough set number (Song et al., 2013; Stojic et al., 2018) is presented to determine the ranking order of container terminals. To implement this study, survey form was distributed to experts.

To ensure reliability and experts have well knowledge, fifteen experts, including the vice director, section and department managers who have more than seven experience years in shipping lines, were invited to assess the importance of criteria and rate container terminals’ performance. The detailed profile of respondents is shown in Table 1.

Criteria related to container terminal selection were investigated through the literature review. This study aims to provide a highly applicable model that decision-makers can use with less complexity. We consider and select six criteria among the top influential factors when choosing the container terminal of the shipping lines. In addition, according to our argument, operational efficiency and quality and reputation have a close and logical relationship with each other. Therefore, operational efficiency is give priority instead of quality and reputation. Table 2 illustrates the criteria and sub-criteria effects to shipping lines’ port selection decisions. The main criteria including six criteria: port infrastructure and capacity, geographical loctation and connectivity, port cost and tariffs, operational efficiency, port safety and security, and port information system.

Table 4 illustrates the weights of criteria at two levels. At the hierarchy level, operational efficiency was determined as the most important criteria, followed by port safety and security, geographical location and connectivity, port infrastructure and capacity, port information system, and port cost tariffs. At the sub-hierarchy, the flexible operation process is the ranked highest position in the terminal selection problem, followed by port security and maritime connectivity. Storage space was the least important among the container terminal criteria. Data on port infrastructure, port costs and tariffs were collected from terminals’ official website. The liner shipping connectivity index data, gathered from the first quarter of 2021 to the third quarter of 2022, was presented for maritime connectivity (United Nations Conference on Trade and Development, 2022). Congestion performance was collected from the World Bank, 2014, and number of mode transportation was considered as efficient inland transport (Pham & Yeo, 2019). Other data obtained thanks to experts’ assessment judgment. Fig 2 visually shows the location of the Ho Chi Minh-Ba Ria Vung Tau port group in the Southern of Vietnam.

After all input data were collected, the rough decision matrix was obtained in Table 5 using Eq. (9) and Eq. (10). Then, the weighted normalized rough matrix with PIS and NIS was determined by Eqs. (11)-(16), and were presented in Table 6. Ranking orders of alternatives are demonstrated in Table 7.

Table 7 shows the ranking order as TCITCMITCat LaiSSIT. TCIT terminal was the optimal alternative, followed by CMIT, Cat Lai, and SSIT terminals. TCIT terminal secured the first rank because of it highest rated criteria in depth alongside, the number of equipment, port authority charges, and port security, which are considered very important in container terminal selection from the shipping lines’ viewpoint. CMIT was ranked second thanks it enjoys the greatest advantages in port safety, port information systems, and maritime connectivity. Cat Lai was placed in the third rank because of its poor performance in length of berth and port charges lack of flexibility. SSIT terminal was placed last due to its lack of competitiveness in terms of the number of berths and equipment, along with an inflexible pricing strategy.

In this section the sensitivity analysis is conducted to demonstrates the robustness and accuracy of the proposed model with conventional method of fuzzy AHP (Chang, 1996) combining fuzzy TOPSIS (Chen, 2020). Fig. 3 shows the results of sensitivity analysis. According to fuzzy AHP combine with fuzzy TOPSIS method, the ranking order is SSIT CMIT TCIT Cat Lai. In fuzzy set theory, fuzzy numbers converted into crisp value and ignores decision makers’ psychology. In addition, many studies have shown that in some cases, the ranking order of alternatives changes significantly when the best alternative is added, and even the worst alternative can become the best choice as (Junior et al., 2014).

Rank reversal is unexpected for selection problem. This is a research flaw in the AHP and fuzzy AHP methods, which have been pointed out in many previous studies (Belton & Gear, 1983; Saaty, 2005).

Compared with the crisp number method, the rough set number enable to characterize parts of the uncertainty in the evaluation process. However, the proposed adopts a flexible interval boundary, allowing it to effectively illustrate the uncertainty of the uncertainty and vagueness of the individual components. In MCDM processes, the use of rough form is much better way they treat the uncertainties

This paper presented an integrated model for container terminal selection based on rough AHP and rough TOPSIS methods. The main contributions of this paper are summarized as follows:

First, this study explored the important criteria related to container terminals were classified into six criteria group, nineteen sub-criteria, which were considered through a literature review. The key criterion for container terminal selection was a flexible operation process, followed by port security and maritime connectivity. This paper indicated TCIT terminal is the optimal container terminal in Southern of Vietnam. This paper contributes by providing guidelines on the container terminal selection process. This paper determines the order priority of factors that helps container terminal manager sort the most critical factors that need special attention to enhance their competitiveness. Furthermore, this study results offer direction for shipping lines, enabling them to quickly choose the best alternative to achieve multiple goals.

Second, AHP and TOPSIS methods based on rough set theory address the interpersonal uncertainty without demanding preset assumptions as required in fuzzy set theory. Furthermore, using quantitative, qualitative and linguistic terms reflect a comprehensive system of criteria.

Third, by the proposed method can help managers of shipping line obtain more accurate and realistic rankings. This method benefits container terminal operator by improving their competitiveness through their customers’ evaluations. This method can be applied to deal with various multi-criteria decision-making problems.

There are several limitations in this paper. First, this work determines and categorizes nineteen sub-criteria into six main criteria. It is difficult to argue that the set of evaluation criteria is perfect because these criteria are selected from literature review and can vary in number practical applications. In the future, the set of criteria should be expanded by considering other factors such as political, legal, environmental, and sustainable factor, making the evaluation more comprehensive and diverse. Considering both qualitative and quantitative criteria are essential in multi-criteria assessment, but experts’ bias can still influence the selection outcome. In the future, an integrated approach should be developed to evaluate the weightings and ratings, aiming to reduce bias of decision-makers. In addition, the rough analytic network process (rough ANP) approach, which considers the interactions between criteria, should be utilized.