The Suitability-Feasibility-Acceptability Strategy Integrated with Bayesian BWM-MARCOS Methods to Determine the Optimal Lithium Battery Plant Located in South America

Abstract

This study aims to help managers develop a proper strategy and policy for their company’s future. After the global COVID-19 pandemic, developed countries decided to change their production and relocate and re-industrialize. The U.S.’s big electronics and automobile companies are not an exception to this rule. The lithium batteries are the main instrument of mobile phone and electric vehicles. The leading lithium battery supplier for the U.S mobile phone companies is China. Argentina, Bolivia, and Chile (in South America) have some of the largest lithium mines in the world; these countries are known as the lithium triangle. Among the 86 million tonnes of lithium resources worldwide, 49.9 million tonnes exist in this area. The researchers in this study surveyed the best country for constructing a battery for companies in the U.S. Because of the growth of electric vehicles and their use of the lithium battery, the world is facing astronomical prices for lithium. To emphasize this issue and help managers create good policy, this study combined multiple methods. The improved suitability-feasibility-acceptability (SFA) strategy is integrated with the Bayesian best-worst method (BBWM) and measurement of alternatives and rankings according to compromise solution (MARCOS) multicriteria methods to determine the best destination. For comparison, based on the SFA strategy, seven criteria are introduced: commercially viable reserves, national minimum wage, corporate income tax, accessibility to mining companies, accessibility to the waterway, population, and political stability index. The Bayesian BWM analysis reveals that the foremost factor is corporate income tax, whereas MARCOS’s findings indicate that Chile is the best country to construct the lithium battery industry. To verify the proposed approach, a comparison analysis also is performed.

1. Introduction

Global warming raises the average temperature of the earth and causes climate change. Global warming will increase the temperature on earth from 3 °C to 5 °C by the year 2100 [1]. The main factor for climate change is the greenhouse gas (GHG) effect. Since industrialization, human behavior has increased and enhanced this effect. The GHGs consist of four significant gases: carbon dioxide (CO₂), methane, nitrous oxide, and hydrofluorocarbons. CO₂ alone contributes to roughly two-thirds of the ‘enhanced greenhouse effect’ [2]. Most CO₂ is due to the transportation sector. Countries are looking at alternatives to traditional vehicles to reduce GHG. Electric vehicles (E.V.s) are an alternative to gasoline and diesel vehicles [3]. Every international automaker is manufacturing E.V.s and working toward discontinuing the manufacture of internal-combustion engines. American car companies, such as Ford Motor, Tesla, and General Motors are producing E.V.s. Other companies, such as Apple, aim to join the competition by launching self-driving E.V.s in 2025 [4]. One of the main components of E.V.s is its battery; battery electric vehicles (BEVs) store electrical energy and can be recharged by a grid [5]. Among the elements used in BEVs, such as nickel–cadmium (Ni–Cd), nickel-metal hydride (Ni-MH), and lead-acid, the lithium-ion (Li-ion) battery is the best because of its high energy, power density, and long service life [6]. Li-ion batteries also are used in mobile phones, laptops, and tablets and supply energy to medical equipment and electrical power systems for some aerospace applications. Lithium is a valuable element for manufacturing batteries and is labeled as a “white gold” or “petroleum of the future”. More than half of lithium reserves worldwide (approximately 58 percent) exist in South America [7]. Argentina, Bolivia, and Chile are the three lithium-rich regions that are called the lithium triangle because of their geographic formation. Outside the lithium triangle, Brazil is one of the largest lithium producers in the world [8]. Based on this information, the importance of these areas in producing lithium becomes clearer.

The COVID-19 pandemic and its impact on supply chains and other events, such as rising labor costs in China and the Far East, shipping costs, and the tariff war between the U.S. and China has caused many American companies to be unable to control the variables of off-shoring [9]. Hence, near-shoring is a strategic plan that companies are turning to. According to the above discussion, the high demand for lithium makes selecting a strategic country for generating batteries in South America more important than ever. Therefore, the researchers use strategic planning in this study to find the best place for constructing a battery company in South America based on a near-shoring strategy for large electronics and automotive companies in the U.S.

In strategic planning, the industry’s future is considered, and a plan is proposed. A critical issue that managers usually face is selecting sets of proper strategies. Some methods help managers to select and analyze strategies. Suitability-feasibility-acceptability (SFA) is one of these methods selected in this research. This method has a framework of three criteria: suitability, feasibility, and acceptability. These criteria use the environment of a system for selecting the best strategy. Although the SFA is an excellent strategic analyzing method, it has some deficiencies that make it unsuitable for a complex problem. The SFA does not introduce a distinct method for calculating the weight of criteria and does not adjust the criteria values by different scales. Thus, this research combines SFA with multicriteria decision-making (MCDM) methods to improve this efficiency. MCDM methods adjust the values by normalization on the same scales and present methods for weighing assumptions. In the presence of multiple decision-makers’ verdicts, the Bayesian best-worst method (BBWM) is used among the MCDM methods to assign weight to the criteria. Finally, the MARCOS method is performed to rank the SFA strategy framework to alternative countries.

This paper is organized as follows: In Section 2, a literature survey is presented. Section 3 introduces the research methodology, including the improved SFA strategy, BBWM, and MARCOS. In Section 4, the application is presented in detail. Section 5 highlights a comparison analysis. Lastly, Section 6 discusses some managerial and policy implications and concludes the results of the research.

2. Literature Review

2.1. Site Selection Works with MCDM Methods

There are numerous studies related to the site selection problem. Some of them can be summarized as follows: Çebi and Otay [10] addressed multicriteria and multistage facility location selection problems via applying interval type-2 fuzzy sets based on the TOPSIS method. Boltürk and Kahraman [11] developed interval-valued intuitionistic fuzzy CODAS to address Turkey’s wave energy facility location selection. Yıldız and Demir [12] used the fuzzy TOPSIS method to select the most suitable location for domestic automobile production, which is strategically vital for Turkey. Kheybari et al. [13] integrated BWM with additive value function to identify the best location for bioethanol production. Biswas and Pamucar [14] applied an integrated group decision-making framework consisting of PIPRECIA and LBWA to analyze facility location selection problems for B-Schools in India. Wang et al. [15] combined the data envelopment analysis (DEA) and grey based multiple criteria decision making (G-MCDM) to select a proper place for solar P.V. power plants.

Seker and Aydın [16] integrated entropy and TOPSIS methods under an interval-valued Pythagorean fuzzy environment to select the most appropriate site location for hydrogen production plants in Turkey. Deveci et al. [17] proposed a three-stage integrated neutrosophic decision-making model for the location selection of an automobile Li-ion battery re-manufacturing facility. They employed hierarchical BWM and advanced type-2 neutrosophic numbers-based CODAS method to select optimal evaluation criteria weights and rank location alternatives, respectively. Wang et al. [18] used a two-stage MCDM-based spherical fuzzy set for the site selection of an offshore wind power station (OWPS). Duffner et al. [19] systematically proposed a methodology to evaluate the location selection for battery manufacturing plants, considering the most relevant parameters, namely cost and knowledge. They applied the proposed methodology to the 28 countries within the European Union. Anastasiadis et al. [20] conducted a computational case study on the selection of charging facility locations for electric vehicle-based ride-hailing services. They presented an optimization approach to model the placement of C.S.s to minimize the empty time travelled to the nearest C.S. for recharging and the installation cost. Zolfani et al. [21] introduced a BWM-MAIRCA model to select suitable locations for people. Yükseltürk et al. [22] developed a mathematical model for locating many lithium battery recollection centers, and they conducted a scenario analysis for Germany from 2020 to 2050. Simic et al. [23] proposed picture fuzzy sets based on CODAS to investigate the multicriteria vehicle shredding facility location problem in the Republic of Serbia. Tadaros et al. [24] developed a mixed-integer programming model to consider the location of facilities and network designs for reverse logistics of discarded lithium-ion batteries in the Swedish market. Eagon and Northrop [25] proposed a novel algorithm for choosing a set of optimized charging station locations based on a set of points based on specific electric vehicle battery demand.

Sherif et al. [26] proposed a three-stage hybrid methodology with a combination of interpretive structural modeling, fuzzy AHP, and fuzzy COPRAS for selecting battery recycling plant locations in a sustainable environment in India. Feng et al. [27] constructed a linguistic entropy weight-fuzzy axiomatic design integrated analysis framework to select the optimal electric-vehicle charging station site. Wang et al. [28] employed principal component analysis of geographic information systems integrated methodology to analyze the site selection problem for a precast concrete component factory in China. Karagöz et al. [29] proposed interval type-2 fuzzy ARAS to evaluate Turkey’s end-of-life vehicles recycling facility locations. Suman et al. [30] compared the two methods, AHP and fuzzy AHP, to address the facility location selection for the furniture industry in Bangladesh.

2.2. Bayesian BWM (BBWM) Studies

Although BWM [31] is a new method, many studies on it or its uncertain extensions have appeared in the literature ([32,33,34]). One of its extensions is the BBWM approach. Studies regarding BBWM can be seen in

Table 1. Studies related to BBWM.

Author(s)	Methodology	Application
Li et al. [35]	BBWM-Multicriteria competence analysis-additive value function	Evaluating crowdsourcing delivery personnel’s competence in China
Liu et al. [36]	BBWM	Determine and rank the challenges of implementing sustainable supply chain block chain technology
Yanılmaz et al [37]	BBWM-FEMA(Federal Emergency Management Agency)-SMUG(seriousness manageability urgency growth)	Conducting comprehensive disaster hazard analysis and proposing potential mitigation measures in Turkey
Liang et al. [38]	BBWM- DQ/GRA (difference-quotient grey relational analysis)	Evaluating the comprehensive performance of 5G base stations
Munim et al. [39]	BBWM	Assessing block chain adoption strategies in the Norwegian oil and gas industry
Zhang et al. [40]	BBWM- Cloud model- Improved Credit Metrics-CVaR	Credit evaluation-risk measurement for electricity retailers in China’s power market
Zhang et al. [41]	BBWM-MARCOS	Assessing the market-oriented business regulatory risk of power grid enterprises in China
Abkenar et al. [42]	BBWM	Identify the multiple barriers to implementing the Internet of Things in the food industry and investigate their priority.
Mohammadi and Rezaei [43]	BBWM	Mobile phone selection
Dogani et al. [44]	BBWM- Hierarchical Analysis Process	Analyze the priority of resilience indicators of Mashhad plain in reducing groundwater resources
Kelly et al. [45]	BBWM	Analyzing the barriers to closed-loop supply chains implementation in Irish medical device manufacturers
Ak et al. [46]	BBWM-VIKOR	Occupational health, safety, and environmental risk assessment in the textile production industry
Gül and Yücesan [47]	BBWM-TOPSIS	Evaluating the performance of Turkish universities
Gül et al. [48]	BBWM-Fuzzy VIKOR	Prioritization of control measures in Fine–Kinney-based risk assessment for a petrol station’s liquid fuel tank area
Saner et al. [49]	BBWM-VIKOR-TOPSIS	Evaluate disaster preparedness of hospitals in Turkey
Sahebi et al. [50]	Fuzzy Delphi method-BBWM	Identify and evaluate supply chain sustainability attributes in the steel industry.
Ma et al. [51]	BBWM-TOPSIS	Selection of the optimal electrochemical energy storage

.

Table 1 shows that BBWM has been integrated with several different methods, such as multicriteria competence analysis, additive value function, DQ/GRA, cloud model, hierarchical analysis process, MARCOS, TOPSIS, and VIKOR. In addition, BBWM has been used in several areas, such as selecting optimal electrochemical energy storage, evaluating university performance and risk assessment, analyzing barriers to closed-loop supply chains implementation, evaluating disaster preparedness of hospitals, conducting disaster hazard analysis, assessing block chain adoption strategies, evaluating credit evaluation-risk measurement for electricity retailers, and evaluating the performance of 5G base stations. The BBWM approach can be employed effectively in solving real-life problems.

2.3. Literature on MARCOS

Many researchers prefer the MARCOS method for ease of calculation, processing speed, and intelligibility. Some recent research related to MARCOS is presented in

Table 2. Studies related to MARCOS.

Author(s)	Methodology	Application
Fan et al. [52]	D number-BWM-MARCOS	Considering FMEA for rotor blades in aircraft turbines
Deveci et al. [53]	Interval rough numbers based on BWM-MARCOS	Off-shore wind farm site selection in Turkey
Stankovic et al. [54]	Fuzzy PIPRECIA-Fuzzy MARCOS	Assessing road traffic risk
Stevic and Brkovic [55]	FUCOM-MARCOS (measurement of alternatives and ranking According to compromise solution)	Evaluation of human resources in an international transport company
Chakraborty et al. [56]	D number-MARCOS	Choosing the best performing supplier in a leading Indian iron and steel-making industry
Badi and Pamucar [57]	Grey theory-MARCOS	Selection of suppliers in the Libyan Iron and Steel Company (LISCO)
Stevic et al. [58]	MARCOS	Sustainable supplier selection in the private healthcare industry in Bosnia and Herzegovina
Boral, S., Chaturvedi, S. K., Howard, I. M., McKee, K., & Naikan, V. A. [59]	fuzzy AHP and fuzzy MARCOS	An integrated approach for fuzzy failure mode and effect analysis
Bakır and Atalık [60]	Fuzzy AHP-Fuzzy MARCOS	Evaluating e-service quality in the airline industry from the point of view of the consumers
Ulutaş et al. [61]	CCSD-ITARA-MARCOS	Selection of the best manual stacker for a small warehouse
Karaaslan et al. [62]	AHP-MARCOS	Determining the regional priorities of renewable energy sources in Turkey
Pamucar et al. [3]	Fuzzy FUCOM-Neutrosophic fuzzy MARCOS	Prioritize the various alternative fuel vehicles for sustainable road transportation in the United States
Simic’ et al. [63]	CRITIC-Fuzzy FUCOM-DEA-Fuzzy MARCOS	Determining the level of traffic safety on road sections under the conditions of uncertainty
Torkayesh et al. [64]	BWM-GIS-Grey MARCOS	Landfill location selection for the healthcare waste system in Iran
Çelik and Gül [65]	Interval type-2 fuzzy BWM-MARCOS	Hazard identification, risk assessment, and control for dam construction safety
Iordache et al. [66]	Interval rough-based Dombi-MARCOS	Analyzing the alternatives of the natural gas grid conversion to hydrogen in Romania
Tesic et al. [67]	DIBR-Fuzzy MARCOS	Location selection for heavy mechanized bridge
Ecer and Pamucar [68]	Intuitionistic fuzzy MARCOS	Identifying insurance companies’ priority ranking in terms of healthcare services in Turkey during the COVID-19 outbreak
Trung [69]	EDAS-MARCOS-PIV-MOORA-TOPSIS	Determining the value of cutting parameters for both the low surface roughness and significant material removal rate in the milling process
Salimian, S., Mousavi, S. M., & Antucheviciene, J. [70]	Extended VIKOR and MARCOS	An interval-valued intuitionistic fuzzy model for sustainable supplier selection in organ transplantation networks for healthcare devices.

.

As shown in Table 2, the MARCOS method has been used in different decision environments, such as fuzzy, interval type-2, intuitionistic, interval rough, neutrosophic, grey theory, and D number. Further, it has been applied with other methods, namely EDAS, PIV, MOORA, TOPSIS, DIBR, BWM, GIS, DEA, FUCOM, CRITIC, AHP, CCSD, ITARA, and PIPRECIA, among others. Application areas of the MARCOS method can be summarized as selecting locations for heavily mechanized bridges, identifying insurance companies’ priority ranking, assessing risk and controlling for dam construction safety, determining the level of traffic safety on road sections, ranking different alternative fuel vehicles for sustainable road transportation, selecting sustainable suppliers in the healthcare industry, evaluating e-service quality in the airline industry, selecting manual stacker for a small warehouse, ranking renewable energy sources, evaluating human resources, and assessing road traffic risk.

2.4. Research Gaps

Lithium batteries are the essential building blocks of future technologies, and thus, the lithium battery manufacturing plant location decision is crucial. The U.S is one of the big customers of lithium batteries because of their large electronics and electric vehicle industries. There is a clear need for a robust and effective decision support tool to supply this demand. According to conditions and intentions for near-shoring, the lithium supply chain is a critical issue for auto and electronics companies. After conducting a detailed literature review, the absence of any other study related to finding the best place for a lithium supply chain is detected. The three countries with the largest lithium sources (lithium triangle) exist in South America; therefore, these countries are a good place for the U.S to look to satisfy their demands for lithium. However, the challenge presented is which of these countries is more suitable for selection. This study uses the SFA with BBWM-MARCOS methodology to distinguish the proper area. It is thought that the study could contribute to the proposed method and application area literature.

3. Research Methodology

3.1. Improved SFA Strategy

The suitability-feasibility-acceptability (SFA) method was proposed by Johnson et al. for strategy selection [71]. This framework consists of options and criteria: suitability, feasibility, and acceptability. Suitability conveys the opportunities and constraints that a company faces, the external environment, and the company’s resources. Acceptability considers the expectations of stockholders and their outcomes. Feasibility surveys the strategy practically and considers the internal capability of the company. The SFA is a good strategy for selecting the best option. However, it has some deficiencies: (i) all the criteria should have numeric values, (ii) it has no straightforward approach for calculating the weight of criteria, and (iii) this method does not use a normalization system for measuring and comparing values.

By keeping in mind the industry’s requirements and strong motivation, the authors decided to use a novel decision-making tool consisting of Bayesian BWM and the MARCOS approach, as the proposed approach combines the advantages of the BBWM and the MARCOS technique. The BBWM approach has an efficient basic algorithm that decision-makers can follow without requiring advanced mathematical information. Additionally, it can provide a very flexible decision-making environment and reach outstanding and logical results with fewer comparisons and computations. In addition, the MARCOS approach is a very stable decision-making frame. Its mathematical expression can help eliminate the impacts of the excessive and undesirable values in the index.

Hashemkhani Zolfani et al. [72], to remove these shortages, proposed that SFA is combined with the MCDM methods. They used the BWM method for weighing and the MARCOS method for ranking options. With this combination, the SFA strategy improved. To show this method’s accuracy, they used it for a real-world case study and implemented a sensitivity analysis. Based on the efficiency of this method, the researchers decided to use the SFA strategy with BBWM and MARCOS methods for selecting the best country for the construction of a lithium battery company in South America.

3.2. The BBWM Approach

BWM was proposed by Jafar Rezaei (2015). The best and worst criteria are determined in this method, and the pairwise comparison is made with other criteria. After solving a min–max problem, the optimal weights of the criteria are obtained. This method uses the preference of one decision-maker. This paper’s researchers could not precisely determine the criteria’s importance and preference (based on the verdict of decision-makers, different best criteria are introduced). Hence, they found that this method is not efficient in in-group decision-making problems (multiple decision-makers are by different preferences).

Mohammadi and Rezaei (2019) extend the BWM as Bayesian BWM (BBWM), which is proper for group decision-making models. This method consists of these steps:

Step 1: Define a set of decision criteria C = {c₁, c₂, …, c_n}.

Step 2: Select the best (C._B.) and the worst (C._W.) criteria.

Step 3: Conduct a pairwise comparison between C._B. and other criteria.

$$A_B=(a_{B1},a_{B2},\dots ,a_{Bn})$$

Step 4: Conduct a pairwise comparison between C._W. and other criteria.

$$A_W={(a_{W1},a_{W2},\dots ,a_{Wn})}^T$$

Step 5: Estimate the probability distribution of each optimal weight ($W^{1:K}$) and the overall optimal weight ($W^{agg}$) given. $A_B{}^{1:K}$ and $A_W{}^{1:K}$ k represent the decision-makers.

The joint probability distribution and the probability of each variable are computed as follows:

$$P(W^{agg},W^{1:K}|A_B^{1:K},A_W^{1:K})$$

(1)

$$P(x)={\displaystyle \sum _{y}p(x,y)}$$

(2)

To build the Bayesian model, we can specify the relation of the variables. Figure 1 shows this relationship [35].

The figure shows that $W^K$ depends on $A_B^K|W^k\approx multinomial(\frac{1}{W^k}),\forall k=1,\dots ,k.$ and $A_B^K$, $W^{agg}$ depends on $W^K$, $A_W^K$, and $A_B^K$ is independent $W^{agg}$. Thus, this independency could be demonstrated by Equation (3):

$$P(A_W^K||W^{agg},W^k)=P(A_W^K||W^k)$$

(3)

By combining the Bayes theorem with a joint probability distribution, the below Equation (4) is obtained.

$$\begin{array}{l}P(W^{agg},W^{1:K}||A_B^{1:K},A_W^{1:K})\mu P(A_B^{1:K},A_W^{1:K}||W^{agg},W^{1:K})P(W^{agg},W^{1:K})=\\ P(W^{agg}){\displaystyle \prod _1^{k}P(}{A}_W^K||W^K)P(A_B^K||W^K)P(W^K||W^{agg})\end{array}$$

(4)

This equation shows that each D.M. gets their decision (based on their preferences) independently. The distribution of elements in the above equation should be distinct. The $A_W^K$ and $A_B^K$ could be modeled perfectly by multinomial distribution because of their integer properties.

$$A_W^K|W^k\approx multinomial(W^k),\forall k=1,\dots ,k.$$

(5)

$$A_B^K|W^k\approx multinomial(\frac{1}{W^k}),\forall k=1,\dots ,k.$$

(6)

Every individual weight $w^k$ must be in proximity of $w^{agg}$. The suitable distribution for weights is the Dirichlet distribution. Therefore, the Dirichlet distribution of weights is determined by Equation (7) [73].

$$Dir(w|\alpha )=\frac{1}{B(\alpha )}{\displaystyle \prod _{j=1}^n{w}_j^{{\alpha }_j-1}}, \alpha \in R^n\mathrm{and}j=1\dots n.$$

(7)

where

$$B(\alpha )={\displaystyle \prod _{j=1}^n\frac{\mathsf{\Gamma }({\alpha }_j)}{\mathsf{\Gamma }({\alpha }_0)}}.$$

(8)

In the above equations, $B(\alpha )$ is a multivariate beta function, $\mathsf{\Gamma }({\alpha }_{})$ is the gamma distribution, and ${\alpha }_j$ is a dimensionless distribution parameter.

Thus, the weight distribution of Equation (4) is:

$$\begin{array}{l}{w}^k\left|\right|w^{agg}\approx Dir(\gamma *w^{agg}), \forall k=1,\dots ,k.\\ which \gamma \approx \mathsf{\Gamma }(a,b),\end{array}$$

(9)

where a and b are shape parameters of gamma distribution, and $\gamma$ is the concentration parameters that denote closeness between $w^k$ and $w^{agg}$.

Finally, for finding the distribution, $w^{agg}$ is used as an uninformative Dirichlet distribution and set as $\alpha$ to 1.

$$w^{agg}\approx Dir(1).$$

(10)

Then, to get output by close form solution, the researchers used the Markov chain Monte Carlo (MCMC) [74] and just another Gibbs sampler (JAGS) [75].

3.3. MARCOS

One MCDM method suitable for solving models with more criteria is MARCOS, proposed by Stevic et al. 2020. This method has three starting points (reference points, relationship between alternatives, and utility degree of alternatives) that help decision-makers make a robust decision. The MARCOS method is compromised of the following steps:

Step 1. Defining an initial decision-making matrix.

Step 2. Defining an extended initial decision-making matrix by introducing the ideal (AI.) and anti-ideal (AAI) solutions.

$$X=\begin{array}{cc}& \begin{array}{cccc}{C}_1& C_2& \dots & C_n\end{array}\\ \begin{array}{c}AAI\\ A_1\\ A_2\\ \dots \\ A_m\\ AI\end{array}& \left[\begin{array}{cccc}{x}_{aa1}& x_{aa2}& \dots & x_{aan}\\ x_{11}& x_{12}& \dots & x_{1n}\\ x_{21}& x_{22}& \dots & x_{2n}\\ \dots & \dots & \dots & \dots \\ x_{m1}& x_{m2}& \dots & x_{mn}\\ x_{ai1}& x_{ai2}& \dots & x_{ain}\end{array}\right]\end{array}$$

(11)

AI. and AAI are defined by Equations (12) and (13):

$$AAI={\min }_i{x}_{ij} \mathrm{if} j\in {B \mathrm{and} \max }_i{x}_{ij} \mathrm{if} j\in C$$

(12)

$$AI={\max }_i{x}_{ij} \mathrm{if} j\in B \mathrm{and} {\min }_i{x}_{ij}\mathrm{if}j\in C$$

(13)

$$C\in \text{group of cost criteria}, B\in \text{Benefit group of criteria}.$$

Step 3. Normalizing the extended initial matrix by Equations (14) and (15).

$$n_{ij}=\frac{x_{ai}}{x_{ij}} \mathrm{if} j\in C, x_{ai} \mathrm{and} x_{ij} \text{are the elements of matrix} X.$$

(14)

$$n_{ij}=\frac{x_{ij}}{x_{ai}} \mathrm{if} j\in B, x_{ai} \mathrm{and} x_{ij} \text{are the elements of matrix} X.$$

(15)

Step 4. Determining the weighted matrix.

$$v_{ij}=n_{ij}\ast w_j,n_{ij} \mathrm{is\; the\; elements\; of\; normalized\; matrix} N.$$

(16)

Step 5. Calculating the utility degree of alternatives.

$$K_i^{-}=\frac{S_i}{S_{aai}}$$

(17)

$$K_i^{+}=\frac{S_i}{S_{ai}}$$

(18)

S_i is the sum of the elements of weighted matrix V and is obtained by Equation (19).

$$S_i={\displaystyle \sum _{i=1}^n{v}_{ij}}$$

(19)

Step 6. Determining utility function of alternatives $f(K_i)$.

$$\begin{array}{l}f(K_i)=\frac{K_i{}^{+}+K_i{}^{-}}{1+\frac{1-f(K_i{}^{+})}{f(K_i{}^{+})}+\frac{1-f(K_i{}^{-})}{f(K_i{}^{-})}}, \\ f(K_i{}^{+}) \text{is utility function in relation to ideal solution}.\\ f(K_i{}^{-}) \text{is utility function in relation to anti-ideal solution}.\end{array}$$

(20)

$f(K_i{}^{-})$ and $f(K_i{}^{+})$ are obtained by the below equations.

$$f(K_i{}^{-})=\frac{K_i{}^{+}}{K_i{}^{+}+K_i{}^{-}}$$

(21)

$$f(K_i{}^{+})=\frac{K_i{}^{-}}{K_i{}^{+}+K_i{}^{-}}$$

(22)

Step 7. Ranking the alternatives based on the final values of the utility functions. The alternative with a higher utility function value is more preferred.

4. Application

International companies always want to have much more revenue from their product, so up to now, they have transferred their industry to other regions (off-shoring), especially Asia. The labor cost, tax rate, transportation cost, and collaborative supply chain in Asia are cheaper than on other continents. Keeping in mind the development in Asian countries, the attraction of this region has decreased, and companies have less intention to off-shoring. Near-shoring is a good substitution for off-shoring, so selecting the best region for companies to supply their demands is a vital and an essential issue. Since all automotive companies are moving to produce E.V.s, the BEV is a vital need that the companies must accept. Lithium is the main battery component used in E.V., mobile phones, laptops, and other electronic instruments. Thus, the goal of this research is to survey and propose the best region for constructing a battery for U.S. automotive and electronic companies, according to the near-shoring discussion.

Based on surveys, three countries were selected for comparison: Chile, Bolivia, and Argentina, which are in the lithium triangle. Approximately 86 million tons of lithium resources are found worldwide in this region, among which 21 million tons exist in Bolivia, 19.3 million tons in Argentina, and 9.6 million tons in Chile (Berg 2021). It is true that Bolivia has the largest lithium reserves in the world, but this lithium is not commercial. Climates and geographic conditions are two parameters that convert lithium reserves to commercial lithium. Lithium exists in hard rock or salt lakes (Salares), and it is easier to extract lithium from hard rock than from a salt lake. Australia, the largest producer of commercial lithium, mines lithium from hard rock, but the reserves of these three countries (Argentina, Bolivia, and Chile) are underneath salt flats. Among countries in the lithium triangle, Chile has commercially viable reserves because of its climate, which make extraction and evaporation easier.

One of the criteria that investors or stakeholders consider for the target region is the national minimum wage (NMW). The NMW is the lowest salary that employers should pay to employees. The NMW of Argentina, Chile, and Bolivia are 862.5, 470, and 309.3 dollars, respectively [76].

The corporate income tax (CIT) rate is one of the issues considered when starting a business in a foreign country. CIT is a form of direct tax imposed on the net profit of a corporation [77]. The CIT of the three countries in 2020 and 2021 are listed in

Table 3. The CIT of three countries.

Years	Chile	Bolivia	Argentina
2020	25%	25%	30%
2021	10% for small business 27% for others	25%	35%

.

China is the world’s biggest mining country [78]. This is due to prominent mining companies that exist there, such as Jiangxi Copper, China Shenhua Energy, Yanzhou, Aluminum Corporation of China (ACH), and Zijin. Consequently, the presence of big mining companies in a region increases the country’s success in becoming a big producer. In Latin America, there are many mining companies, such as Vale, which belongs to Brazil, with a net revenue of 40.84 billion U.S. dollars, and Codelco of Chile with a 14.17 net revenue. In the lithium triangle, Chile has more mining companies, such as Minera Escondida (7.65 net revenue), Anglo American (7.18 net revenue), Antofagasta plc (5.13 net revenue), Codelco Dive. Chuquicamata (4.32 net revenue), and Collahuasi (3.94 net revenue) [8]. Therefore, accessibility to mining companies in a region significantly impacts the success of mining excavation.

Among all the transport modes, the waterway is the most desired shipment method because of its lower cost and higher accessibility [79]. Airplanes and trucks do not have enough capacity to carry a large volume of cargo and a vast amount of goods. Argentina and Chile have accessibility to open waters, as opposed to Bolivia.

The birth rate (number of live births per 1000 people in a year) or fertility rate (average number of children birth by a woman) and the percent of the young population (those people of the country aged less than 15) could be a relatively important issue for decision-makers when selecting a target country. These parameters are listed in

Table 4. The birth rate, fertility rate, and percent of the young population of countries.

	Chile	Bolivia	Argentina
Birth rate (2022) [80]	13.4	21.6	16.5
Fertility rate (2022 [80]	1.6	2.7	2.3
Percent of the young population (2020) [81]	19.8%	30.3%	24%

([80,81]).

The target country should have a stable political system; thus, political stability is a variable that significantly impacts the stockholders’ opinion because it helps companies develop sustainably [82]. The political stability index is measured based on political protest and violence in a country in a year. This index is between −2.5 (weak) and 2.5 (strong). The average value of the political stability index from 1996 to 2020 for Chile, Argentina, and Bolivia are 0.49, −0.6, and −0.48 [83].

According to the above information, the criteria of this research are commercially viable reserves, NMW, CIT, accessibility to the mining company, accessibility to the waterway, the population, which consists of birth rate and percent of young population, and political stability index.

Regarding the SFA framework, the above criteria should be set in suitability, feasibility, and acceptability. The consequence of these definitions in the previous section,

Table 5. The SFA strategy framework by related criteria.

The SFA Framework	Criteria
Suitability	Commercially viable reserves Population Accessibility to the mining company Accessibility to waterway
Feasibility	NMW CIT
Acceptability	Political stability index

, is obtained.

To find the weight of the criteria, this study used the BWM method and its advanced model BBWM. The results are listed in

Table 6. Weights of the criteria by BWM and BBWM.

	Commercially Viable Reserve	Population	Accessibility to the Mining Company	Accessibility to Waterway	NMW	CIT	Political Stability Index
Weights
BWM	0.385542169	0.03614458	0.096385542	0.080321285	0.12048193	0.16064257	0.120481928
BBWM	0.18283285	0.06678955	0.12879743	0.10889358	0.16494893	0.19132	0.1564177

. The researchers of this article used the result of BBWM because they applied the opinions of group decision-makers.

The sub-criteria weights of the population are calculated by BWM, percent of young population (0.8), birth rate (0.1), and fertile rate (0.1). The complete information about the criteria is listed in

Table 7. Decision matrix table.

	Commercially Viable Reserve	Population			Accessibility to the Mining Company	Accessibility to Waterway	NMW	CIT	Political Stability Index
		Young-Percent	Birth-Rate	Fertile-Rate
Weights	0.1828328	0.0667895			0.12879743	0.10889358	0.164948	0.1913	0.1564177
		0.8	0.1	0.1
Max or Min	Max	Max			max	max	min	min	max
Argentina	2	24%	16.5	2.3	2	1	862.5$	35%	−0.6
Chile	5	19.8%	13.4	1.6	5	1	470$	27%	0.49
Bolivia	1	30.3%	21.6	2.7	1	0	309.3$	25%	−0.48

. Some criteria (commercially viable reserve and accessibility to mining company) are nominal, so to convert them into number values, we used grey numbers (1 to 5) and one (yes) or zero (no) for accessibility to a waterway in the Table 7.

To rank alternatives by MARCOS method, the researchers of this study used this site: https://www.mcdm.app for calculation (accessed on 5 April 2022). The obtained results show that the values of Argentina, Chile, and Bolivia are 0.6666497, 0.76949, and 0.3849. Consequently, Chile is the best country for constructing the lithium battery industry.

5. Robustness Test

In this section, a comprehensive sensitivity analysis consisting of three phases was performed to test the validity and practicality of the proposed approach.

a. Examination of changing the criteria weights in the ranking results. We tested the consistency and stability of the model by examining the changing criteria weights in the overall ranking results. For this purpose, we formed ninety different scenarios by following the basic algorithm proposed by Görçün et al. (2021) and Görçün (2022) ([84,85]). The following algorithm is presented as follows.

$$w_{fv}^1=w_{pv}^1-\left(w_{pv}^1.m_v\right)$$

(23)

$$w_{nv}^2=\frac{\left(1-w_{fv}^1\right)}{n-1}+w_{pv}^2$$

(24)

$$w_{fv}^1+{\displaystyle \sum w_{nv}^2}=1$$

(25)

Here, $w_{fv}^1$ denotes the new value of the modified weight of jth factor, and $w_{pv}^1$ represents the previous values of the criterion and the modification degree in terms of percentage (i.e., 10%, 20%, …, 100%). Additionally, $w_{nv}^2$ symbolizes new values of remaining factors, $n$ the number of factors, and the previous values of the remaining criteria.

When the results obtained by applying the model are evaluated, the proposed model is mainly consistent and stable. Severe and significant changes are not observed in the overall ranking results despite excessive modifications, which cannot be seen in real-world conditions. Additionally, the average similarity coefficient is computed as 0.941, which can be accepted as high. Changes are noticed when the weight of criterion C3 is changed by over 30%. The main reason is that the values of the alternatives concerning this criterion are very close. However, these changes did not change the overall ranking results. Thus, the obtained results prove that the proposed model is mainly consistent and stable for decision-makers and can be accepted as reliable for practitioners.

b. Comparative analysis. We compared some popular decision-making approaches with the proposed model in the second stage. For this purpose, decision-making tools, such as MAUT, TOPSIS, ARAS, COPRAS, EDAS, and WASPAS, were implemented, and the ranking results were compared. The comparative analysis results are presented in Figure 2.

Figure 2 shows that the best alternative, A2, is ranked the same for all applied decision-making approaches. In addition, the ranking positions of the A1 and A3, alternatives have changed concerning the results of EDAS and TOPSIS techniques. The remaining approaches have provided the same ranking results as the proposed model. In addition, the average correlation coefficient among the results has been computed as 0.796.

c. Test the proposed model’s resistance to the rank reversal problem. The rank reversal problem is the main challenge of the many decision-making approaches. Hence, the proposed model was tested to examine the resistance of the model to the rank reversal problem. For this purpose, we generated two scenarios by eliminating the worst alternative in each scenario. The obtained results are presented in

Table 8. Test results of the model’s resistance to the rank reversal problem.

Scenario	Ranking
Original	A2 > A3 > A1
Scenario-1	A2 > A3
Scenario-2	A2

.

Table 8 shows that no change has been observed in the ranking performance of the alternatives. It proves that the proposed approach is maximally consistent and stable, providing robust, practical, and efficient decision-making frames.

6. Conclusions

The COVID-19 pandemic changed countries’ off-shoring destination from China. The big companies in developed countries have decided to use near-shoring instead of off-shoring. By near-shoring, companies move their industries and supply chains to neighboring countries. Therefore, the automotive companies making E.V.s and mobile phone companies producing phones need batteries, which lithium is the main component. This research surveys it. Ford Motors has decided to allocate 40% of its sales globally to E.V.s by 2030 [86]. Credit Suisse analyzes that, in 2022 and 2023, mining lithium will produce approximately 588,000 and 736,000 tonnes, but the forecast demands 689,000 and 902,000 tonnes, respectively, with two-thirds of that allocated to E.V.s’ batteries [87]. This report shows that the world will face a shortage of lithium soon because of the growth of using lithium batteries for E.V.s and other electronic instruments. This magnitude of future demand for lithium has guided companies and managers to make strategic decisions and policies for their industries’ future. This research aims to supply the raw material of batteries to big companies in the U.S. with the most negligible supply chain risks.

Considering the near-shoring supply chain strategy, the countries on the American continent are considered major suppliers. The researchers consider three countries, Argentina, Bolivia, and Chile, as alternatives for selecting the best place for suppling lithium. In order to introduce related criteria for on-shoring, this study proposes using the SFA strategy method. SFA method has a framework that provides the condition for researchers to introduce related criteria. This framework consists of suitability-feasibility-acceptability. The criteria that can be considered a constraint to reaching goals are imported in the suitability field. The feasibility field considers the criteria that shows the efficiency of the strategy, if this strategy is implemented practically. Acceptability imports the criteria that stakeholders notice. The criteria introduced in this study are based on the popularity of Asian countries and the SFA framework. The criteria used in this research are commercially viable reserves, national minimum wage, corporate income tax, accessibility to the mining companies, accessibility to the waterway, the population, which consists of birth rate and percent of young population, and political stability index. SFA is a good strategy selection method but has some deficiencies. This method does not introduce a distinct approach to calculating criteria weights and evaluating options. Due to these deficiencies, this work combines MCDM methods. The Bayesian BWM method is used for weighing the criteria since this research implements the opinion of multiple decision-makers, and the MARCOS method ranks the criteria. The weight of the criteria that are obtained by BBWM method are w1 = 0.18283285, w2 = 0.06678955, w3 = 0.12879743, w4 = 0.10889358, w5 = 0.16494893, w6 = 0.19132, and w7 = 0.1564177. The result of the BBWM-MARCOS method is compared to BBWM-ARAS and BBWM-COPRAS methods. Eventually, three methods show that Chile is the best target country as a lithium raw material supplier. Further, a comprehensive comparison analysis supports the findings.

For the basis of the calculation in this context, this report has determined that Chile is the best country to be used for near-shoring because of the lithium supply chain. This key supplier of lithium (Chile), with 9.6 million tons of commercially viable reserves, can supply the demand of the U.S. automobile and electronics companies for constructing batteries. A small number of criteria can be considered a limitation of this study. Future studies can be planned to include more criteria. Furthermore, models performed under uncertainty, such as fuzzy sets and rough sets, can be considered to better express human thoughts and perceptions. It is necessary to mention the researchers assume that the best place to construct a lithium battery company is near lithium resources, and based on this assumption, we proposed that Chile is the best place for building a battery company.

In addition, the sensitivity analysis performed to test the validity and applicability of the proposed model approves the stability, robustness, and practicality of the model. Despite the excessive modifications, it has not seen changes affecting the overall results.