Workshop Location Selection using Best Worst Method (BWM) and Additive Ratio Assessment

. Selecting the best new workshop location is one of the businesses that can support a company's success. In this study, we used two combined methods: the BWM method was used to determine the weight of the criteria and to evaluate new location alternatives against the site selection criteria, while the ARAS method was used to rank the location alternatives. This study was conducted by collecting data on criteria for choosing the best location, which are profit (price and market), convenience (workshop access, land area, and environment), and support (location of suppliers and labor). The best new workshop location is obtained by filling out the BWM questionnaire for weighting each criterion and evaluating location alternatives, and then ranking the location alternative using the ARAS method. The numerical example of a case study shows that location K2 was chosen as the best new location for the welding workshop because it has the highest score in the alternative ranking of 0.9713. Hence, by combining BWM dan ARAS methods, the decision maker could make their best decision for selecting their new workshop location with multicriteria consideration.


Introduction
Along with global economic improvement, it provides opportunities for business or industrial sectors to maximize their potential to advance their business.There are several factors that influence the development of an industry, one of which is workshop location.Choosing the right location has a considerable impact on the progress and development of an industry [1].Selection of a suitable location following the required criteria could easily facilitate the industry to carry out the logistics, production, and procurement of raw materials [2].Thus, choosing the most suitable location will be able to support the sustainability of their supply chain management properly [3].However, determining the best location requires careful consideration of the required criteria.The location of a business or workshop must provide maximum benefits from all existing aspects.
Multi-Criteria Decision Making (MCDM) is a supporting method in the decision-making mechanism by determining the best alternative from the existing alternatives according to predetermined criteria or subcriteria [4].There are several MCDM methods that can be used to assist in decision-making, such as the Best-Worst Method (BWM) and Additive Ratio Assessment (ARAS) methods.
This relatively new BWM method was developed by Dr. Jafar Rezaei in 2015.The BWM method aims to rank and determine the best alternative by evaluating these alternatives by weighing the specified criteria and calculating the value of these alternatives [5].This method is used to determine the weight of the criteria by comparing the best and the worst vector [6].The BWM method can generate a higher consistency ratio compared to traditional methods, such as the Analytical Hierarchy Process [7].In this study, the BWM method was used to determine the weight of the criteria and to evaluate location alternatives for the selection criteria for a new workshop location.
The ARAS method is also relatively new in MCDM [8].The ARAS method is one of the methods in MCDM which is based on the concept of ranking using a utility degree, which compares the overall index value of each alternative to the optimal alternative overall index value [9].The ARAS method is more recommended in ranking than the COPRAS method and others because the ARAS method has the advantage of being relatively easy to implement and has a more consistent utility value [10].
Based on the background described above, we will research selecting new workshop locations using the Best Worst Method (BWM) in weighing criteria and Additive Ratio Assessment (ARAS) in ranking the new location alternatives.The use of the BWM method in weighting in this study is due to its application which matches the existing problems and the utility value more consistent than other methods [11].In addition, the ARAS method is also used in ranking because of its application easiness [12].

Best Worst Method (BWM)
In 2015, Jafar Rezaei developed a method in multicriteria decision-making to determine the weight of the criteria by comparing the best and the worst vector [7].Some steps can be taken in determining the weight on the criteria using the BWM method, which are as follows [13].
1. Identify location selection criteria.2. Determine the best and worst criteria from the criteria that have been identified.3. Determines the best criterion to be used for other vectors.4. Determine another vector for the worst criterion.5. Determine the optimal weight of each criterion.
WB Wj denotes the optimal weight of each criterion; that is each pair of comparison of the criteria weight against other criteria is the same as the preference set by the decision maker from the best criterion to other criteria, which is denoted by  , and the preference of other criteria to the worst criterion is denoted with ɑjw .The formula used in finding the optimal weight of the criteria is as follows: The solution of Equation (2) as a network has a solution ( w1 *, w2 *,... wn*).  * which is considered as a good indicator of the consistency of the comparisons [13].We can utilize BWM Solver to support the solution model developed in Microsoft Excel.
BWM calculations are consistent when ɑBj x ɑjw = ɑBW.Since the results of calculations may not have complete consistency, researchers can calculate the level of consistency using a rough index called the consistency ratio, which formulation is as follows: The CR value is in the range of 0 to 1.The smaller the CR value or close to 0, the more consistent the comparison will be, hence the more reliable results.The consistency ratio index table is as follows.

Additive Ratio Assessment (ARAS)
ARAS is a criteria ranking method in MCDM which better used as an addition to other methods such as SAW, BWM, COPRAS, and others.The steps taken in ranking with the ARAS method include the following [14].
1. Form the decision-making matrix.
X= [ Where, m = Number of alternatives n = Number of criteria Xij = Performance value and alternative i to criterion j X0j = The optimum value of criterion j 2. Normalize the decision matrix for all criteria.
If the criteria that have been proposed have the larger better (benefit) value, then the normalization of the decision matrix is as follows: However, if the criteria that have been proposed are smaller better (cost) value, then the normalization of the decision matrix will be in two stages, as follows: 3. Calculate the matrix weights that have been normalized.
X ̂= [ With the value of: X ̂ij =The weighted normalization value of the i-th alternative to the j-th criterion  ̅ ij =Normalized value of the i-th alternative to the j-th criterion  j =weight of the j-th criterion 4. Calculate the value of the optimum function.
= Total weighted normalized values of the i-th alternative 5. Determine the rank order.
The final step is to determine the rank order based on the following Equation: =Utility value of the i-th alternative   =Optimum function value of the i-th alternative  0 =Optimum function value on the optimum alternative

Results and Discussions
This research is applied in a case study of a welding company in Purwokerto, Indonesia.This company plans to build a welding workshop at the new location.The decision maker, the company's owner, is interviewed regarding the criteria needed for selecting a new location for a welding workshop.The results of the criteria for selecting a new location for a welding workshop are obtained.There are seven criteria for selecting a new location for a welding workshop which will be classified into three factors.The criteria for selecting a new location for the welding workshop in this study can be seen in Fig. 1.

Fig. 1. Selection Criteria for a New Welding Workshop Location
The next step is weighting the criteria using the BWM method by filling out the BWM questionnaire, which is choosing the best and worst criteria in selecting a location.The best and worst criteria are seen in Table 2.

Labor
After determining the best and worst criteria, the decision maker continued filling out the BWM questionnaire to determine the weight of the criteria.Determining the weight of the criteria is done by comparing the best to others and others to the worst criteria.The assessment criteria are based on a priority scale with a value range of 1-9.The greater the weight value, the more important the criterion is.The results of the weighted criteria are as follows.Based on the calculation of the criteria weight above, the most prominent weight value is in the price criterion, with a value of 0.5605.It shows that the price criterion will have a significant impact in calculating the ranking of alternative locations for new welding workshop.
After obtaining the weight of the sub-criteria needed to select a new location, the next step is calculating the ranking of location alternatives using the ARAS method.By using the interview method with the owner and based on product order data in 2022, an alternative location is obtained as follows: 1. Mersi, East Purwokerto 2. Kaliori, Banyumas.

Purbalingga.
After obtaining data on alternative locations for the new welding workshop, the next step is to evaluate alternative locations for the new welding workshop.To facilitate the evaluation of alternative locations against the criteria for selecting a new welding shop location, the rating scale is determined as follows.
1. Affordable land or building prices.1) Land price ≥ 800 million IDR 2) The price of land is 700 -800 million IDR.
3) The price of land is 600 -700 million IDR.

The location of the welding workshop is close
to the majority of consumers.
1) The distance between the workshop location and the consumer is ≥ 10 km.
2) The distance between the workshop location and the consumer is 8-9 km. 3) The distance between the workshop location and the consumer is 6-7 km.4) The distance between the workshop location and the consumer is 4-5 km. 5) The distance between the workshop location and the consumer is ≤ 3 km.3. Easy access to the location of the welding workshop.
1) The distance of 3 km to the location of the welding workshop can be reached in > 25 minutes.
2) The distance of 3 km to the location of the welding workshop can be reached in 21 -25 minutes.
3) The distance of 3 km to the location of the welding workshop can be reached in 15 -20 minutes.4) The distance of 3 km to the location of the welding workshop can be reached in 9 -14 minutes.5) The distance of 3 km to the location of the welding workshop can be reached in < 9 minutes.1) The location of the welding workshop has a land area of ≤ 250 m 2 .
2) The location of the welding workshop has a land area of 251 -300 m 2 .
3) The location of the welding workshop has a land area of 301 -351 m 2 .4) The location of the welding workshop has a land area of 351 -400 m 2 .5) The location of the welding workshop has a land area of ≥ 401 m 2 .5. Conducive environment.
1) The distance between the location of the welding workshop and the school, campus, and office areas is ≤ 100 m.
2) The distance between the location of the welding workshop and the school, campus, and office areas is 101 -150 m.
3) The distance between the location of the welding workshop and the school, campus, and office areas is 151 -200 m. 4) The distance between the location of the welding workshop and the school, campus, and office areas is 201 -250 m. 5) The distance between the location of the welding workshop and the school, campus, and office areas is ≥ 251 m. 6.The distance between the supplier of raw materials and the welding workshop.
1) The distance between the location of the welding workshop and the supplier of raw materials is ≥ 30 minutes.
2) The distance between the location of the welding workshop and the supplier of raw materials is 30-25 minutes.
3) The distance between the location of the welding workshop and the supplier of raw materials is 24-20 minutes.4) The distance between the location of the welding workshop and the supplier of raw materials is 19-15 minutes.5) The distance between the location of the welding workshop and the supplier of raw materials is ≤ 14 minutes.7. The distance of the domicile of the labor.
1) The distance between the location of the welding workshop and the domicile of the labor is ≥ 60 minutes.
2) The distance between the location of the welding workshop and the domicile of the labor is 45 -59 minutes.
3) The distance between the location of the welding workshop and the domicile of the labor is 30-44 minutes.4) The distance between the location of the welding workshop and the domicile of the labor is 15 -29 minutes.5) The distance between the location of the welding workshop and the domicile of the labor is ≤ 14 minutes.The decision-making matrix for alternative locations can be seen in Table 12.Based on Table 12 above, A0 is the optimum value of each alternative whose value is determined in a way that if these criteria include benefits, then A0 is the maximum value of the assessment.If A0 is a cost, then the value of A0 is the minimum value of evaluation.Alternative A1 represents the alternative location in Mersi, alternative A2 represents an alternative location in Kaliori, and alternative A3 represents an alternative location in Purbalingga.The next step is normalizing the decision matrix, as shown in Table 13.
In Table 13, there are differences in the color of the table; the benefit criteria are green, while the cost criteria are yellow.Table colors are distinguished because the normalization process is based on different cost and benefit criteria.The next step is to determine the alternative weighted normalization matrix.To find out the results of weighted normalization on the normalization matrix will be shown in Table 14.Based on Table 15 above, the optimum function value (S0) is 0.2961.This optimum function value will then be used to compare the optimum function value for alternative locations.The optimum function value for a location in Mersi (S1) obtained a value of 0.1964, while the optimum function value for a location in Kaliori (S2) is 0.2876, and the optimum function value for a location in Purbalingga (S3) is 0.2192.The last step is to determine the rank order of location alternatives.The following is the rating for choosing a new location for the welding workshop, shown in Table 16.Based on Table 16 above, the rating value for a location in Mersi (K1) is 0.6635, while the rating value for a location in Kaliori (K2) is 0.9713, and the rating value for a location in Purbalingga (K3) is 0.7404.Therefore, the first order is the alternative location in Kaliori, the second order is the alternative location in Purbalingga, and the third order is the alternative location in Mersi.
Alternative location A1 in Kaliori, Banyumas is in first place for alternative locations through the results of ranking calculations using the ARAS method with a relatively large value of 0.9713.To get a value of 0.9713, it is done by calculating the results of the optimum value of alternative S2 0.2876 divided by the value of S0 0.2961, where the weighted normalization value of each criterion affects the optimum value.Some criteria greatly influence or significantly impact the optimum value for a location in A1, which is the price criterion.Based on the weighted normalization calculation on the price criterion, it obtained a value of 0.1751.This value is the criterion value that is the largest among other alternative locations, so it greatly impacts the weight of workshop location selection.Most of the weighted normalization values at A1 have the highest value of the other alternatives, except for the supplier location and labor criteria.However, this does not really matter because the weight for the supplier location and labor criteria is low.Hence, Kaliori, Banyumas was proposed as the best alternative for the new workshop location.

Conclusion
The following conclusions are obtained based on the analysis and discussion carried out in the research case on selecting a new location for the welding workshop using the BWM and ARAS methods.Seven criteria are being considered in selecting a new location: price, market, workshop access, land area, environment, location of suppliers, and labor.These criteria are classified into three main criteria, namely: profit, convenience, and support.By using the BWM method, we determined the weight of each criterion based on the preference of the decision maker.In this case, the weight of each criterion is obtained as follows: price (0.5605), market (0.1121), workshop access (0.1522), land area (0.1522), 0577), environment (0.0262), supplier location (0.0727), and labor (0.0181).The price criterion is obtained as the best or the priority criterion with the most significant weight, and the labor criterion as the worst or lowest priority criterion with the smallest weight.
Finally, the rank order for selecting the new workshop locations is obtained based on alternative ranking calculations using the ARAS method.The ranking results show that location K2, located in Kaliori, has the highest score of 0.9713.From this case study for numerical examples, it is shown that by combining BWM dan ARAS methods, the decision maker could make their best decision for selecting their new workshop location with multi-criteria consideration.

Table 2 .
Best and Worst Criteria

Table 3 .
BWM Pairwise Comparison Result of Best Criteria In Main Criteria

Table 5 .
BWM Pairwise Comparison Result of Best Criteria In Profit Criteria

Table 6 .
BWM Pairwise Comparison Result of Worst

Table 7 .
BWM Pairwise Comparison Result Of Best Criteria In Convenience Criteria

Table 8 .
BWM Pairwise Comparison Result of Worst

Table 9 .
BWM Pairwise Comparison Result Of Best CriteriaIn Supporting Criteria

Table 10 .
BWM Pairwise Comparison Result Of Worst Criteria In Supporting Criteria

Table 11 .
The Weight of The Criteria

Table 13 .
Normalized Decision Matrix

Table 14 .
Weighted Normalization MatrixThe next step is to determine the optimum function value for each alternative location.The following table shows the optimum function values for each alternative.

Table 16 .
Rank Order of Location Alternatives