Designing a mathematical model for dental tourism supply chain

Tourism Management 75 (2019) 404–417

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Tourism Management journal homepage: www.elsevier.com/locate/tourman

Designing a mathematical model for dental tourism supply chain Fatemeh Ahmadimanesh, Mohammad Mahdi Paydar , Ebrahim Asadi-Gangraj

T

∗

Department of Industrial Engineering, Babol Noshirvani University of Technology, Babol, Iran

ARTICLE INFO

ABSTRACT

Keywords: Tourism Dental tourism Supply chain Accommodation centers Mathematical model Sensitivity analyses

In recent decades, medical tourism has grown rapidly and has attracted much attention. This study investigates the design of a dental tourism supply chain network as one of the medical tourism subcategories, and for the first time, it presents a mathematical model for this supply chain. The proposed supply chain consists of three parts: tourists, medical facilities, and accommodation. The purpose of this model is to determine the optimal number of medical and accommodation units and the final capacity of medical centers. The proposed model is verified using a real case study in Mazandaran province, Iran. The obtained results show that the proposed model can be used for strategic planning and effective investment in this field. One of the important applications of this research is to provide suggestions for designing the proposed supply chain network using the outputs of the mathematical model.

1. Introduction In recent decades, the growth of global competition has led to more attention to supply chains rather than individual companies. According to a comprehensive definition of Simchi-Levi, Kaminsky, & Simchi-Levi, 2000, supply chain is defined as ‘‘a set of approaches utilized to efficiently integrate suppliers, manufacturers, warehouses, and stores, so that merchandise is produced and distributed at the right quantities, to the right locations, and at the right time, in order to minimize systemwide costs while satisfying service level requirements’’. Supply chain management (SCM) has now become a vital source of competitive advantage for the organizations. SCM is one of the most lucrative management approaches, which has become an essential part of any kind of business (Chen, 2009; Zhang, Song, & Huang, 2009). When all members of the supply chain are integrated and function as a single entity, efficiency increases throughout the chain. In the field of tourism, there is also the ability to use supply chain optimally and seamlessly according to its significant progress in various industries. The tourism industry plays a significant role in the economic cycle as one of the top ten industries in the world and has an important contribution to wealth creation and foreign exchange for countries. Nowadays, the intense global competition in the tourism industry has focused on supply chains, rather than an emphasis on separate firms. Tourism supply chain management (TSCM) aggregates a wide range of participants to satisfy the tourists' expectations more effectively. Global competition has caused new markets. Medical tourism is one of these markets, which is a direct result of healthcare globalization

∗

(Bernal, 2007). Medical tourism refers to activities related to travel and host a tourist who stays at least one night at the destination region to obtain high-quality medical treatment at a lower cost, in order to maintain, improve or restore health through medical intervention (Musa, Thirumoorthi, & Doshi, 2012). Medical services can be categorized as preventive medical services, fertility, dental care, surgery, cosmetic surgery, organ, cell and tissue transplants, and cardiology (Heung, Kucukusta, & Song, 2011). Medical tourism industry is growing fast. It is worth noting that the global medical tourism market was valued at around US $46.46 billion in 2016, it is anticipated to reach a worth of US$160.8 billion by the end of 2025 (Market, 2015). The global tourism market is expanding at a rate of 15–20% and the highest rate of absorption in Mexico, Southeast and South Asia. On average, the medical tourism industry in Asia increases by 20% annually and it generates about US $ 4 billion a year (Heung et al., 2011). A thriving subset of medical tourism is dental tourism that is described by American Dental Association as ‘the act of traveling to another county for the purpose of obtaining dental treatment’. It involves individuals seeking dental care outside their local healthcare systems and may be accompanied by a vacation. The global market provides more opportunities for the growth of dental tourism. Since dental tourism is a subset of medical tourism, so they have a similar supply chain. The definition of medical tourism supply chain (MTSC) can also be used for the dental tourism supply chain (DTSC). MTSC is defined as a network of entities that plans, sources, funds, and distributes the medical services, manages associated information, and finances from the manufacturers to the medical service delivery points (Barratt,

Corresponding author. E-mail addresses: [email protected] (F. Ahmadimanesh), [email protected] (M.M. Paydar), [email protected] (E. Asadi-Gangraj).

https://doi.org/10.1016/j.tourman.2019.06.001 Received 8 October 2018; Received in revised form 29 May 2019; Accepted 1 June 2019 Available online 19 June 2019 0261-5177/ © 2019 Elsevier Ltd. All rights reserved.

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2004). Lee & Fernando, 2015 shown that coordination and information sharing have a direct impact on organizational performance in the MTSC. Dental care tourists are divided into two categories by Chandu (Lunt, Horsfall, & Hanefeld, 2015). The first category is related to classic dental tourists. People travel to a foreign country to receive dental treatment, either for dental treatment as part of their vacation, or the sole purpose of dental treatment. The second category is migrant tourists. Migrant tourists are defined as people who return to their native country for a holiday or visit relatives and then receive dental treatment during their vacation. According to Chandu (Lunt et al., 2015), dental care can be classified into two types; general and specialized dental care. General dental care comprises scaling and polishing, simple fillings and tooth whitening. While specialized dental care is performed by dental specialists such as complex restorative treatment and surgery. Contrary to the demand for urgent health care that is unpredictable, the demand for dental care is considered nonemergency dominated. Moreover, not-immediately treated dental illnesses rarely lead to dramatic health consequences compared to demands for other health care. In addition, the same or similar dental care is required by most people throughout their lifetime (Österle, Balazs, & Delgado, 2009). Despite the intense interest in medical tourism research, investigations of dental tourism remain limited. Unlike many previous studies in this field that focused on the impact of quality, price reasonableness, travel motivations, and satisfaction and so on, this research is the first study to consider a mathematical model for dental tourism supply chain. This paper presents a new framework to help the dental tourism managers to design an optimized network. The mathematical model was evaluated based on a real case study in Mazandaran Province, Iran. In the proposed model, three main parts of the dental tourism supply chain are considered: medical centers (hospitals and clinics), accommodation centers (hotels and hotel-apartments), and tourists. This model can calculate the profit of dental tourism in the destination country. Furthermore, the optimal number of accommodation and medical centers and the optimal capacity of the medical centers are also specified. The purposes of this research are as follows:

hospitality suppliers, souvenir shops, travel agencies, public sectors and so on, which supply the goods and services for the tourists. Therefore, coordination and collaboration between tourism service providers within the supply chain is an essential element in creating an integrated experience (Lambert & Cooper, 2000). Tourism industry is fundamentally different from other physical goods manufacturing industries. By contrast, a mobile population who visit destinations to consume products, services, and experiences, whereas a service supplier is geographically fixed (Lee & Fernando, 2015). There are two main distinguishing features of the tourism industry. Firstly, on the supply side, tourism products are naturally complex and a mixed of services and goods. In general, tourism products are heterogeneous and compound, consisting of diverse service components such as accommodation, transportation, and sightseeing, dining, and shopping. On the other hand, tourism products are perishable because tourism services cannot be stored for future use (March & Wilkinson, 2009; Zhang et al., 2009). Secondly, on the demand side, tourism demand has high volatility and sensitivity, therefore, it is known as a complication (Sigala, 2008). There is often a higher uncertainty in tourism demand than in other industries. Many factors affect this uncertainty (e.g. effective advertising, negative word-of-mouth effect, and economic conditions in destination countries) (Zhang et al., 2009). According to the mentioned features, Zhang et al., 2009 stated that a tourism supply chain can be examined based on seven perspectives, including demand management, two-party relationships, supply management, inventory management, product development, TSC coordination, and information technology. They reviewed the details of each perspective by reviewing the articles. Based on the concept of supply chain operations reference (SCOR) model, there are three major focuses on the TSC research framework; designs, relations, and performance measurements (Council, 2009). Firstly, the vital starting point of TSCM is supply chain design. By default, the supply chain should be designed based on what targeted tourists want. Some other aspects that can be addressed include strategy, distribution, pricing, facilities, inventory, etc. (Chopra & Meindl, 2007, pp. 265–275). Secondly, the TSCM core is a relationship among stakeholders. In the TSCM, the connection is between the firsttier and second-tier suppliers, tour agencies/tour operators, and tourists, whereas in the typical SCM only the buyer-seller relationship is examined. Thirdly, performance measurement contains four aspects including external (customer satisfaction), financial (margin, profitability), operational (efficiency, effectiveness, reliability, and etc.), and development (sustainability) (Johnston & Clark, 2008). Huang stated that most previous studies have used costs or revenues as indicators for measuring performance (Huang, 2018). Due to the review of the issue of the tourism supply chain in the literature, it emerged that researches in this field could be divided into two stages. The first stage is the period before 2007. The first paper in this field was published in late 1993. In this era, only conceptual framework articles were presented and experimental articles are not observed. The interest of researchers in the field of tourism supply chain has flourished since 2007. Hence, the beginning of the second stage can be considered from 2007. Moreover, in this stage, experimental studies were conducted more than conceptual framework articles. Despite the significant importance of tourism and the issue of tourism supply chain management in the field of socio-economic development of regions and countries, the number of publications in this area is low (Szpilko, 2017).

• What is the optimum flow of tourists and patients in the proposed network? • How much is the response rate to patients and tourists' demand? • How much is the optimal capacity of medical centers? • How many and which medical and accommodation centers should be selected?

The rest of paper is organized as follows. Section 2 presents an overview of the tourism supply chain management, and medical and dental tourism supply chain. In Section 3, the problem is stated and a mathematical model is proposed to solve the problem. In Section 4, the results of the proposed model are described. Then, a sensitivity analysis is conducted to validate the model. Finally, conclusions and future researches are provided in Section 5. 2. Literature review 2.1. Tourism supply chain management (TSCM) TSCM is a developing research agenda in the tourism industry (Zhang et al., 2009). Zhang et al., 2009 defined tourism supply chain as a network of tourism organizations that comprises various activities, including providing the different components of tourism products/services such as flights and accommodation to the distribution, and marketing of the final tourism product at a specific tourism destination. This network includes a wide range of contributors in both the private and public sectors. Peng, Xu, & Chen, 2011 have identified the TSCM components as follows: attraction providers, transportation companies,

2.2. Medical and dental tourism supply chain Supply chain plays an essential role in the healthcare industry (Kumar, Ozdamar, & Ning Zhang, 2008). MTSC has a complex structure such as tourism supply chain and needs support from different sectors to provide goods and services to the customers. MTSC is also similar to all other supply chains, like the manufacturing and service supply 405

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chains that they cooperate to prosper the business operations in the supply chain (Tapper & Font, 2004). Considering the medical tourism and supply chain, MTSC is defined as a supply chain that includes different members of the medical tourism industry that work together to provide a complete medical and holiday service to the user, therewith serving healthcare communities, reducing supply chain costs, and increasing performance among the suppliers (Lee & Fernando, 2015). Effective factors in the MTSC should be properly identified and participants in the MTSC should completely comprehend them in order to grow the industry and the demands of medical tourists. Travel motivation is an important factor in determining a destination (Musa et al., 2012). Motivation is defined as “a psychological condition in which an individual is oriented towards and tries to achieve a kind of fulfillment” (Jang & Wu, 2006). Due to that dental tourism is a subset of medical tourism, it can be concluded that their motivations are quite similar. Based on literature review, motivations are cost-savings, timely service, combining medical care and holiday, cultural similarity, regulations of certain medical treatment or procedures, quality of medical services, information availability and support services (Barrowman, Grubor, & Chandu, 2010; Hall, 2012, pp. 19–44). Ferrer & Medhekar, 2017 have used cost, waiting time and privacy factors related choices by individuals as criteria to predict the demand for the global medical tourism service supply chain. Among these motivations, reasonable costs, quality of dental care services, cultural similarity and the combining dental care and vacation are main travel motivations for the dental tourism (Barrowman et al., 2010; ElliottSmith, 2010; Vequist & Stackpole, 2012) In some studies, dentists' kindness, humility, speed, comfortable and friendly environment, and special treatments are recognized as the main motivations (Carmagnola et al., 2012; Kovacs & Szocska, 2013; Österle et al., 2009). In addition, highly qualified doctors are the main driver of medical tourists' satisfaction (Zailani, Ali, Iranmanesh, Moghavvemi, & Musa, 2016). Costsavings is arguably the most important motivation in dental tourism (Kovacs & Szocska, 2013). Dental services are unaffordable in some countries (Turner, 2008). The cost of dental care and after-care services in home country are often more than the dental tourism destinations (Lunt et al., ). Some studies have shown that when medical tourists travel to less developed countries, they save significant costs (Eissler & Casken, 2013). Moreover, time-saving by using speedy completion of the treatment plan in destination countries and good accesses to the dental care services are the important motivations for the dental tourism (Barrowman et al., 2010; Kovacs & Szocska, 2013). Motivations are very diverse and vary among treatments (Lunt, Horsfall, & Hanefeld, 2016). These motivations can be classified into two types: push and pull factors (Dann, 1977). Push factors are related to internal forces. These factors generate the demand for the medical tourism: high costs, physician and facility reputation and hospital accreditation, domestic waiting lists and lack of access to treatment are important push motivations (Alsharif, Labonté, & Lu, 2010). While pull factors refer to external forces. Therefore, pull motivations determine destination attractions: healthcare costs, popular tourist destination, quality care, accreditation, reputation of doctors (Hsu & Huang, 2008, pp. 14–27). Fig. 1 shows how push and pull factors encourage or attract the medical tourists.

Due to the complexity of the MTSC networks that include many members, good collaboration is vital. Supply chain collaboration is very effective in improving overall performance and is beneficial for all members of the chain (Simatupang & Sridharan, 2005). Establishing trustworthy relationships in the supply chains lead to reduce costs, promote cooperation, boost timely reactions, and fortify competitive abilities (Chen, 2009). Vijayasarathy, 2010 showed that trust, commitment, and mutual dependency significantly affect supply chain formation. Considering that supply chain members are dependent upon each other for resources and information, and not considered as independent members (Arshinder, Kanda, & Deshmukh, 2011, pp. 39–82), and it can be argued that supply chain coordination derives from the interdependence of the supply chain members (Xu & Beamon, 2006). Thus, dependency management is an essential process in collaboration. Most existing studies indicate that supply chain formation leads to better organizational performance and more competitive advantage (Gimenez, van der Vaart, & Pieter van Donk, 2012; Leuschner, Rogers, & Charvet, 2013). The collaboration is planned for the longterm vision and the final goal is to increase organizational performance and sustainability. In fact, more collaboration among the medical tourism chains is essential to support the medical tourism service of a country. In order to improve organizational performance, medical organizations should adopt MTSC measures. If involved organizations in the MTSC sustain such businesses, a country can achieve a competitive advantage and become a good medical tourism destination (Lee & Fernando, 2015). Table 1 summarizes some studies on the dental tourism. As can be seen in Table 1, researches in this field are very limited and all reviewed papers focused on the factors affecting dental tourism from the perspective of patients, and there is no research on the supply chain in dental tourism. Nowadays, the advantages of considering the supply chain in different fields and its efficiency are obvious to all. However, there is no research to examine the involved sectors in the dental tourism supply chain and the positive effects of creating a supply chain in this field. Showing the relationships between the involved sectors in this supply chain and examining these relationships is very effective in creating and improving a dental tourism supply chain in the real world and it helps to manage better these relationships. In addition, research that describes the relationships in this supply chain with mathematical modelling cannot be found either. A mathematical model and analyze the results, can significantly help the managers of this field to make strategic decisions and the generated positive results by the mathematical model can well be a motivation for the dental tourism managers to be more confident in investing in this field. This paper is the first study that provides a mathematical model for the dental tourism supply chain. 3. Problem description Due to the identified opportunities in Mazandaran province, Iran in the field of dental tourism, this research is organized based on a real case study. Although considering that dental tourism is a subset of medical tourism, the proposed model can be generalized to the medical tourism by applying small changes. In order to design the proposed supply chain, it is assumed that tourists travel to another country to receive their dental services. The destination country must respond to the tourists’ demand by providing adequate accommodation and medical centers and earning money in this way. In the destination country, there are a number of candidate accommodation and medical centers, which requires setup cost to continue their activities. The final capacity of the medical centers is considered as a decision variable. Thus, considering existing demand, it is determined that whether existing services capacity will be increased or new services will be added by incurring specified costs, or there will be no capacity increase in the model. This capacity extension is dependent on the medical centers current serviceability. Thus, a parameter was considered as

Fig. 1. Pull and push factors of the medical tourism (Fetscherin & Stephano, 2016). 406

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Table 1 Review of the dental tourism research. Author

Title

Description

Turner (2008) Österle et al. (2009)

Cross-border dental care: ‘dental tourism’ and patient mobility Traveling for teeth: characteristics and perspectives of dental care tourism in Hungary Dental implant tourism

Discussing driving factors in medical tourism Investigating Hungary's ability to attract dental tourists

Barrowman et al. (2010) Carmagnola et al. (2012) Kovacs and Szocska (2013) Jaapar, Musa, Moghavvemi, and Saub (2017) Lovelock, Lovelock, and Lyons (2018)

A survey of Significant Issues for clinician and patient in Dental Tourism A survey aimed at investigating the perception of dental tourism by Italian patients who have recently received dental care abroad Survey the reasons for maintaining a leading position for Hungary in dental tourism Measuring tourist profiles, travel motivation and satisfaction among inbound dental tourists in Malaysia A report on the perceived impacts of dental tourism on the generating region

A survey on the experience with dental tourism in a sample of Italian patients ‘Vacation for your teeth'–dental tourists in Hungary from the perspective of Hungarian dentists Dental tourism: Examining tourist profiles, motivation, and satisfaction The impact of outbound medical (dental) tourism on the generating region: New Zealand dental professionals' perspectives

Cost to extend the unit capacity of dental service s of candidate medical center k Cost of newly setup capacity of dental service s of candidate medical center k Number of required days to receive medical service s Number of days required to receive the set of dental services m. dmm = max{dss × ddsm} Attendant coefficient of customer group g Demand of customer group g for the set of dental services m 1 if dental service s exists in the set of dental service m, otherwise, 0 Initial capacity of medical center k for dental service s Capacity of accommodation center h Additional capacity in dental service s of candidate medical center k by setup setting new equipment with a cost of cks

Maximum allowable number of capacity extension of candidate medical center k for dental service s 1 if dental service s is served initially at medical center k. It will be equal to 0 if dental service s is only served by capability extension. It will be equal to −1 if dental service s cannot be served at medical center k even with extra cost. Profit of dental service s at candidate medical center k Profit of accommodation center h per person-night Group demand rate g for quality level q. for each group q gq = 1

Minimum rate of group demand g must be satisfied 1 if accommodation center h is at quality level q Decision Variables: Lks Final capacity of medical center k for dental service s 1 if candidate medical center k is selected, otherwise, 0. 1 if candidate accommodation center k is selected, otherwise, 0. The number of patients with dental service s in group g is assigned to the medical center k. The number of tourists with the set of dental services m in group g is assigned to the accommodation center h. 1 if dental service s is newly served by medical center k, otherwise, 0. The number of additional unit of capacity extended for dental service s at candidate medical center k. The number of satisfied demand of patients with the set of dental service m in group g

Fig. 2. The proposed dental tourism supply chain network.

serviceability for each center. This parameter can take three values 0, 1, and −1. The value of 1 indicates the medical center is currently available for that particular service. The value of zero means that providing the specified service depends on the costs and capacity extension for that service. Finally, the value of −1 expresses that the medical center cannot provide the specified service even by spending additional cost. Fig. 2 illustrates the proposed dental tourism supply chain. The proposed model determines the profit of the dental tourism supply chain, the capacity of each medical center, a number of selected medical and accommodation centers, the allocation of tourists to each medical and accommodation center, an amount of current medical services and new medical services increased capacity for each medical center.

Objective function:

max z =

3.1. Mathematical model

k

s

pks × Xgks +

Yk +

k

s

g

h

m

(cksextend × Uks +

× Wh

h

× dmm × Zghm

ckssetup

× Tks ) (1)

Constraints:

Tks Indices: s g k h

Yk

Xgks

1

Xgks g

407

s

(3)

k, s

M×

g

Setup cost of candidate accommodation center h

(2)

k, s

Tks + rks

dental services customer groups candidate medical center candidate accommodation center (hotel). q: quality level of accommodation center m: the set of dental services, m = 1, 2 …, 2k−1 Parameters: c assign Setup cost of candidate medical center k k

g

c assign × k k + h chassign

Tks + rks + 1 2

M × Yk

k

k, s

(4) (5)

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Fig. 3. The selected regions for the case study.

md gm

degm

Xgks =

ddsm × md gm,

k

g, s

(7)

m

md gm

g

× degm

g, m

(8)

eks × Tks + bks × rks + Uks = Lks Xgks

Lks

(9)

k, s

k, s

luks ×

Zghm g

Tks + rks + 1 2

M × Wh

k, s

g

×

h

gq

(12)

× md gm]

g, m, q

h

dmm × Zghm g

bh × max{dss}

m

Yk , Wh, Tks

Xgks , Lks

0

h

(13) (14) (15)

{0,1}

Zghm, Uks, mdgm

In this paper, a field research was conducted to obtain data related to the real-world proposed network supply chain. Mazandaran province was selected as a case study in this research. The important features of Mazandaran health tourism include equipped medical centers, expert physicians, proximity to the sea, beautiful beaches, jungle, mineral springs, rivers and waterfalls, and mild, humid and unique climate. Mazandaran province has many tourist attractions and the development of the medical sector and investment in the medical tourism can lead to increase absorption of foreign tourists in this province. The case study includes medical service providers, accommodation providers, and customer groups. Four medical centers are considered for the provision of dental services and 16 hotels to accommodate tourists (Fig. 3). There are four types of dental services and three quality levels for the hotels (3, 4, and 5-star hotels). The selected medical centers are located in Babol and Sari cities. Babol Dentistry Faculty and Nikan Dental Clinic in Babol, Sari Dentistry Faculty and Iranian Dental Clinic in Sari are considered. There is only one 5-star hotel in this case study and there are five 4-star hotels and ten 3-star hotels. These hotels are considered in six cities in Mazandaran province. As noted previously, four types of dental services were considered in this model: oral surgery and dental implants, cosmetic dentistry and dental restoration, orthodontics, and root canal therapy. The services provided in the field of dentistry are very wide, but the interest of tourists for the four mentioned services, these services were selected as the preferred services. There are numerous sources for demand for medical tourism in Iran. About 5 to 6 million Iranian people live abroad, mainly in North America, Europe, the Persian Gulf States, Turkey, Azerbaijan, Australia, and the broader Middle East. Lack of insurance coverage or low coverage and the high cost of treatment abroad has led Iranians living abroad to seek healthcare at a very low cost in Iran. Iran's advantages in attracting foreign patients and medical tourists include many specialized medical centers, low costs, natural and religious attractions, proximity to the Arab market, and the similarity of culture and language with some neighboring countries. Moreover, Iran has a huge potential for attracting medical tourists from non-neighboring countries, especially from Europe and North America. These regions are very important because they are highly developed and consequently have

(11)

m

fqh × Zghm = [

4. Case study

(10)

g

Uks

group is proportional to the demand of that group and according to the requested quality level. Constraint (14) limits this allocation to the capacity of accommodation centers. Finally, constraints (15)–(17) determine the value domains of decision variables used in the proposed model. The proposed model has nonlinear terms, which the linearization of the model is explained in Appendix A.

(6)

g, m

0, integer

(16) (17)

Equation (1) shows the objective function that maximizes the total profit. This equation includes revenues and costs of the medical and accommodation centers. Constraint (2) states that selected medical centers can increase the capacity of new medical services. Constraint (3) specifies the relationship between the current serviceability and capacity extension capability for each medical center. Constraint (4) shows that allocating patients to the medical centers is possible if that center is able to provide the medical service at present, or can provide the medical service by capacity extension. Constraint (5) ensures that patients are only assigned to the selected medical centers. Constraint (6) specifies the maximum responsibility to the demand of each customer group for each set of dental services. Constraint (7) guarantees that the allocation of patients is equal to the answered demand for each medical service. Constraint (8) imposes the model to satisfy a minimum certain rate of the demand of each customer group. Constraint (9) determines the capacity of each medical center for each medical service. Constraint (10) ensures that the allocation of patients to each medical center is proportional to the center capacity. Constraint (11) determines how much each service can increase if needed to increase the capacity of existing medical services. Constraint (12) guarantees the allocation of tourists to the selected accommodation centers. Constraint (13) shows that the allocation of tourists of each customer 408

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selected to respond to the demand of tourists and serve tourists. Among all the candidate accommodation centers, the only 5- star hotel in the case study, Morvarid Khazar Mahmoudabad is selected. Salardareh hotel and Badeleh hotel in Sari from 4-star hotels and Asram hotel in Sari and Ariane hotel in Noor from 3-star hotels are selected. Final capacity of the medical centers was a decision variable, which its optimal value is determined after solving the model. In addition, the capacity of cosmetic dentistry and dental restoration and capacity of oral surgery and dental implants are extended in Babol Dentistry Faculty and Sari Dentistry Faculty, respectively. The capacity extension for the current dental services in medical centers is expressed in Table B16 and the final capacity of these centers is presented in Table B17. The amount of demand was met for the customer groups, the number of tourists assigned to the medical centers and the number of tourists assigned to the accommodation centers are exhibited in Tables B18, B19, and B20, respectively.

Table 2 Setup cost of candidate medical centers. Medical center

1

2

3

4

Fixed setup cost

11,000

9,800

10,000

8,900

high purchasing power. However, medical tourists travel to developing countries like Iran due to insurance problems, long queues, and medical services at lower costs. According to the mentioned points, the origins intended for the demand for dental tourism in Iran are as follows: 1) Neighboring countries, 2) countries with the same language, 3) Iranians residing abroad (Iranian diaspora or Iranians abroad), 4) Persian Gulf States, and 5) Other regions (America, Europe, and Africa). 4.1. Input data In order to participate in the dental tourism supply chain, each of the candidate health and accommodation centers has some costs such as hiring employees who can speak English fluently and preparing workplace. The total annual cost of the mentioned costs was considered as the fixed setup cost. Tables 2 and 3 indicate the fixed setup cost of the medical and accommodation centers, respectively. The required time to provide each dental service is shown in Table B1 in Appendix B. The total number of incoming tourists to the destination country is calculated by a new coefficient as an attendant coefficient. This coefficient is specified in Table B2. Each accommodation center has a limited capacity to serve tourists as shown in Table B3. In addition, the profit of stay of tourists in these centers per person-night is expressed in Table B4. The model should satisfy at least a rate of the demand for each customer group; the values associated with this minimum rate are given in Table B5. As mentioned earlier in section 3, the model has the potential to increase the capacity of current dental services or new dental services. The cost of this capacity extension is presented in Tables B6 and B7, respectively. With these costs, the capacity of each medical center can be increased to a predetermined extent, which is expressed in Tables B8 and B9. Moreover, the medical centers provide dental services at different prices, which can be seen in Table B10. Due to medical centers limitations, they have limited ability to provide the dental services. The capacity of medical centers and the ability to provide dental services are listed in Tables B11 and B12, respectively. The demand for customer groups for the set of dental services is presented in Table B13. Finally, accommodation centers have different quality levels and a different rate of demand for each quality level is considered, which are reported in Tables B14 and B15, respectively.

4.3. Sensitivity analyses The profit of this supply chain will increase if more demand is met. This will be achieved when available accommodation and medical centers can respond to more tourists' demand and have the necessary capacity. One way that can increase demand response is reducing the setup cost for accommodation centers or reducing the costs of the capacity extension of dental services for medical centers by granting donations and government subsidies. As previously stated, the proposed dental tourism supply chain considers two sections; accommodation and medical centers. These sectors were considered as the private sectors and main drivers in the proposed supply chain, and the cooperation of this sector with the governmental sector can contribute to the enhancement of the private sector motivations and profit of this supply chain. Considering the economic importance of dental tourism in developing countries, the government can increase its income and foreign exchange by investing in this field. The private sector has to work with the government to develop plans for sustainable and profitable growth. Public-Private Partnership in tourism is to be employed with a combination of policy reforms, institutional support, incentives, and financing modalities to encourage the private sector participation in financing, constructing, managing infrastructure and other related development projects. It provides an alternate to budgetary constraints, enables the tourism industry to build assets, and maximizes the use of private sector skills. For private sector, the potential benefits of Public-Private Partnership can include: risk sharing, by its very nature, Public-Private Partnership involves the sharing of project risks and in addition, encourage private sector investment in tourism by reducing costs. By reducing the setup cost of accommodation centers, more centers are selected in the proposed supply chain, which leads to a significant increase in the amount of objective function and the response of accommodation and medical centers. The government will increase the supply chain profit up to 58,710,000 Tomans by entering into this field and spending 62,500,000 Tomans. However, in order to help to reduce the cost of the capacity extension of dental services and spending 23,575,000 Tomans, the supply chain profit will increase up to

4.2. Results The proposed model is conducted on a personal computer with Intel® Core™ i7-6700 CPU 4.00 GHz and 32.00 GB RAM and GAMS version 24.9.1. The optimal value of the objective function is obtained 2,771,940,000 Tomans. All the candidate medical centers should be Table 3 Setup cost of candidate accommodation centers. Row

Accommodation center

Fixed setup cost

Row

Accommodation center

Fixed setup cost

1 2 3 4 5 6 7 8

Morvarid Khazar hotel in Mahmudabad city Salardareh hotel in Sari city Badeleh hotel in Sari city Navid hotel in Sari city Mizban hotel in Babolsar city Sadaf hotel in Mahmudabad city Narenj hotel in Sari city Asram hotel in Sari city

25,000 19,000 23,000 16,000 18,000 18,000 11,000 17,000

9 10 11 12 13 14 15 16

Niloofar hotel in Amol city North Olympic hotel in Amol city Shahr hotel in Amol city Mahan hotel in Mahmudabad city Oxin apartment hotel in Mahmudabad city Ariane hotel in Noor city Negin hotel in Noor city Marziyeh in Babolsar

12,000 16,000 12,000 13,000 10,000 12,000 15,000 13,000

409

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Fig. 4. Total response rate of the model.

demand response means more profit of the dental tourism supply chain. As shown in Fig. 5, the lowest rate of lack is found at the point of 60% in all levels of quality and the highest rate of lack occurs in the demand of 5-star hotels. The proposed supply chain includes only a 5-star hotel and is not able to meet the total demand for this level of quality. As a result, the number of 5-star hotels should be increased to grow the response rate of 5-star hotels. By increasing the number of 5-star hotels in the dental tourism supply chain, the total rate of accommodation centers response increases, thus the entire rate of lack in the dental tourism supply chain decreases. As the results show, when the number of attendants increases, the profit of the dental tourism supply chain also increases, and in addition, the lack in this supply chain is reduced. Therefore, activists in this field should seek advertising that is more effective in order to attract more tourists. On the other hand, advertising in developed societies is interpreted as a tourism revolution. The importance of advertising in the field of tourism cannot be neglected. Nowadays, promotional activities in the tourism industry are not considered as costly activities; it is also a fundamental and principled investment for the promotion of organizational and national goals and if implemented correctly and principled, it can bring valuable achievements. Any neglect or misuse of advertising leads to the backwardness in the tourism marketing competitions and ultimately lead to failure and bankruptcy in the correct and principled marketing in the international arena. If a country has many tourist attractions, but the methods of introducing these attractions and delivering it to the target market are not in its macro plans, definitely will not succeed. Furthermore, due to the many problems that some countries face in terms of tourism development and tourist attraction, the role and importance of using professional and modern advertising and huge investments in this regard is much more

39,100,000 Tomans. However, there is no significant increase in the response rates of accommodation and medical centers. When the setup cost of hotels and the capacity extension of dental services are decrease simultaneously, the government's share is 111,750,000 Tomans, which cause to increase the supply chain profit up to 100,030,000 Tomans. In this case, the highest increase in the demand response of the dental tourism supply chain is observed. Table B21 shows the details of the cost reduction and its impact on the proposed supply chain. As can be seen in Fig. 4, the demand response of medical centers is at an acceptable level, and the main cause of shortage in the dental tourism supply chain is accommodation centers. To overcome this problem, the number of hotels in this supply chain should be increased. Another factor that provides useful information from the proposed supply chain is the attendant coefficient of customer groups. The attendant coefficient represents that on average, each customer group travels to a destination country with several people as a fellow traveler. As this coefficient increases, demand for accommodation centers increases, but demand for dental care remains constant. It is expected that as demand for accommodation centers increases, more centers will be selected to meet existing demand. Table 4 indicates the results of changes in the attendant coefficient. In order to investigate changes in the dental tourism supply chain, the attendant coefficient factor increased. The upper bound of the growth rate of attendant coefficient obtained with respect to the change in the lack of dental services. The rate of this lack remains constant until 70% increase, but after 70% increase, the lack of dental services also increases. Therefore, further increase in this rate cannot be justified. Observations declare that the higher coefficient causes a higher demand for the accommodation centers, and more accommodation centers have selected that respond to the more demand of tourists. This growth in Table 4 The effects of changing the attendant coefficient on the model.

Percentage growth rate of attendant coefficient

Changes in the model

objective function rate of change in the objective function lack rate of dental services lack rate of 5-star hotels lack rate of 4-star hotels lack rate of 3-star hotels

current situation

20%

40%

60%

70%

2771940 – 1.2% 14.13% 9.64% 6.16%

3181170 14.76% 1.2% 8.79% 6.27% 5.04%

3554370 28.23% 1.2% 8.5% 5.94% 4.11%

3903400 40.82% 1.2% 8.06% 4.79% 4.1%

4010020 44.66% 1.6% 11.19% 6.34% 5.26%

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Fig. 5. The effects of changing the attendant coefficient on the model.

prominent.

shortcomings of the medical tourism industry is the lack of access to the doctor after the treatment period and the time of occurrence of side effects. This defect can be debugged to a significant extent by providing support services. This factor has a significant effect on tourist satisfaction and destination satisfaction leads to higher tourists' return intention to the destination country for subsequent trips.

4.4. Managerial suggestions The purpose of this study was to determine the importance of dental tourism and to assess the level of income of this field for the destination country, especially in developing countries. In addition, the use of the proposed model can make significant contributions to the dental tourism managers in strategic decisions. According to conducted research in the field of medical tourism in Iran, it can be seen that Iran has not yet reached its proper place in this field despite its potential capabilities, such as tourist attractions, skilled physicians, and affordable dental services. In Iran, despite the possible opportunities in this field, few cases can be called the Medical Tourism Pole. Due to the significant growth of healthcare in recent years in Iran, now it has a position that can supply its desirable medical services to the world. In fact, if Iran can take advantage of the existing capabilities in the medical field in the tourism sector, it is hoped that in recent years, medical tourism will become a significant source of income for Iran. In the following, some management suggestions are presented to improve the dental tourism industry in Iran:

5. Conclusions In this paper, a mathematical model for dental tourism supply chain is presented. This model provides an optimal design methodology of dental tourism supply chain to determine the location, the applicable dental services, and the corresponding capacities for each medical center. To create this supply chain, three components of the sectors involved in the dental tourism supply chain were considered: tourists to create demand in this supply chain, medical centers to provide medical services to the tourists, and accommodation centers for the stay of tourists during their treatment. The proposed mathematical model assigns tourists to the candidate medical and accommodation centers, and decides the set of applicable emergency dental services of each candidate medical center and its capability while maximizing the total profit. In this study, a real-world network of the six cities of Mazandaran, Iran is investigated. An optimal solution of the proposed mathematical model was derived by using CPLEX solver. The results show that all four medical centers should be selected, and in order to meet the demand, the two medical centers need to increase their capacity for some of their current medical services. Among the candidate accommodation centers, five centers were selected to fulfill the demand of tourists. According to the analyses, the considered region was faced with a shortage of 5-star hotels and improving the quality of existing hotels or the establishment of the new 5-star hotels is considered to be necessary. In addition, it was found that government financial subsidies for the private sector can reduce the cost of medical and accommodation centers, and in turn, motivate the supply chain decision-makers to form a more efficient supply chain and also increase the supply chain profit. On the other hand, advertising has a significant impact on increasing the profitability of this supply chain. As observed, when tourists travel to a destination country with more attendants, there is less shortage and more profit in supply chain. As a result, it is required to pay specific attention to advertising in this field. Lastly, there are some promising research directions. First, demand was considered as a certain parameter in this study, while in the real world, there are many demand fluctuations and considering these fluctuations makes the mathematical model more realistic. Therefore, future researches can consider uncertainty in demand. Second, in this research, only the objective function of the profit was optimized, while in future researches, other functions, such as minimizing the lack of demand for tourists, can also be considered. Third, the proposed model can be solved with meta-heuristic algorithms or exact methods. Finally,

• Providing government grants to the accommodation and medical

•

•

•

•

centers: In order to enter into the dental tourism supply chain, accommodation and medical centers require paying some costs to achieve the level of standards set. While government grants facilitate the entry of these centers into the dental tourism supply chain, which leads to more response of demand and more revenue from this chain. Providing advertisements in the medical centers for the more introduction of different accommodation centers and vice versa: In order to coordinate and collaborate more closely between the different sectors of this supply chain, each of these sectors can advertise their colleagues. This will lead to a better acquaintance of tourists with different centers and increase the absorption of tourists. Providing diverse and attractive service packages to attract more tourists: Identifying the different needs of tourists will help provide attractive service packages for tourists. Considering the factors such as the price of services, the quality of services, and the provision of recreational services at different levels can help to meet better the demands of tourists. Continuous improvement of service quality in the dental tourism supply chain: Tourists are always looking for the best destinations for their trip. Therefore, the quality of the centers and services in this supply chain should always be improved, and in order to increase the number of tourists entering the country, involved sectors in the dental tourism supply chain should be equipped with the state of the art equipment and facilities. Keep in touch with tourists and provide support services: One of the 411

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in the proposed model, only the medical centers and accommodation centers were considered in the dental tourism supply chain. This chain includes sections such as travel agencies, tour operators, restaurants,

transportation, and recreation centers that can be incorporated into future researches.

Appendix A. Linearization of the model The proposed model has nonlinear constraints. Constraints (3), (4), (11) and (13) require linearization. In constraint (3), since rks is not a decision variable, it is easy to divide this constraint into two linear constraints (A1) and (A2).

Tks

rks

1,

k, s, rks =

Tks + rks

1,

k, s, rks = 0 or 1

(A1)

1

(A2)

Non-linear constraint (4) includes the decision variable tks. Therefore, for its linearization, a new binary decision variable named Nks is introduced. This constraint is rewritten in the following linear constraints:

Xgks

M × Nks

k, s

(A3)

g

Nks

Tks + rks + 1 2

Nks

{0,1}

k, s

(A4) (A5)

k, s

The constraint (11) is converted to a linear constraint by the new defined binary variable Nks.

Uks

luks × Nks

(A6)

k, s

In constraint (13), there is a decision variable in the integral part that causes the non-linearization of this constraint. In order to linearization this constraint, a new decision variable is defined as an integer, the constraint is replaced by the following constraints:

fqh × Zghm = dgmq

g, m, q

g, m, q

(A7)

h

dgmq

g

×

gq

× md gm

dgmq

g

×

gq

× md gm

dgmq

0, integer

g, m, q 1+

(A8)

g, m, q

(A9) (A10)

g, m, q

Appendix B. Input data and results Table B1

Number of required days to receive dental services Dental service

1

2

3

4

Number of required days

2

7

3

4

Table B2

Attendant coefficient of customer groups Customer group

1

2

3

4

5

Attendant coefficient

1.4

1.6

1.6

1.4

2

Table B3

Capacity of accommodation centers Accommodation center

1

2

3

4

5

6

7

8

Capacity Accommodation center Capacity

250 9 150

150 10 150

154 11 100

180 12 41

140 13 112

150 14 100

80 15 220

165 16 65

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Table B4

Profit of inhabitancy at accommodation centers per person-night Accommodation center

1

2

3

4

5

6

7

8

profit Accommodation center Profit

500 9 200

350 10 195

340 11 190

300 12 160

290 13 185

250 14 190

200 15 200

210 16 220

Table B5

Minimum rate of group demands must be answered Customer group

1

2

3

4

5

Minimum rate of demand fulfillment

0.5

0.5

0.6

0.7

0.8

Table B6

Cost to extend the unit capacity of the dental services of candidate medical centers Dental service Medical center

1 800 1,200 1,150 0

1 2 3 4

2 850 0 1,150 1,050

3 1,200 1,150 1,100 750

4 950 750 0 650

Table B7

Cost of newly setup capacity of dental services of candidate medical centers Dental service Medical center

1 2 3 4

1 0 0 0 2,600

2 0 1,000 0 0

3 0 0 0 0

4 0 0 0 0

Table B8

Additional capacity in dental services of candidate medical centers by setting new equipment Dental service Medical center

1 2 3 4

1 0 0 80 0

2 0 55 0 0

3 0 0 0 0

4 0 0 0 0

3 48 96 42 48

4 48 50 0 70

Table B9

Maximum allowable number of capacity extension of candidate medical centers for dental services Dental service Medical center

1 2 3 4

1 36 72 110 0

2 73 0 55 57

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Table B10

Profit of dental services at the candidate medical centers Dental service Medical center

1 140 120 155 160

1 2 3 4

2 1,700 1,400 2,300 1,800

3 560 400 460 360

4 420 450 350 270

2 132 0 99 105

3 88 176 77 88

4 88 88 0 121

3 1 1 1 1

4 1 1 −1 1

Table B11

Initial capacity of the medical centers for dental services Dental service Medical center

1 66 132 198 0

1 2 3 4

Table B12

Serviceability for each center Dental service Medical center

1 1 1 1 0

1 2 3 4

2 1 0 1 1

Table B13

Demand of customer groups for the set of dental services Set of dental services 1 Customer group

1 2 3 4 5

2

23 20 24 23 20 23 25 25 19 18 Set of dental services 9 10 14 8 9 9 12 9 11 9 9 13

1 2 3 4 5

3

4

5

6

7

8

21 21 22 20 16

16 13 12 12 14

12 12 11 15 13

13 14 12 15 12

11 12 10 12 13

10 14 11 12 14

11 6 6 8 8 6

12 9 7 6 8 7

13 6 5 5 6 6

14 7 6 6 9 5

15 4 5 5 6 4

Table B14

Quality level of accommodation centers Accommodation center

Quality level

1 2 3 1 2 3

1

2

3

4

5

6

7

8

1 0 0 Accommodation 9 0 0 1

0 1 0 center 10 0 0 1

0 1 0

0 1 0

0 1 0

0 1 0

0 0 1

0 0 1

11 0 0 1

12 0 0 1

13 0 0 1

14 0 0 1

15 0 0 1

16 0 0 1

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Table B15

Groups demand percentage for quality levels Quality level

Customer group

1 2 3 4 5

1

2

3

0.3 0.3 0.1 0.1 0.2

0.5 0.4 0.3 0.2 0.3

0.2 0.3 0.6 0.3 0.5

Table B16

Number of additional unit of capacity extended for dental services at candidate medical centers Dental service Medical center

1 0 0 0 0

1 2 3 4

2 0 0 15 0

3 0 0 0 0

4 0 44 0 0

3 88 176 77 88

4 88 132 0 121

Table B17

Final capacity of medical centers for dental service s Dental service Medical center

1 66 132 198 88

1 2 3 4

2 132 55 114 105

Table B18

Number of met demand of patients

Customer group

1 2 3 4 5

Set of dental services 1 2 3 22 20 21 23 23 21 20 23 22 14 25 20 18 18 16

4 15 13 12 10 13

5 12 12 11 15 13

6 13 14 12 15 12

7 11 11 10 10 13

8 10 14 11 12 14

9 14 9 12 10 9

10 8 9 9 9 13

11 6 6 8 8 6

12 8 7 6 8 7

13 6 5 5 6 6

14 7 6 6 9 5

15 4 5 5 6 4

Table B19

Number of patients is assigned to the medical centers Customer group

1 2 3 4

5

Medical center

2 3 4 2 3 4 1 2 1 2 3 4 1 2 3

Dental service 1

2

3

4

47 36 0 0 84 0 59 19 7 0 0 88 0 0 78

54 0 25 0 0 80 80 1 52 0 39 0 0 0 75

20 0 56 4 77 0 4 74 84 0 0 0 0 78 0

0 0 73 17 0 48 0 65 18 50 0 0 70 0 0

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Table B20

Number of tourists is assigned to the accommodation centers Customer group

1

2

3

4

5

Accommodation center

1 2 3 8 15 1 2 3 8 15 1 2 3 8 15 1 2 3 8 15 1 2 3 8 15

Set of dental services 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

9 15 0 6 0 11 14 0 11 0 3 9 0 19 0 3 6 0 10 0 7 10 0 18 0

8 14 0 0 5 11 0 14 0 11 3 11 0 21 1 3 7 0 0 10 7 10 0 18 0

8 0 14 0 5 10 0 13 0 10 3 10 0 21 0 2 5 0 8 0 6 0 9 0 16

6 10 0 0 4 6 8 0 0 6 1 0 5 0 11 1 2 0 0 4 5 7 0 0 13

5 0 8 0 3 5 0 7 0 5 1 0 5 10 0 2 0 4 6 0 5 7 0 13 0

5 9 0 0 3 6 0 8 6 0 1 5 0 11 0 2 4 0 6 0 4 7 0 0 12

4 0 7 1 2 5 7 0 0 5 1 0 4 0 9 1 2 0 4 0 5 7 0 1 12

4 0 7 0 2 6 0 8 6 0 1 0 5 0 10 1 3 0 0 5 5 0 8 14 0

5 0 9 0 3 4 5 0 4 0 1 0 5 0 11 1 2 0 0 4 3 5 0 0 9

3 5 0 0 2 4 5 0 0 4 1 0 4 0 8 1 0 2 0 3 5 7 0 0 13

2 0 4 0 1 2 0 3 2 0 1 0 3 7 0 1 0 2 0 3 2 3 0 0 6

3 5 0 0 2 3 4 0 0 3 0 0 2 0 5 1 0 2 0 3 2 0 4 0 7

2 0 4 1 0 2 3 0 2 0 0 0 2 0 4 0 1 0 2 0 2 0 3 6 0

2 0 4 0 1 2 0 3 2 0 0 0 2 5 0 1 1 1 0 3 2 3 0 0 5

1 0 2 0 1 2 3 0 2 0 0 0 2 0 4 0 0 1 0 2 1 0 2 0 4

Table B21

relationship between cost reduction and demand response System situation

Changes in the model

objective function total response rate total response rate of accommodation centers response rate of 5-star hotels response rate of 4-star hotels response rate of 3-star hotels total response rate to medical services response rate to the first service response rate to second service response rate to the third service response rate to the fourth service response rate to the first customer group response rate to the second customer group response rate to the third customer group response rate to the fourth customer group response rate to the fifth customer group

Current situation

50% reduction in setup cost of hotels

Rate of change

50% reduction in cost of capacity extension

Rate of change

Simultaneous reduction in setup cost and cost of capacity extension

Rate of change

2771940000 98.55% 90.85% 85.87% 90.36% 93.84% 98.80% 98.12% 99.75% 99.75% 97.43% 98.33% 98.89% 100% 96.89% 98.82%

2830650000 99.78% 91.92% 85.87% 92.45% 94.57% 99.75% 99.77% 100% 99.75% 99.43% 100% 99.44% 100% 99.48% 100%

58710000 1.23% 1.07% 0 2.09% 0.73% 0.95% 1.65% 0.25% 0 2% 1.67% 0.55% 0 2.59% 1.18%

2811040000 98.99% 91.16% 85.87% 90.57% 94.39% 99.18% 98.83% 99.51% 99.50% 98.86% 97.78% 99.44% 100% 98.45% 99.41%

39100000 0.44% 0.31% 0 0.21% 0.55% 0.38% 0.71% −0.24% −0.25% 1.43% −0.55% 0.55% 0 1.56% 0.59%

2871970000 100% 91.92% 85.87% 92.45% 94.57% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100%

100030000 1.45% 1.07% 0 2.09% 0.73% 1.20% 1.88% 0.25% 0.25% 2.57% 1.67% 1.11% 0 3.11% 1.18%

Author contribution Mohammad Mahdi Paydar and Fatemeh Ahmadimanesh conceived of the presented idea. They developed the mathematical model and performed the computations. Moreover, they verified the proposed mathematical model. Fatemeh Ahmadimanesh collected the data from the case study. All of authors carried out the implementation and performed the calculations. Moreover, all authors discussed the results and contributed to the final manuscript. Finally, all of authors cooperated to write the manuscript.

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Fatemeh Ahmadimanesh received the BS and MS degrees from the Babol Noshirvani University of Technology, Iran. Her research activities include tourist management, supply chain and Application of OR.

Mohammad Mahdi Paydar is an associate Professor of Industrial Engineering in the Department of Industrial Engineering at the Babol Noshirvani University of Technology, in Babol, Iran. He received his BS and MS degrees in Industrial Engineering from Mazandaran University of Science and Technology, Babol, Iran, in 2007 and 2009, respectively; and PhD degree in Industrial Engineering from Iran University of Science and Technology in 2014. His research interests include supply chain design, operations research, multi-objective optimization, and Cellular manufacturing. He has published more than 70 papers in international journals and conferences including Expert Systems with Applications, Computers & Mathematics with Applications, Computers & Operations Research, Journal of Cleaner Production, Computers & Industrial Engineering, Knowledge-Based Systems, Applied Mathematical Modelling and etc. Ebrahim Asadi-Gangraj received his BS degree in Industrial Engineering from Isfahan University of Technology, Isfahan, Iran, in 2005; MS degree in Industrial Engineering from the Tarbiat Modares University in 2008; and PhD degree in Industrial Engineering from the Tarbiat Modares University, Iran, in 2014. He is currently Assistant Professor of Industrial Engineering at Babol Noshirvani University of Technology, Babol, Iran. His research interests include applied operations research, sequencing and scheduling, production planning, and supply chain management.

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