The Problem of Assigning Patients to Appropriate Health Institutions Using Multi-Criteria Decision Making and Goal Programming in Health Tourism

Abstract

Health tourism is an increasingly vital sector for both Kayseri and Türkiye, contributing significantly to exports and foreign currency inflows. Recent investments in health tourism infrastructure have positioned Kayseri as one of the leading cities in the country, particularly due to its strong healthcare facilities. This study explores Kayseri’s potential in health tourism, with a focus on bariatric surgery, by employing Multi-Criteria Decision Making (MCDM) and optimization methods. The study first provides an extensive literature review to identify the key factors influencing patients’ selection of health institutions for bariatric surgery. Subsequently, the Group Best-Worst Method (G-BWM) is applied using expert input from managers of bariatric surgery centers to determine the relative importance of these factors. Based on the G-BWM findings, nine health institutions in Kayseri offering obesity surgery services are evaluated and ranked using the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), which generates institutional performance scores. Building on these results, a Goal Programming model is developed to assign patients to suitable health institutions while simultaneously considering the health institution’s revenue and patient satisfaction. This study offers several novel contributions. It integrates MCDM techniques with goal programming in the context of health tourism—a combination not widely explored in the literature. Additionally, it provides a comparative assessment of the factors influencing health tourists’ decision-making processes, offering policymakers a strategic framework for resource allocation. Lastly, by presenting a mathematical model for patient-institution assignment, the study offers practical guidance for health tourism organizations aiming to enhance both health institution revenue and patient satisfaction in the health tourism sector.

1. Introduction

It is an irrefutable fact that health occupies a pivotal position in the human condition. When the expanding global population is considered as a factor, there has been an escalation in the costs of healthcare expenditures and services. The advent of technological developments and enhanced communication and transport infrastructure has had a profound impact on the field of health, as it has in other domains. This has given rise to the “medical tourism” sector, which could be defined as “travelling across international borders to obtain a broad range of medical services” [1]. Individuals experiencing health concerns who cannot receive treatment from the nearest health institution due to various reasons like long waiting times, very high costs, or lack of medical insurance, tend to seek treatment from an external source beyond the borders of the inhabited country. This phenomenon has been a catalyst for the rise of health tourism, where individuals seek healthcare services beyond their immediate vicinity, often travelling to other cities and countries to avail themselves of specialised medical care [2].

The global health tourism market, which was valued at 115.6 billion dollars in 2022, is one of the fastest-growing sectors in the tourism industry worldwide. Furthermore, it is projected to expand at an annual rate of approximately 11.59% and is anticipated to generate a turnover contribution of around 346.1 billion dollars by 2032 [3]. Notably, the expenditure of a health tourist is estimated to be approximately 12 times that of a typical tourist [4]. The global presence of an estimated 11 million cross-border patients, with an average expenditure per visit ranging from 3500 to 5000 US dollars, further substantiates the financial viability of health tourism for various countries [5]. Beyond the economic aspects, the enhancement of the reputation of health institutions at the local, national, and international levels is a notable benefit of health tourism. The development of health tourism has been shown to lead to an increase in the value of human capital in parallel with the development of human resources and expertise [5]. It is evident that health tourism benefits not only health institutions and their employees but also commercial organisations such as cinemas, cafes, restaurants, sports clubs, and other tourism organisations. Beyond its economic impact, health tourism exerts a considerable influence on the promotion of countries. The multiplier effect of a health tourist leaving a foreign country by receiving good health, accommodation, transport, etc., services and promoting the country and its facilities through ‘word of mouth’ is very important for the promotion of the country in question [6,7]. It is imperative that tourism and health tourism are approached in a sustainable manner. This can be achieved by incorporating principles of sustainable development, ensuring optimal customer satisfaction, and promoting sustainable practices. The completion of this undertaking may be achieved through the provision of services that are both of the highest quality and reasonable in price, while taking into consideration the environmental and social impacts [8]. The phenomenon of health tourism is characterised by a series of significant challenges, the surmounting of which is dependent upon the implementation of effective facilitators such as branding, international cooperation, and government support [9]. For this purpose, health tourism is an extremely dangerous field to be carried out by unqualified people with hearsay information, unplanned and unprogrammed, intuitively.

Errors or deficiencies in planning can directly impact the quality of services received by health tourists, potentially leading to a decline in the reputation of the health tourism destination. Consequently, health tourism necessitates meticulous planning and analysis at every stage, ensuring the allocation of appropriate resources and consideration of health tourists’ preferences. In this context, the present study plans to utilise various scientific methods, including Multi-Criteria Decision Making (MCDM) methods such as Group Best-Worst and TOPSIS and mathematical modelling methods such as Goal Programming, to elucidate the stages in health tourism. We have selected Kayseri, a prominent city in Central Anatolia, as the context for this study. Kayseri has recently received significant investments in technological infrastructure and human capital in the medical field, climbing to a position as one of the best cities that attract medical tourists in Türkiye [10,11].

The objective of this paper is to utilise the stated analytical methods to evaluate and rank healthcare providers within Kayseri, thereby facilitating the allocation of health tourists to the most suitable facility. To this end, a multifaceted evaluation framework has been devised, encompassing both objective and subjective criteria, with the input of domain experts in health tourism. These criteria have been judiciously weighted to reflect their relative importance. The assignment of patients to healthcare facilities is then determined by a meticulous consideration of patient profiles, requests, capacity, and other pertinent factors. This process is intended to ensure optimal patient-supplier matching, thereby enhancing the efficacy and efficiency of the health tourism ecosystem. The present study aims to resolve the issues with an industrial engineering perspective, a viewpoint that is currently understudied in the health tourism literature. Consequently, while offering a distinctive and novel viewpoint on the prevailing challenges in health tourism, the study also seeks to assist intermediary companies and authorised institutions engaged in health tourism to provide services to health tourists by developing algorithms with a scientific perspective and with a minimised error rate.

Particularly, our main research questions are as follows: What are the most important and least important factors affecting the choice of health institutions in health tourism? How are health institutions ranked among themselves according to the factors affecting health tourism? Considering all these criteria and the ranking of hospitals, how should the health tourists be assigned to the most suitable health institutions?

This study makes a significant contribution to the existing literature by employing a unique combination of multi-criteria decision-making and goal programming methods. Moreover, while the factors influencing patients’ choice of health facilities in the context of health tourism have been the subject of numerous studies, there remains a paucity of research evaluating the relative importance of these criteria using multi-criteria decision-making methods. Furthermore, while the patient assignment problem is a frequently studied topic, this topic remains underexplored in the context of health tourism. Consequently, the present study aims to address these knowledge gaps by offering a novel approach to the analysis of health tourism decision-making processes.

The structure of the paper is as follows. Firstly, Section 2 reviews the relevant literature. Secondly, Section 3 covers the methodology, receiving expert opinion, and data collection procedures. Finally, the results, discussion, and conclusions are presented in Section 4, Section 5, and Section 6, respectively.

2. Literature Review

Personnel and patient scheduling problems are among the significant topics of operations research [12]. Knight et al. [13] determined that the implementation of artificial intelligence and machine learning technologies will yield several advantages in this field. These include the capacity for healthcare providers to conserve time, enhance patient satisfaction, and optimise resource allocation and task assignments, thereby fostering efficiency. As asserted by Abdalkareem et al. [14], healthcare scheduling plays a pivotal role in optimising costs and enhancing patient flow. Youn et al. [15] demonstrate that the Bayesian method has the capacity to reduce overall cost functions by up to 24.2%, encompassing patient waiting time, physician idle time, and overtime. Moreover, a discrete event simulation model reveals that a novel scheduling method has the potential to curtail patient waiting times by up to 13% in comparison with the prevailing emergency department scheduling system.

In addition to mathematical programming models, MCDM methods are also utilised frequently in this line of research. Asadi & Daryaei [16] employed the Delphi method to identify the factors influencing health tourism in Iran, determining the weights of criteria through pairwise comparisons and utilising the TOPSIS method to rank suppliers based on their scores. In a similar vein, Buyukozkan et al. [17] utilised the hesitant fuzzy linguistic (HFL) AHP-HFL multi-attributive border approximation area comparison (MABAC) methodology and Strengths, Weaknesses, Opportunities, and Threats (SWOT) analysis to select the most effective strategy for the implementation of health tourism in Istanbul. The utilisation of artificial intelligence-supported multi-criteria decision-making methodologies has been demonstrated to offer effective solutions for enhancing the sustainability of healthcare supply chains and the management of medical requirements [18]. The weight and priority of the risk factors with regard to the data security of patients can be measured by methods such as fuzzy AHP, while the effect of the attributes on different alternatives can be determined with the help of fuzzy TOPSIS [19]. Frej et al. [20] presented a binary linear programming model based on a portfolio selection approach with the objective of maximising the number of patients expected to survive in intensive care units during their hospital stay. In their study, Habib et al. [21] propose a novel multi-criteria decision-making (MCDM) framework, underpinned by linear Diophantine fuzzy sine-trigonometric aggregation operators (LDFSTAOs), with the objective of assessing the performance of healthcare supply chain (HSC) suppliers within the context of Industry 4.0. To the best of the authors’ knowledge, no study has hitherto been conducted that has employed the G-BWM, TOPSIS, and Goal Programming methods in the context of health tourism. Consequently, this study is hypothesised to be of significant value in addressing this lacuna in the existing literature. Lubowiecki-Vikuk & Bialk-Wolf [22] emphasised the importance of interdisciplinary work and different perspectives in health tourism. It is important to note that the present study combines engineering and social science perspectives.

It is noteworthy that India is a prominent player in the health tourism sector. This is attributable to the government’s endorsement of health tourism, significant investments by private organisations in the field, and India’s provision of health services at a lower cost than competing countries [23]. Additionally, Thailand, Singapore, Malaysia, Poland, Austria, and Saudi Arabia are recognised as leading countries in health tourism [24]. Malaysia’s status as a competitive destination for affordable, high-quality healthcare services has resulted in substantial socioeconomic benefits. These benefits encompass augmented revenue in the healthcare sector, enhanced job prospects, and advancements in healthcare infrastructure [25]. However, Türkiye has also emerged as a major player in recent years in this field [2]. Unfortunately, studies focusing on the Turkish case are quite scarce. Among these, Karadayi-Usta & Bozdag [7] focused on the ‘health service provider selection problem’ of health tourism in their study. Intermediary organisations should be the primary point of contact for patients. These institutions are staffed by knowledgeable and experienced professionals who are able to direct patients to the most appropriate health institutions and doctors for their particular ailments. At this juncture, intermediary companies are obligated to facilitate the most suitable patient-hospital match for each health tourist.

There is a plethora of perspectives on the factors that engender success in health tourism. Jain & Ajmera [26] posit that price, treatment and care quality, and the availability of specialists are the most significant factors. The Medical Tourism Index (MTI), which is developed by Fetscherin & Stephano [27], is a multidimensional construct consisting of four dimensions (country, tourism, medical costs, and medical facilities and services) and 34 core items. The results demonstrate that the MTI facilitates the measurement of substantial disparities between countries, not only at the aggregate level but also in each sub-index. Ghosh & Mandal [28] revealed that Medical Tourism Experience (MTEX) has seven dimensions: treatment quality, medical service quality, medical tourism expenditure, medical tourism infrastructure, destination attractiveness, destination culture, and ease of access. Furthermore, MTEX has been demonstrated to have a positive effect on medical tourist satisfaction and medical destination loyalty. Kilavuz [29] assesses these factors in the context of Türkiye and asserts that Türkiye possesses a substantial competitive advantage due to its superior service quality, hospitals equipped with state-of-the-art equipment, geographical location, and attractive prices, which are considerably more advantageous for patients compared to its competitors. In a survey conducted by Sevim & Sevim [30] with 284 health tourists visiting Türkiye, it was found that service quality, modernity of the selected institutions, and Türkiye’s natural beauties were the prominent factors in health tourism. Moreover, Ustun & Uslu [31] concluded that the quality of the services provided by health institutions and the quality and cost of the facilities were the prominent factors for Türkiye to be a health tourism destination. Ozisik et al. [32] emphasised the crucial role of accreditation and audits in ensuring quality and safety. Yildiz & Khan [33] identified cost and quality as the pivotal factors influencing the demand for health services by international patients in Türkiye. In a case study conducted by two hospital managers and 12 healthcare professionals, Ulas & Anadol [34] identified government support, infrastructure, cost, capacity, and human resources as the most significant factors affecting the success of health tourism. In a separate study, Ozan-Rafferty et al. [35] identified cost, the absence of treatment options in patients’ home countries, and inadequate insurance coverage as key factors driving health tourism. The same study also identified Türkiye as a popular destination for health tourism, citing its low costs, the expertise and sensitivity of its medical professionals, and its familiarity and appeal to patients as key factors in this trend. Furthermore, Kowalewski et al. [36] identified that the most prevalent health tourism operations in the domain of obesity surgery are sleeve gastrectomy and gastric bypass.

Within Türkiye, some cities come into prominence in terms of their medical infrastructure and attraction for medical tourists. After Istanbul, Ankara, and İzmir, Kayseri has emerged as a popular medical tourism destination in recent years [37]. Bayram & Uzunlu-Akkulah’s [37] ‘Current Situation Analysis and Action Plan for the Development of Health Tourism in Kayseri’ is a significant study providing a comprehensive overview of existing health institutions in Kayseri, a detailed SWOT analysis of Kayseri in the field of health tourism, the identification of target countries for attracting medical tourists, and a detailed action plan for the development of health tourism.

Whilst the extant literature mostly tends to focus on investigating the factors that influence the choice of health institutions by health tourists and evaluating the effectiveness of these factors, the assignment of medical tourists to the most appropriate health facility is often overlooked. In this regard, the contributions of this study are manifold: Firstly, evaluating the relative weights of the decision factors is novel and provides an important contribution to the literature, as well as providing a practical guide for policymakers who try to find an optimal allocation of limited resources to promote health tourism. Secondly, the hybrid use of multi-criteria decision-making and goal programming methods in assigning patients to the appropriate facilities has not been performed in the health tourism context before, which also addresses an important gap in the literature and would have practical applications.

3. Materials and Methods

In the context of this study, a mixed-method approach is utilised: The study begins with a detailed literature review and interviews (expert opinions) with key stakeholders to identify the factors influencing health tourists’ choice of bariatric surgery institutions in Kayseri. This process led to the identification of nine key decision criteria that are indicated as the most prominent in the decision-making process of health tourists in the literature. To determine the relative importance of these criteria, the Group Best-Worst Method (G-BWM), a multi-criteria decision-making approach, was employed. Experts in health tourism were individually interviewed and asked to identify the most and least important factors, then rate the other criteria accordingly using the Saaty scale (1–9).

Data were also collected from nine authorised health institutions in Kayseri, including quarterly patient numbers and their capacity to serve bariatric surgery patients within the scope of health tourism. These inputs were used to develop a mathematical model. Based on the G-BWM-derived weights, the institutions were ranked using the TOPSIS method, and the resulting scores were incorporated into a goal programming (GP) model.

The GP model aimed to simultaneously maximise the health institutions’ revenue obtained from the health tourism and the institutional score of the facilities the patients were assigned to. It accounted for institutional capacity and 2023 treatment figures and was solved separately for each quarter to reflect seasonal variations and ease computational complexity. Two additional demand scenarios were analysed: one assuming a twofold increase and another a threefold increase in patient numbers per quarter.

The following subsections clarify the details of each step of this analytical process.

3.1. Factors Affecting Hospital Selection in Health Tourism and Finding Them

A plethora of factors have been identified as affecting hospital selection in health tourism. However, only nine of them are incorporated in our analysis, as these are the factors that appear most frequently in the relevant literature. The following section reveals these nine factors, as identified through a comprehensive examination of scientific publications in the field of health tourism.

3.1.1. Health Services Fees

This criterion signifies the mean value of the fees of health services received by health tourists in US dollars ($). It is a quantitative (objective) criterion. Since high prices are not desirable for health tourists, this is a cost criterion. In recent years, the development of health services in developing countries, the advancement of information and communication technologies, the enhancement of quality standards, the support of governments, and other factors have prompted individuals in developed countries to increasingly seek health services in developing countries, given the lower costs associated with these services [38,39]. Additionally, the rising average age in developed countries has been linked to increased healthcare expenditures and a heightened demand for health tourism services. The considerable disparities in healthcare costs across different nations represent a pivotal element in the proliferation of health tourism. The magnitude of these disparities is evidenced by the range of 40% to 90% observed in the cost of healthcare services received by individuals in foreign countries compared to their own. A notable illustration of this is the contrast in the cost of a bypass surgery, which is estimated at $110,000 in the USA, while in countries such as Türkiye, Thailand, or India, the cost is between $10,000 and $12,000. This substantial variation in healthcare expenditures can be attributed to the significant disparity in wages received by healthcare professionals between developed and developing countries [40].

In line with this criterion and drawing on in-depth interviews with the managers of nine health institutions offering health tourism services in the field of obesity surgery in Kayseri, it was determined that the three most preferred treatment types are Gastric Sleeve Gastrectomy, Gastric Bypass, and Gastric Balloon. Within the scope of this criterion, the average treatment fees of these three treatment types were obtained in US dollars ($) for each institution.

3.1.2. Duration of Treatment

The second criterion pertains to the duration of treatment, which is defined as the time interval between the health tourist’s admission to the institution providing health services and their discharge. This criterion can be likened to lead time in factories, as it is a quantitative (objective) criterion. The length of time required to process health tourists is not desirable, so this is a cost criterion. The advent of protracted waiting times for operations covered by health insurance in Western countries has precipitated the exploration of alternative solutions by people residing in these countries [27,39,40]. The underlying factors contributing to this phenomenon include the presence of specialised medical professionals, reduced waiting times, economic considerations, the accreditation and certification held by hospitals, and the services they provide [41].

In the context of this study, the authorities of certified health institutions in Kayseri were consulted about the average treatment time for Gastric Sleeve Gastrectomy, Gastric Bypass, and Gastric Balloon operations in the institutions they represent. The average values were recorded in days.

3.1.3. Marketing Activities and Recognition (Reputation)

In recent years, advancements in internet technology, particularly social media applications, have significantly augmented the marketability of health tourism services. These developments have empowered health tourists to access information about health institutions, evaluate them, and make informed decisions by comparing different options [40,41]. In this context, promotional activities undertaken by health institutions to highlight the range of services they offer can significantly enhance their success [41]. Bayram & Uzunlu-Akkulah [37] emphasise that systematic and continuous promotional activities are a crucial factor in patients’ preference for Türkiye as a health tourism destination. The existence of significant scientific studies and academic publications in this field, focusing on countries that have gained prominence in the domain of health tourism, such as Malaysia, Thailand, and India, has been identified as a contributing factor to the advancement of health tourism in these nations [37].

It is important to note that this criterion is qualitative in nature and subject to interpretation. The higher the score a hospital receives for this criterion, the better it is, so it is a benefit criterion. In order to ascertain the marketing and promotion activities of health institutions in Kayseri, an investigative approach was adopted, whereby the interviewees were posed a series of questions. The nature of these questions pertained to the marketing and promotional activities (advertisements, social media, billboards, etc.) employed by said health institutions to promote their services in the field of obesity surgery and to reach health tourists. The results of this study were synthesised in a way that each health institution received a score ranging from 1 to 5 based on its marketing and promotional activities.

3.1.4. Infrastructure and Technological Facilities of Health Facilities

The factors contributing to the clinical safety of healthcare organisations, as outlined by Aydin & Karamehmet [40], encompass sanitation and disinfection standards, the expertise and experience of the medical team, technological infrastructure and advanced healthcare technologies, and the safety and impact of healthcare processes. In line with the findings of Mahmoudifar et al. [42], it is asserted that technological sophistication represents a pivotal factor in the selection of health tourism organisations. Oberoi & Kansra [41] underscore that infrastructure and service suitability emerge as the predominant reasons for preference.

A high score on this criterion is beneficial to healthcare organisations and is therefore a benefit criterion. This criterion is of a qualitative nature and is subjective. To determine the scores regarding this criterion, the physical infrastructure of health institutions and the technological competence of the health equipment inside are evaluated by experts. In the context of this criterion, the interviewees were consulted on the infrastructure and technological facilities available in their institution for delivering bariatric surgery services. The responses received were synthesised to ensure that each health institution received a score ranging from 1 to 5 for this criterion.

3.1.5. Health Tourism Department and Number of Staff Fluent in Foreign Languages

The capacity of patients to articulate their health concerns accurately is a pivotal criterion in facilitating their adaptation to the environment and optimising the efficacy of health tourism services [40]. The efficacy of doctor-patient communication during and after the operation and the thoroughness of patient education prior to surgery have been demonstrated to exert a substantial influence on patient satisfaction [38]. The capacity to overcome communication barriers and provide the epicrisis to the patient in English serves to highlight the health institution that has made this improvement [37].

This quantitative (objective) criterion signifies the number of foreign languages spoken by the health institution. In order to ascertain the foreign languages in which services can be provided by health institutions providing bariatric surgery services in Kayseri, senior officials of these institutions were asked in which foreign languages the institutions they represent can provide services. The health institutions received points equal to the number of different languages they can serve in. The ability of healthcare institutions to provide services in different and numerous foreign languages is an advantage for them. Therefore, we can evaluate this criterion as a benefit criterion. To avoid imbalances, the number of different languages that institutions can provide services in has been limited to a maximum of 10 in this study. This decision was made by considering the profiles of health tourists visiting Kayseri and the languages spoken, as evaluated in the study by Bayram & Uzunlu-Akkulah [37].

3.1.6. Accreditations and Service Quality

International accreditation and quality assurance certificates are important indicators of service quality for international patients, as they can help to make decisions. In recent years, there has been an increasing emphasis on accreditations that verify the compliance of health services with international health standards. It has been observed that health tourists tend to prefer health institutions with strong accreditations [2]. Among these accreditations, JCI (Joint Commission International) is one of the most widely accepted, as it evaluates health institutions in accordance with global standards [40]. The quality of healthcare organisations can be evaluated according to parameters such as accreditation, patient evaluations, and success rate of treatments [40,43]. The selection of hospitals by health tourists is influenced by a number of factors, including, but not limited to, the following: high-quality standards (ISO, NCQA, ESQA), international accreditations of health institutions (JCI, ISQUA), state-of-the-art medical equipment, reputation of hospitals and doctors, and health quality indicators (postoperative infection rates, etc.) [27]. A substantial proportion of Arab health tourists indicated that their selection of Türkiye as a healthcare destination was influenced by the superiority of the health services offered in comparison to those available in their own countries [39].

This criterion is quantitative in nature and evaluates health institutions based on the accreditations they possess at both the national and international levels, as well as the service quality they deliver. In order to make measurements within the scope of this criterion, the senior officials of the health institutions providing health tourism services in Kayseri were asked about the current Health Quality Standards (HQS) score of their hospitals as a result of the audits carried out by the Ministry of Health of the Republic of Türkiye [44]. A high HQS score is an advantage for healthcare institutions and, therefore, a criterion for benefit. The score received was directly recorded. The HQS is characterised by its inclusiveness, with all hospitals in Türkiye undergoing the same inspection and scoring stages [44].

3.1.7. Medical Expertise and Experience

The quality of service provided by doctors and nurses is identified as a significant criterion in the selection of hospitals by health tourists [37]. Bayram & Uzunlu-Akkulah [37] assert that patients engage in health tourism to access healthcare services of a higher calibre, as evidenced by data from Patients Beyond Borders. The expertise and experience of medical professionals can be determined by various factors, including their experience, the number of years of experience, the level of education and training, and the number of successful medical procedures.

Factors such as the quality of the training received by all health professionals working in health institutions, the number of successful cases in their work and their ratio to all cases, and the duration of experience in their fields of expertise on an annual basis are important factors for health tourists in choosing a health institution [17,37]. This criterion is a quantitative (objective) criterion in which specialists in the relevant field are evaluated on a year-by-year basis according to the average duration of general surgery specialisation (the time elapsed on a year-by-year basis from the time they received their specialisation in the relevant field to the present day) in health institutions providing health tourism services in Kayseri. The higher the value of this criterion, the more beneficial it is, as it indicates that the relevant healthcare institution provides medical tourism services with highly specialised physicians in their field.

3.1.8. Relationships and Agreements with Intermediary Insurance Companies

Intermediary companies have been shown to have a significant impact on the identification of patients seeking healthcare services and the direction of these patients to healthcare institutions [40]. It is therefore vital for healthcare organisations to establish the right relationships with reliable intermediary companies if they are to ensure a successful future in the field of health tourism. Oberoi & Kansra [41] found that the recognition of health institutions by reputable tourism agencies has a very strong impact on their promotion in international health tourism. Intermediary companies can assist health tourists in obtaining visa procedures and legal permits for operations when necessary [38]. Yildiz & Khan [39] found that the most important reason for Arab health tourists to prefer Türkiye is that health services are not covered by insurance.

This criterion is of a qualitative nature and is subjective. It takes into account the number and functionality of the agreements that healthcare organisations have with health tourism intermediary companies and insurance companies. Within the scope of this criterion, the senior officials of the health institutions in Kayseri were asked what kind of relations and agreements they have with which intermediary and insurance companies. The results were synthesised to provide an evaluation score assigned to each health institution for this criterion, ranging from 1 to 5. It is a criterion of benefit.

3.1.9. Additional Services and Facilities

In the context of all health tourism processes involving patients, the hospitality packages offered by organisations in terms of transportation, accommodation, and safety assurance have a significant impact on patients’ preferences. The provision of culturally appropriate food and beverage services, catering to the dietary requirements, religious beliefs, and preferences of health tourists, is another factor influencing their decisions [38]. Ensuring and emphasising the safety of the city and the accommodation provided is of paramount importance in attracting health tourists [37].

This criterion is of a qualitative nature and is subjective. These additional services may include transportation, accommodation, food, security, sightseeing, and extra facilities provided in the hospital. At this point, senior officials of hospitals with health tourism authorisation certificates in Kayseri were asked what additional services and facilities are offered to health tourists other than the standard facilities and services offered to patients. In consequence of a subjective evaluation of the responses submitted, each health institution was assigned a score ranging from 1 to 5 for this criterion. Benefit criterion.

3.2. Multi-Criteria Decision-Making Methods

For the next two phases of the analysis, two Multi-criteria decision-making (MCDM) methods, namely the Group Best-Worst Method (G-BWM) and the TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) method, will be used. MCDM problems are characterised by the evaluation of a set of alternatives (options) against a set of criteria (attributes), with the objective being the selection of the most optimal alternative, the ranking of all alternatives, or the classification of alternatives into a set of classes [45].

3.2.1. Group Best-Worst Method (G-BWM)

The Best-Worst Method is a Multi-Criteria Decision Making (MCDM) technique developed by Jafar Rezaei (Delft University of Technology) in 2015 [45].

The BWM can be utilised for the evaluation of alternatives against established criteria, particularly in instances where objective metrics for evaluating alternatives are not available. Additionally, it can be employed to ascertain the relative importance (i.e., weight) of the criteria employed in identifying a solution that aligns with the primary objectives of the problem [45].

BWM has been used to solve many real-world BWM problems in areas such as business and economics, healthcare, IT, engineering, education, and agriculture. It can be used by a single decision maker or a group of decision makers [45].

BWM is a relatively recent method. AHP, a highly regarded pairwise comparison-based MCDM method, necessitates the undertaking of pairwise comparisons of the full complement of n decision criteria, amounting to n(n − 1)/2 pairwise comparisons. In contrast, BWM requires only reference pairwise comparisons, i.e., 2n − 3 pairwise comparisons. In addition to this feature, which renders BWM a more data-efficient method compared to AHP, it has several other interesting features. Firstly, it introduces a structured approach by identifying the best and worst criteria and then utilising these to compare all other criteria. This structure assists the decision-maker (DM) in producing more reliable pairwise comparisons. Additionally, the unique structure of BWM results in the generation of two integer-only vectors, thereby circumventing a critical distance problem that arises from the utilisation of fractions in pairwise comparisons [46].

The Best-Worst Method (BWM) is a multi-criteria decision-making method that finds the optimum weights of a set of criteria based on the preferences of a single decision maker (DM) (or evaluator). However, it is important to note its limitations in scenarios involving group decision-making, where the preferences of multiple decision-makers or evaluators must be considered. Mohammadi & Rezaei [46] have introduced a Bayesian BWM to overcome this problem and determine the aggregated final weights of the criteria for a group of DMs in a single step [46]. To this end, the BWM framework is examined from a probabilistic perspective, and a Bayesian hierarchical model is adapted to compute weights in the presence of a group of DMs. Furthermore, a new ranking scheme for decision criteria, called credal ranking, is presented, in which a confidence level is assigned to measure the extent to which a group of DMs prefers one criterion over another. The credal ranking is visualised by a weighted directed graph, where the relationship between criteria and confidence levels to each other is only apparent [46].

The following list enumerates the steps of the method in question [47,48]:

Step 1: The initial step in this process is to identify a set of decision criteria and the relevant decision makers. In this step, the decision makers $\left\{D{M}_1, D{M}_2, \dots \dots , D{M}_n\right\}$ determine the m criteria $\left\{C_1, C_2, \dots \dots , C_m\right\}$ that will be utilised in the decision-making process.

Step 2: The second step in the process is for each decision maker to identify the most desirable and important criteria and the least desirable and least important criteria.

Step 3: Determination of the most suitable criterion in relation to all other criteria using a number between 1 and 9. The relative preference of the most suitable criterion over all other criteria is determined using a number between 1 and 9 (1: equally important, 3: moderately more important, 5: very important, 7: much more important, 9: extremely important).

The result of this step is a vector, Best-Others ($A_{Bj}$), which moves from the best to the others. The vector should be expressed as follows:

$$A_{Bj}=\left(a_{B1}, a_{B2}, \dots , a_{Bm}\right),\left(j=1, 2, 3, \dots , m\right)$$

(1)

It can be concluded that each element of the vector $A_{Bj}$, indicates the preference of the best criterion B over criterion $j$. Furthermore, it can be shown that $a_{BB}=1$, which indicates that the most important criterion will be compared with it.

Step 4: In the fourth step of the process, the relative importance of the remaining criteria in relation to the least favourable option is determined by the decision maker. This is achieved by assigning a number between 1 and 9 to each criterion, with 1 representing the least important criterion and 9 representing the most important. The result of this step is a vector representing the relative importance of the criteria in relation to the least favourable option.

$$A_{jW}=\left(a_{1W}, a_{2W}, \dots \dots a_{mW}\right), \left(j=1, 2, 3, \dots , m\right)$$

(2)

In this vector, it is evident that each $a_{jw}$, denotes the preference of criterion $j$ over the worst criterion $W$, with $a_{ww}=1$. This indicates that the worst criterion will be subjected to comparison.

Step 5: In the fifth step of the process, decision makers are grouped according to their preferences regarding the optimal and least optimal criteria. Those who select the same criteria for both best and worst fall into group $G_i$, where $i=1, 2,\dots k$ and $k$ denotes the total number of groups. The outcome of this grouping process is as follows:

$${Group}_{DM}=\left(G_1, G_2, \dots \dots , G_k\right)$$

(3)

Step 6: In the sixth step of the process, the geometric mean is calculated for each group. This is derived from the total preference of the best criterion over the other criteria (Total $A_{Bj}$) and the total preference of all criteria over the worst criterion (Total $A_{jW}$). Within this step, the evaluations of the decision makers for each Total $A_{Bj}$ and Total $A_{jW}$ are calculated using the geometric mean. For each group $\left(G_1, G_2, \dots \dots , G_k\right)$:

$${\left({{\displaystyle \prod }}_{i=1}^{n}Total a_{Bj\left(D{M}_i\right)}\right)}^{1/n}=\sqrt[n]{a_{Bj\left(D{M}_1\right)}}\times a_{Bj\left(D{M}_2\right)}\times \dots \times a_{Bj\left(D{M}_N\right)}$$

(4)

$${\left({{\displaystyle \prod }}_{i=1}^{n}Total a_{jW\left(D{M}_i\right)}\right)}^{1/n}=\sqrt[n]{a_{jW\left(D{M}_1\right)}}\times a_{jW\left(D{M}_2\right)}\times \dots \times a_{jW\left(D{M}_N\right)}$$

(5)

Step 7: In the seventh step of the process, the most appropriate weight should be determined for each group and criterion $\left(w_1, w_2, \dots , w_n\right)$.

The objective of this step is to ascertain the optimal weights for the criteria, thereby ensuring maximum absolute differences. It is evident that the optimal weights for the criteria are $w_B/ w_j=a_{Bj}$ and ${\displaystyle \frac{w_j}{w_W}}=a_{jW}$ for each pair $w_B/w_j$ and $w_j/w_w$, respectively.

It is imperative to ascertain the existence of $\left\{\left|w_B-a_{Bj}{w}_j\right|, \left|w_j-a_{JW}{w}_w\right|\right\}$ values of $j$ for which the maximum absolute differences are minimised. This can be expressed in the following minimum-maximum model:

Within the confines of these constraints:

$$\min \max \left\{\left|{\displaystyle \frac{w_B}{w_j}}-a_{Bj}\right|, \left|{\displaystyle \frac{w_j}{w_W}}-a_{jW}\right|\right\}$$

(6)

$${{\displaystyle \sum }}_{j=1}^n{w}_j=1$$

(7)

$$w_j\ge 0, \mathrm{for}\mathrm{all}j\mathrm{values}$$

(8)

The problem equation is transferred to the following linear programming problem:

$$min=\xi$$

(9)

$$\left|{\displaystyle \frac{w_B}{w_j}}-a_{Bj}\right|\le \xi , \mathrm{for}\mathrm{all}j\mathrm{values}$$

(10)

$$\left|{\displaystyle \frac{w_j}{w_w}}-a_{jw}\right|\le \xi , \mathrm{for}\mathrm{all}j\mathrm{values}$$

(11)

$${{\displaystyle \sum }}_{j=1}^n{w}_j=1$$

(12)

$$w_j\ge 0, \mathrm{for}\mathrm{all}j\mathrm{values}$$

(13)

The determination of the optimal values of $\left(w_{n1}, w_{n2}, \dots , w_{nn}\right)$ and $\xi$ for each group can be achieved through the resolution of the Equations (9)–(13). According to the model, the total weight of the criteria is equivalent to 1. The criteria with higher weight values are prioritised over those with lower values.

Following the completion and analysis of the model, the optimum weights $\left(w_{n1}, w_{n2}, \dots , w_{nn}\right)$ and $\xi$ (Ksi) values have been obtained. The $\xi$ (Ksi) value demonstrates the consistency ratios of the analyses. It is evident that as the value increases, the reliability of the comparisons decreases, and their consistency becomes weaker. Conversely, as the value decreases, it can be deduced that the consistency rates are higher [49].

Step 8: The calculation of the final weights is achieved through the utilisation of the mean values obtained for each group. The optimal weight value that has been ascertained for each criterion in each group is then multiplied by the number of decision makers in that group. Thereafter, the sum of the results is divided by the number of decision makers.

$$w_j={\displaystyle \frac{{{\displaystyle \sum }}_{k=1}^n\left(w_{jk}\times n_k\right)}{N}} \forall j$$

(14)

The quantity $n_k$, denotes the number of decision-makers in the $k\mathrm{th}$ group, with the total number of decision-makers, $N$, being equal to the sum of all $N=\left(n_1, n_2,\dots , n_n\right)$.

3.2.2. The Technique for Order of Preference by Similarity to Ideal Solution Method (TOPSIS)

TOPSIS (The Technique for Order of Preference by Similarity to Ideal Solution) was developed by Hwang & Yoon in 1981 [50]. The TOPSIS method has been applied in a variety of sectors, and its primary advantage is that it can provide both the positive (best) ideal solution and the negative (worst) ideal solution simultaneously. A review of the literature revealed that the TOPSIS method has yielded high and reliable results in national and international studies. In this study, the TOPSIS method was selected due to its ability to compare different criteria. However, it is important to note that the method is not without its limitations. A key disadvantage is the subjective nature of the process of evaluating alternatives and determining the weighted average or equal ratio according to the importance of the criteria [51].

The TOPSIS method consists of a 6-step process:

Step 1: The first step in the process is to create the decision matrix (A). The rows of the decision matrix contain the decision points whose advantages are to be ranked, and the columns contain the evaluation factors to be used in decision-making. Matrix A is the initial matrix created by the decision maker. The decision matrix is shown below:

$$A_{ij}=\left[\begin{array}{ccc}{a}_{11}& \dots & a_{1n}\\ ⋮& \ddots & ⋮\\ a_{m1}& \dots & a_{mn}\end{array}\right]$$

(15)

In the matrix $A_{ij}$, m denotes the number of decision points, and n signifies the number of evaluation factors.

Step 2: Determination of the Standard Decision Matrix (R) The Standard Decision Matrix is derived by employing the elements of matrix A and the subsequent formula.

$$r_{ij}={\displaystyle \frac{a_{ij}}{\sqrt{{{\displaystyle \sum }}_{k=1}^m{a}_{kj}^2}}}$$

(16)

The R matrix is obtained as follows:

$$R_{ij}=\left[\begin{array}{ccc}{r}_{11}& \dots & r_{1n}\\ ⋮& \ddots & ⋮\\ r_{m1}& \dots & r_{mn}\end{array}\right]$$

(17)

Step 3: Thirdly, the Weighted Standard Decision Matrix (V) is to be constructed.

• Initially, the weight values ($w_i$) for the evaluation factors are to be determined.

$$({{\displaystyle \sum }}_{i=1}^n{w}_i=1)$$

(18)

Subsequently, the matrix in each column of the R matrix is multiplied by the corresponding $w_i$ value to form the V matrix.

$$V_{ij}=\left[\begin{array}{ccc}{w}_1{r}_{11}& \dots & w_n{r}_{1n}\\ ⋮& \ddots & ⋮\\ w_1{r}_{m1}& \dots & w_n{r}_{mn}\end{array}\right]$$

(19)

Step 4: Construction of Ideal ($A^{*}$) and Negative Ideal ($A^{-}$) Solutions

The TOPSIS method is predicated on the assumption that each evaluation factor exhibits a monotonic increasing or decreasing trend.

The largest of the weighted evaluation factors in the V matrix, i.e., the column values (the smallest if the relevant evaluation factor is minimising), is utilised to construct the ideal solution set. The following formula demonstrates the process of finding the ideal solution set.

$$A^{*}=\{(\max v_{ij}, j ϵ J), (\min v_{ij}, j ϵ J^{\prime })\}$$

(20)

The negative ideal solution set is formed by selecting the smallest of the weighted evaluation factors in the V matrix, i.e., the column values (the largest if the relevant evaluation factor is maximising). The following formula is used to find the negative ideal solution set:

$$A^{-}=\{(\min v_{ij}, j ϵ J), (\max v_{ij}, j ϵ J^{\prime })\}$$

(21)

In both formulae, $J$ indicates gain (maximisation) and $J^{\prime }$ indicates loss (minimisation). Both the ideal solution set and the negative ideal solution set consist of m elements, i.e., the number of evaluation factors.

Step 5: Calculate the discrimination measures

The TOPSIS method uses the Euclidean distance approach to find the deviations of the evaluation factor value for each decision point from the ideal and negative ideal solution set. The deviation values obtained for the decision points are called the Ideal Separation ($S_i^{*}$) and the Negative Ideal Separation ($S_i^{-}$) measures. The calculation of the Ideal Separation ($S_i^{*}$) measure is shown in Equation (22), and the calculation of the Negative Ideal Separation ($S_i^{-}$) measure is shown in Equation (23).

$$S_i^{*}=\sqrt{{{\displaystyle \sum }}_{j=1}^n{\left(v_{ij}-v_j^{*}\right)}^2}$$

(22)

$$S_i^{-}=\sqrt{{{\displaystyle \sum }}_{j=1}^n{\left(v_{ij}-v_j^{-}\right)}^2}$$

(23)

The number of ($S_i^{*}$) and ($S_i^{-}$) to be calculated here will, of course, be the number of decision points.

Step 6: Calculate the relative closeness to the ideal solution

Ideal and negative ideal separation measures are used to calculate the relative closeness ($C_i^{*}$) of each decision point to the ideal solution. The criterion used here is the proportion of the negative ideal separation measure in the total separation measure. The calculation of the closeness to the ideal solution is shown in the formula below.

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

(24)

Here, $C_i^{*}$ takes a value in the range $0\le C_i^{*}\le 1$, with $C_i^{*}=1$ indicating the absolute closeness of the relevant decision point to the ideal solution, and $C_i^{*}=0$ indicating the absolute closeness of the relevant decision point to the negative ideal solution [51].

3.2.3. Goal Programming

Finally, goal programming will be utilised to provide the most efficient patient allocations to the health institutions in Kayseri by taking into account several objectives. In circumstances where a decision-maker is confronted with a multitude of objectives that are not inherently compatible, it may appear counterintuitive for the feasible region of a linear programming (LP) model to be capable of fulfilling all of these objectives. In such a scenario, the decision-maker must seek an alternative approach to reach a satisfactory resolution. Goal programming emerges as a viable technique in these situations [52]. The objective of goal programming, a specialised form of linear programming, is not to maximise or minimise an objective function but rather to minimise the deviation from a set of given objectives [53]. GP provides a flexible, accessible approach to multi-criteria planning [54].

As argued earlier, Kayseri holds significant potential in health tourism. This study leverages goal programming to classify health tourists based on their service needs and match them with suitable healthcare institutions. The objectives to be achieved are twofold: firstly, to maximise the total health institution revenue obtained in health tourism, and secondly, to ensure that these patients are treated in health institutions with a maximum total institution score. An equation is formulated that incorporates both objectives, and the intended threshold values are determined for this equation. In the event that the primary objective is not met, i.e., the total institution revenue is lower than targeted, the penalty is applied to the total institution revenue, less revenue than the target that was achieved. Similarly, in the case of failing to meet the secondary objective, i.e., when the institution score is less than the determined threshold value, the penalty is applied to the total institution score objective, with the institution score being less than the target. The weights assigned to these two objectives are equal. The assignment of health tourists to the most appropriate health facilities in accordance with the given objectives and constraints is to be achieved using goal programming. The assignment of patients for each quarter of the year will be conducted separately, thereby ensuring the prevention of inaccurate results due to periodic demand differences during the year and the attainment of more efficient results by circumventing potential constraints that may arise due to the solver programme (GAMS). It is assumed that all parameters and values in the model are deterministic prior to the presentation of the model.

• The decision variables are expressed as follows:

$x_{ij}=1$ if patient i is assigned to health institution j

$x_{ij}=0$ otherwise

In this model, $x_{ij}$ denotes a decision variable, with i denoting the patient and j denoting the health institution. It should be noted that each i and j corresponds to different patients and health institutions, respectively. For instance, $x_{12}$ corresponds to patient number 1 and health institution number 2. When $x_{12}=1$, it signifies that patient number 1 is assigned to health institution number 2; otherwise (when $x_{12}=0$), it signifies that patient number 1 is not assigned.

• $d_R^{+}$: Positive deviation for goal 1
• $d_R^{-}$: Negative deviation for goal 1
• $d_S^{+}$: Positive deviation for goal 2
• $d_S^{-}$: Negative deviation for goal 2
• Parameters

c(j): Capacity of the $j\mathrm{th}$health institution.

Each health institution has allocated a certain quota for health tourism patients in the relevant field. The number of patients treated in the relevant field cannot exceed the number in this quota.

f(j): Treatment fees charged by the $j\mathrm{th}$healthcare institution.

Each healthcare facility has an average treatment fee. These fees vary for each healthcare facility and are listed separately for each facility.

p(j): The institutional score obtained by a patient when assigned to the $j\mathrm{th}$ health institution.

In the first part of this work, each health institution was ranked according to the criteria weighted by Group Best-Worst in the first part of this work, using the TOPSIS method, and an institution score was obtained. p(j) is the institution score of the health institution in the relevant field, denoted by j, obtained by TOPSIS.

• Scalars:

R: Total institution revenue target

R corresponds to the total revenue that institutions aim to obtain from treated patients.

S: Total institution score target

S corresponds to the total institutional score that assigned patients are targeted to receive.

m: Total number of patients

m is the parameter corresponding to the top index for patients in the sum symbol, i.e., the total number of patients.

n: Total number of health institutions

n is the parameter corresponding to the top index for the health facility in the total symbol, i.e., the total number of health facilities.

• Goals:

Goal 1: The sum of the institutional revenue of the health institutions where the treated patients are treated should be at least as high as the targeted total institutional revenue (R).

Goal 2: The sum of the institutional score of the health institutions where the treated patients are treated should be at least as high as the targeted total institutional score (S).

• Objective Function

$$\min Z=P_1+P_2$$

(25)

The objective function is defined as the minimisation of the penalty to be obtained from the targets, denoted by the variables $P_1$ and $P_2$, with equal weight attributed to both.

• Constraints

$$P_1=d_R^{-}/R$$

(26)

$$P_2=d_S^{-}/S$$

(27)

Penalty constraints $P_1$ and $P_2$ are defined as follows: if the total revenue to be earned, expressed as $\sum f\left(j\right)\ast x_{ij}$, is less than the ‘total institution revenue target’, denoted by R, then penalty points $P_1$ are incurred by the number of times negative deviation value of goal 1 which is $d_R^{-}$ divided by goal 1 value which is R; otherwise, no penalty points are incurred. Also, if the total number of points received by the assigned patients from the institutional score p(j) is less than the ‘total institutional score target’ expressed by S, penalty points $(P_2)$ will be incurred as many as the negative deviation value of goal 2 which is $d_S^{-}$ divided by goal 2 value which is S. Otherwise, no penalty points are released.

$$\sum f\left(j\right)\ast x_{ij}+d_R^{-}-d_R^{+}=R$$

(28)

Within the specified constraints, if equation is less than R value, we have $d_R^{-}$ to make up for lack, otherwise we have $d_R^{+}$ to reduce excess.

$$\sum p\left(j\right)\ast x_{ij}+d_S^{-}-d_S^{+}=S$$

(29)

Within the specified constraints, if the equation is less than S value, we have $d_S^{-}$ to make up for lack, otherwise we have $d_S^{+}$ to reduce excess.

$${{\displaystyle \sum }}_{i=1}^m{x}_{i1}\le Capacity 1$$

(30)

$${{\displaystyle \sum }}_{i=1}^m{x}_{i2}\le Capacity 2$$

(31)

$$\dots$$

$${{\displaystyle \sum }}_{i=1}^m{x}_{in}\le Capacity n$$

(32)

For each value j, the sums corresponding to all i values are taken respectively. Consequently, the sum of the i values corresponding to each j value, respectively, must be less than or equal to the capacity of the hospital with that j value. This constraint ensures that the total number of patients assigned to each health institution in each area is less than or equal to the capacity of that health institution in that area.

$${{\displaystyle \sum }}_{j=1}^n{x}_{1j}\le 1$$

(33)

$${{\displaystyle \sum }}_{j=1}^n{x}_{2j}\le 1$$

(34)

$$\dots$$

$${{\displaystyle \sum }}_{j=1}^n{x}_{mj}\le 1$$

(35)

For each value of i, the sums corresponding to all j values are taken, respectively. Consequently, the sum of the j values corresponding to each i value, respectively, must be less than or equal to 1. This constraint enables each patient to be assigned to at most one hospital in each area. Thanks to this constraint, it is not possible to assign each patient to more than one health institution in the relevant area.

$$d_R^{+}, d_R^{-}, d_S^{+},d_S^{-}\ge 0$$

(36)

$$x_{ij}\in \left\{0,1\right\}$$

(37)

4. Results

4.1. Demographic Data

In the course of the study, expert opinions were obtained from 11 authorities in the field of health tourism on the factors affecting the patients’ choice of health institution in the context of obesity surgery in Kayseri. The demographic data of the people whose expert opinions were received is shown in

Table 1. Demographic Data of the Experts whose Opinions were Received.

Demographic Information	Gender	Age Range	Education Status	Sector of the Organization	Position in the Organization	Total Range of Work Experience
Expert 1	Male	25–34	Master	Public	Researcher/Scholar	2–5 years
Expert 2	Female	18–24	Associate	Private	International Health Services Consultant	Less than 2 years
Expert 3	Male	35–44	Doctorate	Public	Chief Physician	11–15 years
Expert 4	Female	45–54	Master	Private	Hospital Director	20+ years
Expert 5	Male	54+	Master	Private	Hospital Director	20+ years
Expert 6	Male	35–44	Bachelor	Private	Deputy Business Director	20+ years
Expert 7	Female	35–44	Master	Private	Quality Expert	20+ years
Expert 8	Female	35–44	Bachelor	Private	Director of Health Services	20+ years
Expert 9	Female	35–44	Associate	Private	Corporate Communication Officer	20+ years
Expert 10	Female	35–44	Associate	Private	Quality Management Officer	16–20 years
Expert 11	Male	25–34	Bachelor	Private	Corporate Marketing Expert	6–10 years

below.

The survey was conducted with a total of 11 health tourism experts, 6 of whom were female and 5 of whom were male, thus indicating a balanced gender distribution. Since 6 of the experts fall within the 35–44 age range, this group is given the greatest weight. With regard to educational attainment, the distribution is balanced overall, with the exception of doctoral degrees, which include three associate degree holders, three bachelor’s degree holders, four master’s degree holders, and one doctorate holder. The fact that nine of the eleven experts are employed in the private sector, while only two are employed in the public sector, underscores the significance of private health institutions in the realm of health tourism. The survey participants’ extensive work experience, with six possessing over 20 years of experience, one between 16 and 20 years, and one between 11 and 15 years, attests to the expertise and knowledge of the surveyed population. The analysis of the participants’ roles within their respective institutions reveals an emphasis on administrative management within health institutions.

4.2. Group Best-Worst Results

To facilitate the employment of the G-BWM method, the experts were asked to select the most important and least important criteria and then to evaluate the most important criteria according to the other criteria and the other criteria according to the least important criteria according to the Saaty 1–9 scale [55].

Table 2. Criteria Evaluations of Experts (Best to Others).

Experts/Criterion (Best to Others)	The Best Criteria	C1	C2	C3	C4	C5	C6	C7	C8	C9
Expert 1	C7	3	9	5	3	5	2	1	9	8
Expert 2	C1	1	3	3	2	3	4	3	6	3
Expert 3	C4	6	6	5	1	6	4	5	9	3
Expert 4	C4	2	7	7	1	7	7	9	3	3
Expert 5	C7	2	5	8	3	7	4	1	6	9
Expert 6	C7	7	5	7	9	3	7	1	9	9
Expert 7	C7	3	3	3	7	9	3	1	8	4
Expert 8	C7	7	5	7	3	9	7	1	9	9
Expert 9	C7	5	7	3	2	7	9	1	9	8
Expert 10	C3	9	7	1	7	7	7	7	9	9
Expert 11	C1	1	9	3	5	7	6	3	9	5

presents the most significant criteria as identified by each expert, along with the comparison of these criteria with respect to other criteria. Conversely,

Table 3. Criteria Evaluations of Experts (Others to Worst).

Experts/Criterion (Others to Worst)	The Worst Criteria	C1	C2	C3	C4	C5	C6	C7	C8	C9
Expert 1	C2	7	1	6	8	5	8	9	4	3
Expert 2	C8	9	8	7	7	8	6	8	1	7
Expert 3	C8	6	5	4	9	6	4	5	1	4
Expert 4	C8	3	6	6	9	7	8	9	1	5
Expert 5	C9	8	6	4	7	3	5	9	3	1
Expert 6	C9	9	8	7	8	9	6	9	7	1
Expert 7	C8	6	8	8	8	6	6	9	1	8
Expert 8	C2	7	1	5	8	7	5	9	7	5
Expert 9	C8	7	8	9	8	6	3	9	1	7
Expert 10	C4	9	7	9	1	7	3	7	9	9
Expert 11	C5	9	3	5	5	1	7	8	6	3

illustrates the least significant criterion and the evaluation of each criterion with respect to this least significant criterion.

The weights of the ‘factors affecting the choice of health institution by patients (health tourists) in the field of bariatric surgery were determined by executing the MATLAB code (The calculations were performed using the MATLAB R2024a (version 24.1.0.2537033) software) prepared by Mohammadi & Rezaei [46] employing the Group Best-Worst Method (G-BWM). The summation of all weights yielded a value of 1.0 (100%), indicating a perfect alignment of preferences.

The most significant criterion was identified as ‘Medical Expertise and Experience’, accounting for 16% of the total weight. This was followed by ‘Infrastructure and Technological Facilities of Health Facilities’, which received 13.45% of the weight, and ‘Health Services Fees’, which accounted for 13.4% of the weight. Conversely, ‘Relationships and Agreements with Intermediary Insurance Companies’ received the lowest ranking, with a weight value of 7%. Criteria weights obtained as a result of the G-BWM are given in

Table 4. Criteria Weights.

Criterion	Criteria Weights
C1 (Health Services Fees ($))	0.134
C2 (Duration of Treatment (Day))	0.0969
C3 (Marketing Activities and Recognition (Reputation) (1–5))	0.1163
C4 (Infrastructure and Technological Facilities of Health Facilities (1–5))	0.1345
C5 (Health Tourism Department and Number of Staff Fluent in Foreign Languages (Number of Languages))	0.0968
C6 (Accreditations and Service Quality (HQS Score))	0.1029
C7 (Medical Expertise and Experience (Years))	0.1601
C8 (Relationships and Agreements with Intermediary-Insurance Companies (1–5))	0.0703
C9 (Additional Services and Facilities (1–5))	0.0882

below.

The Group Best-Worst method has introduced the ‘Credal Ranking’ system as an innovation, enabling a comparison of all criteria pairs and the display of all criteria in colour [46]. As illustrated in Figure 1, $A{\to }^{d}B$, criterion A is indicated as being more significant than criterion B with a confidence level of d. This analysis demonstrates that the ‘Medical Expertise and Experience’ criterion is significantly more important than many other criteria. Conversely, the ‘Duration of Treatment’ criterion is more significant than the ‘Health Tourism Department and Number of Foreign Language Speaking Staff’ criterion, although the confidence level for this latter comparison is only 0.5.

4.3. TOPSIS Results

The values of all nine hospitals in Kayseri regarding the factors affecting the choice of health tourists in the field of bariatric surgery are presented in

Table 5. Hospitals and Their Values of Criteria.

HFN/C	C1	C2	C3	C4	C5	C6	C7	C8	C9
H1	2500	7	5	3	7	94.6	0	5	5
H2	2500	2.67	5	4	6	88	20.4	5	5
H3	2750	2.33	3	4	3	96.6	23.33	3	4
H4	2370	2.33	5	5	4	88	16.67	4	4
H5	12000	1.56	2	3	3	97.74	17.5	3	2
H6	2750	5	2	4	3	92	20.5	1	3
H7	3833	4	5	4	10	88	16.5	5	2
H8	2500	2.67	2	3	4	86	14	5	5
H9	3550	4	1	5	2	97.3	30	2	2

. These values are evaluated using the TOPSIS method, in conjunction with the criteria weights. The objective is to rank the hospitals among themselves using the institution score.

HFN/C, abbreviated from Health Facility Name/Criteria, is located in the upper-left corner of Table 5. H1–H9 designate hospitals offering health tourism services in Kayseri in the domain of bariatric surgery, while C1–C9 signify the criteria influencing the selection of a health institution in the field of bariatric surgery.

In the study by Bayram & Uzunlu-Akkulah [37], it was stated that, according to the frequencies of foreign languages served in institutions in Kayseri, there are 7 different languages: English, German, Arabic, Flemish, Russian, Persian, and French. In addition, according to their frequencies, health institutions in Kayseri have websites in 11 different foreign languages: English, Arabic, German, French, Russian, Flemish, Azerbaijani, Albanian, Bosnian, Romanian, and Bulgarian. In view of the aforementioned information, in order to avoid any potential manipulation of the research results, the maximum value that the criterion ‘Health Tourism Department and Number of Foreign Language Speaking Staff (Number of Languages)’ expressed as C5 can take is limited to 10. Consequently, despite Hospital 7 being a chain hospital with 27 different interpreter services available from its headquarters for its patients, it has received the maximum value of 10 from this criterion.

The MATLAB code (The calculations were performed using the MATLAB R2024a (version 24.1.0.2537033) software) developed by Mathew [56] was executed, and the health institutions specialising in bariatric surgery in Kayseri were evaluated using the TOPSIS method. The TOPSIS score obtained was utilised to determine the ranking of these institutions. The final TOPSIS scores and the ranking of the health institutions are illustrated in

Table 6. Ranking of Health Institutions According to TOPSIS Scores.

HFN	TOPSIS Score
H2	0.76209
H4	0.69233
H7	0.68973
H3	0.6829
H9	0.61436
H8	0.6079
H6	0.59111
H1	0.5196
H5	0.37526

.

According to Table 6, Hospital 2 emerges as the most accomplished health tourism institution serving in the field of obesity surgery in Kayseri with its TOPSIS score of 0.76209. It is followed by Hospital 4 with a score of 0.69233, Hospital 7 with 0.68973, and Hospital 3 with 0.6829. The least successful hospital in this field is Hospital 5 with a TOPSIS score of 0.37526.

4.4. Goal Programming Results

As illustrated in

Table 7. Number of patients treated and can be treated by hospitals.

HFN	NPT-Q1	NPT-Q2	NPT-Q3	NPT-Q4	CP-Q1	CP-Q2	CP-Q3	CP-Q4
H1	15	10	10	5	0	0	0	0
H2	720	540	810	450	1350	1350	1350	1350
H3	0	0	1	0	60	60	60	60
H4	230	250	275	108	270	270	270	270
H5	6	4	0	0	60	60	60	60
H6	17	15	18	13	15	15	15	15
H7	1	1	1	0	225	225	225	225
H8	9	8	12	7	900	900	900	900
H9	0	0	0	0	90	90	90	90

, there are two distinct data types. The initial data type, designated as NPT-QX, pertains to ‘the number of patients treated in the health institution in the relevant row within the scope of health tourism and tourist health in the field of bariatric surgery in the $X\mathrm{th}$ quarter of 2023’. The subsequent data type, denoted as CP-QY, corresponds to ‘the number of patients that can be treated in the given health institution within the scope of health tourism in the field of bariatric surgery in the $Y\mathrm{th}$ quarter of 2025. That is to say, these columns refer to the amount of capacity reserved by the given health institution in the $Y\mathrm{th}$ quarter for health tourists in the field of bariatric surgery’.

Table 7 provides a comprehensive overview of the key variables and their corresponding acronyms:

HFN: Health Facility Name

NPT-QX: Number of Patients Treated in the $X\mathrm{th}$ Quartile of 2023

CP-QY: Capacity in the $Y\mathrm{th}$ Quartile of 2025

As demonstrated in Table 7, it is evident that Hospital 1 has not allocated a quota of any patients for bariatric surgery treatment in 2025, a decision that is likely influenced by the institution’s recent restructuring, which has led to the departure of a specialist physician. Conversely, Hospital 2 and Hospital 4 have garnered attention in the domain of bariatric surgery tourism, with both institutions reporting the treatment of over 100 health tourists in each quarter of 2023.

As demonstrated in Table 7, in 2023, a total of 3536 patients were treated by nine hospitals in Kayseri that have a health tourism authorisation certificate in the field of bariatric surgery. The patients were distributed across the year, with 998 being treated in the first quarter, 828 in the second quarter, 1127 in the third quarter, and 583 in the fourth quarter. This figure falls significantly short of the expected capacity of the city’s hospitals, which stands at 2970 patients per quarter and a total annual capacity of 11,880 patients. As Bayram & Uzunlu-Akkulah [37] have previously demonstrated, Kayseri possesses considerable potential in the domain of health tourism. Consequently, the targeted number of patients per quarter (TNP) is calculated as 75% (3rd quarter) of the total number of patients arriving in 2023, which is 3536 ∗ 0.75 = 2652. When we receive the third quarter of the treatment fees, we find that $3550. As a result, the targeted institution revenue (TIR) was determined to be 2652 ∗ 3550 = $9,414,600. Furthermore, a data series comprising the TOPSIS scores of the nine health institutions referenced in this study was sorted in the statistical plane, resulting in a range of 0.68973 for the third quarter (Q3). Consequently, the targeted institution score (TIS) was determined to be 2652 ∗ 0.68973 = 1829.16396. The overarching objective is to ensure that health tourists receive treatment in health institutions that treatment fee and institution score in the highest-level quarter (Q1) as much as possible.

The GAMS code (The calculations were performed using the GAMS Community Licence (Academic User) software, version 48.6.0.), the open form of which is given in Appendix A, was written and executed for this study. By using the goal programming method, the health tourists arriving in 2023 were reassigned for the year 2025, but this time by taking into account various parameters such as the factors affecting the health tourists’ choice of health institutions, the relative weights of these factors, the average treatment fees, the TOPSIS scores of the health institutions, and the capacities.

According to the Presidency of Communication [57], Türkiye received 1 million 150 thousand health tourists in 2024, generating $2.3 billion in revenues. Moreover, Türkiye aims to host 3 million health tourists and generate $10 billion in health tourism revenues annually [58]. In light of the aforementioned data, this study also examined the impact of scenarios in which the number of incoming tourists doubled and tripled. Consequently, the study yielded a total of 12 results for each quarter, encompassing the present scenario (based on the number of health tourists arriving in Kayseri every quarter in 2023 to receive treatment in the domain of bariatric surgery), the multiplication of the number of health tourists arriving in the present scenario by 2 (scenario 2) and by 3 (scenario 3). A total of 4 quarters and 3 scenario 4 ∗ 3 = 12 results are obtained in total. The results obtained are presented in

Table 8. Goal Programming Results Comparison.

(a)
Scenario	Quarter	SNP	SIR	TIR	MRT (%)	SIS	TIS	MST (%)
1	1	998	3,459,425	9,414,600	36.75	707.779	1829.164	38.69
1	2	828	3,034,425	9,414,600	32.23	578.224	1829.164	31.61
1	3	1127	3,781,925	9,414,600	40.17	806.089	1829.164	44.07
1	4	583	2,421,925	9,414,600	25.73	391.512	1829.164	21.40
2	1	1996	5,941,995	9,414,600	63.11	1448.874	1829.164	79.21
2	2	1656	5,104,425	9,414,600	54.22	1209.235	1829.164	66.11
2	3	2254	6,583,075	9,414,600	69.92	1610.442	1829.164	88.04
2	4	1166	3,879,425	9,414,600	41.21	835.810	1829.164	45.69
3	1	2994	8,373,075	9,414,600	88.94	2045.699	1829.164	111.84
3	2	2484	7,158,075	9,414,600	76.03	1750.259	1829.164	95.69
3	3	3381	8,373,075	9,414,600	88.94	2045.699	1829.164	111.84
3	4	1749	5,342,925	9,414,600	56.75	1278.208	1829.164	69.88
(b)
Scenario	Quarter	dR_pos	dR_neg	dS_pos	dS_neg	P1	P2	Z
1	1	0	5,955,175	0.000	1121.385	0.633	0.613	1.246
1	2	0	6,380,175	0.000	1250.940	0.678	0.684	1.362
1	3	0	5,632,675	0.000	1023.075	0.598	0.559	1.158
1	4	0	6,992,675	0.000	1437.652	0.743	0.786	1.529
2	1	0	3,472,605	0.000	380.290	0.369	0.208	0.577
2	2	0	4,310,175	0.000	619.929	0.458	0.339	0.797
2	3	0	2,831,525	0.000	218.722	0.301	0.120	0.420
2	4	0	5,535,175	0.000	993.354	0.588	0.543	1.131
3	1	0	1,041,525	216.535	0.000	0.111	0.000	0.111
3	2	0	2,256,525	0.000	78.905	0.240	0.043	0.283
3	3	0	1,041,525	216.535	0.000	0.111	0.000	0.111
3	4	0	4,071,675	0.000	550.956	0.432	0.301	0.734

below.

Table 8 provides a comprehensive overview of the key variables and their corresponding acronyms:

SNP: Sum of Number of Patients

SIR: Sum of Institution Revenue

TIR: Targeted Institution Revenue

MRT (%): Percentage of Meeting Revenue Target

SIS: Sum of Institution Score

TIS: Targeted Institution Score

MST (%): Percentage of Meeting Score Target

Except for scenario 3, quarter 1 and scenario 3, quarter 3, all incoming patients were assigned to healthcare facilities. In scenario 3, quarter 1 and scenario 3, quarter 3, the number of patients assigned was limited to the monthly capacity (2970 people).

5. Discussion

The results of the previous section provide significant insights into many aspects of health tourism.

First of all, the G-BWM analysis results provide the answer to the first research question: “What are the most important and least important factors affecting the choice of health institution in health tourism?” Among the factors that were ascertained from the literature review, the “Medical Expertise and Experience (C7)” criterion stands out as the most prominent one, with a weight of 16%, according to the expert opinions. It is followed by the criteria ‘Infrastructure of Health Facilities and Technological Facilities (C4)’ and ‘Health Services Fees (C1)’ with weights of 13.45% and 13.4%, respectively. According to the experts, medical tourists value the expertise and experience of the healthcare professionals and the medical infrastructure of the facility, which both contribute to the quality of the service they would receive. Next, the fact that medical tourism expenses deserve the third rank is also consistent with the fact that Türkiye is especially famous for the low-cost treatment opportunities provided in the scope of health tourism. These results are also consistent with the findings of the literature. Buyukozkan et al. [17] identified that a robust infrastructure of health institutions and the presence of qualified specialist doctors in their field were two of the three most significant factors influencing health tourism. Similarly, Bayram & Uzunlu-Akkulah [37] emphasised the importance of affordable health services as a key driver of health tourism preferences. This study underscores the paramount importance that health tourists ascribe to the expertise and experience of the medical team, the technical capabilities of the healthcare facility, and the equipment utilised. It is noteworthy that health tourists do not relinquish the expectation of receiving these services at an affordable price. In summary, it can be concluded that health tourists prioritise the price/performance ratio (health services fees/treatment quality) in the context of health tourism. Conversely, the findings indicate that the criteria pertaining to relationships and agreements with intermediary-insurance companies and additional services and facilities are of least importance within the purview of this research. This suggests that health tourists seeking bariatric surgery services prioritise successful treatment and surgery, as opposed to considerations such as holidays and entertainment, in order to achieve the most cost-effective outcome.

Secondly, the TOPSIS method enabled us to answer the second research question: “How are health institutions ranked among themselves according to the factors affecting health tourism?” by rank ordering the healthcare facilities with respect to their overall evaluation on the nine decision factors. In this analysis, Hospitals 2, 4, 7, and 3 stand out as the most prominent healthcare facilities in the context of medical tourism services in bariatric surgery. The reasons for other hospitals not being as attractive are manifold. For instance, bariatric surgery fees typically range from $2370 to $3833, with Hospital 5 being an outlier at $12,000, thereby reducing its appeal based on this criterion. The 7-day treatment duration at Hospital 1 is nearly double the arithmetic mean of 3.51 days observed among the nine healthcare organisations offering bariatric surgery tourism services in Kayseri, which might be the main reason that contributed to the failure of Hospital 1. The analysis reveals that health institutions in Kayseri have HQS scores ranging from 86 to 97.74, with an arithmetic mean of 92.03, substantiating the city’s suitability and readiness to cater to health tourism in the domain of bariatric surgery. The arithmetic mean of the specialisation experience of the doctors of the eight health institutions in Kayseri that can actively provide health tourism services is 19.86 years, which suggests that the success of the health institutions in Kayseri is not surprising and clearly reveals the potential of the city in this field.

The results of the TOPSIS analysis are not surprising when one considers the number of patients currently treated at said institutions. With a TOPSIS score of 0.76209, Hospital 2 is manifestly the preeminent health tourism provider in Kayseri in the domain of bariatric surgery. The data reveal that 2520 out of a total of 3536 patients (71.27%) who came to Kayseri in 2023 to receive healthcare services in the field of bariatric surgery expressed a preference for Hospital 2, thereby validating its position as the leading healthcare institution in Kayseri. The TOPSIS results further indicate that Hospital 4 ranks second among the healthcare institutions, with a score of 0.69233. Among the 3536 health tourists who visited Kayseri in 2023, Hospital 4 was selected by 863 individuals, constituting 24.41% of the total. This positions Hospital 4 as the second most preferred healthcare institution in Kayseri for bariatric surgery-related health tourism. Furthermore, it is noteworthy that Hospital 2 and Hospital 4 collectively treated 3383 out of the total 3536 patients, thereby establishing Hospital 4 as the leading health tourism destination in Kayseri for bariatric surgery, with an overwhelming dominance of 95.67% in terms of the number of patients treated. It is also noteworthy that although Hospitals 7 and 3 have the potential to attract a significant number of health tourists, with TOPSIS scores of 0.68973 and 0.6829, respectively, they appear to be underutilising this potential in the field of health tourism. This may be attributable to the strategic decisions of the management of Hospitals 7 and 3. The findings indicate that significant investment in health tourism is particularly recommended for Hospitals 7 and 3. While Kayseri possesses the capacity to accommodate 11,880 health tourists annually in the domain of bariatric surgery, the observed figure of 3536 health tourists treated indicates that only 29.76% of the capacity is utilised, which is considerably below the city’s health tourism potential. Consequently, it is imperative for the city to prepare for scenarios where the number of incoming health tourists is twofold or threefold the current situation.

Finally, the results obtained from the TOPSIS analysis are fed into the mixed-integer programming model, which is solved by GAMS/Cplex. The results of the assignment, which provide the answer for the third research question: “Considering all these criteria and the ranking of hospitals, how should the health tourists be assigned to the most suitable health institutions?” are shown in Table 8. Since the model tries to achieve both revenue maximisation and patient satisfaction simultaneously, the results are not obvious, especially for the scenarios where the total capacity surpasses the patient numbers. In these cases, the model assigns the patients to the hospitals that would provide the best performance/price ratio, enabling the improvement of both goals of the model. In the current solution, with the exception of scenario 3, quarter 1 and scenario 3, quarter 3; the targeted organisational revenue or the targeted organisational score were not achieved. In those solutions where the targets for the institutional revenue and the institutional score were achieved, the penalty functions and therefore the objective function were found to be 0 because there was no penalty for not achieving the target. It is noteworthy that, with the exception of scenarios 3 (1st quarter) and 3 (3rd quarter), capacity-related challenges did not emerge during the assignment process. This finding substantiates the capacity of Kayseri to accommodate health tourism services in the domain of bariatric surgery, with the potential to receive 2–3 times the number of incoming health tourists. Following the aforementioned revisions, it can be concluded that Q1 of scenario 3 and Q3 of scenario 3 represent the most desirable health tourism scenarios in Kayseri.

6. Conclusions

This study has emerged from the paucity of industrial engineering perspectives in the health tourism literature, with previous research frequently investigating the factors affecting the choice of health facilities in health tourism, yet neglecting to consider the systematic assignment of health tourists to health facilities by considering these factors. This has led to the study’s consideration of health tourism as an operations research supply chain, addressing the problem as comprising several steps, with the appropriate analytical techniques applied at each step. The investigation commenced with an examination of the factors influencing health tourists’ selection of health facilities. Utilising the Group Best-Worst method, complemented by expert insights, the analysis identified ‘Medical Expertise and Experience’ as the paramount factor, followed by ‘Infrastructure and Technological Facilities of Health Facilities’ and ‘Health Services Fees’. The TOPSIS method was then employed to evaluate nine health institutions specialising in bariatric surgery in Kayseri, taking into account the criteria weights. The results of this evaluation revealed that Hospital 2 achieved the highest score, followed by Hospital 4, Hospital 7, and Hospital 3, which had almost identical scores. Finally, considering the incoming patient data in 2023, these patients were systematically reassigned to health institutions in regard to the two goals of revenue maximisation and patient satisfaction. In addition, within the scope of Türkiye’s health tourism targets, scenarios with 2 times and 3 times the current number of patients were studied, and it was seen that Kayseri province could successfully serve in these scenarios.

This study is expected to contribute to the development of health tourism on a nationwide scale, with Kayseri province selected as a pilot province for the study’s initial phase. The primary objective of the study is to find the most efficient way to allocate health tourists seeking bariatric surgery to suitable health institutions in Kayseri. This study will facilitate the categorisation of health tourists who seek services through official sources, such as USHAŞ (International Health Services Incorporated Company) and Türkiye’s international health tourism brand: Health Türkiye, across various health domains beyond bariatric surgery (e.g., ophthalmology, dentistry, aesthetic medicine). Note that the model presented in this study could be extended in various ways to accommodate more complicated patient allocation problems. For instance, it is possible to extend the problem to include various healthcare operations that share a common capacity of the same institution. Additionally, it could enable the strategic allocation of patients to different cities based on multiple factors, including patient preferences, the medical infrastructure of each location, and the expertise of healthcare professionals. This approach aims to ensure a more structured and efficient distribution of health tourism patients across Türkiye or any given country, with assignments managed from a centralised system.

In addition to the aforementioned points, the efficacy of this study could be enhanced by updating the criteria and weights for different cities, countries, and regions worldwide. At this juncture, the establishment of an artificial intelligence-supported system could prove beneficial. This system would facilitate the collection of data from diverse global locations, encompassing various social, educational, and income levels, as well as individuals from diverse religious, national, cultural, and ideological backgrounds. Through artificial intelligence, it would be possible to learn and identify different patient profiles and subsequently match them with the most suitable country, city, health institution, and even doctors according to their profile. This approach has the potential to enhance the success of health tourism treatments and patient satisfaction while simultaneously increasing the efficiency for all stakeholders involved in the process.

Furthermore, this study makes significant contributions to both academic literature and practical applications. Beyond offering valuable insights into the relative importance of decision factors, it introduces a novel methodology for addressing medical tourism allocation challenges. The proposed three-step approach integrates the Group Best-Worst Method (G-BWM), Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), and Goal Programming to optimise the allocation of medical tourists to healthcare institutions. This methodology is adaptable to various contexts and can be employed to solve similar allocation problems in medical tourism. For instance, intermediary companies seeking to match clients with suitable healthcare facilities could utilise this approach to simultaneously maximise patient satisfaction and health institution revenue. We believe that both academics and practitioners can benefit from the methods and findings of this study.

That being said, the study is not without its limitations. While the TOPSIS results reveal that four hospitals stand out significantly in terms of patient satisfaction scores, and the Goal Programming (GP) scenarios offer insights into how patient allocations may shift under varying demand levels, the robustness of the findings could be enhanced through a comprehensive sensitivity analysis. Additionally, the relative importance of key decision factors was derived from the perspectives of sector professionals; however, the views of health tourists themselves may differ and warrant further investigation. Despite these limitations, we believe the study offers valuable insights for both policymakers and practitioners. Policymakers may utilise the findings to develop more effective resource allocation strategies for promoting health tourism, while practitioners can refer to the results as a guide for optimising patient-institution assignments. Finally, our findings highlight a notable gap in the application of mathematical modelling within the health tourism sector. We hope this study encourages further academic inquiry into this critical and emerging area.