Office location selection by fuzzy AHP and VIKOR

36 Int. J. Information and Decision Sciences, Vol. 11, No. 1, 2019 Office location selection by fuzzy AHP and VIKOR Tayfun Arar*, Serhat Karaoğlan and Ceren Dirik Department of Business Administration, Kirikkale University, 71450, Kirikkale, Turkey Email: [email protected] Email: [email protected] Email: [email protected] *Corresponding author Abstract: In a globalised business world, reaching the basic goal of companies which is profit maximisation has become such competitive for both manufacturing and service firms. While reaching this basic goal, increasing income is not sufficient, but also minimising the costs is required. One of the long-term cost decisions, location selection, needs to be considered in detailed by business firms. Especially for a firm in service sector, there are other goals and responsibilities such as satisfying permanently changing needs and expectations of customers. As the wedding sector has a growing share in the economy, the choice of office location for companies operating in this sector has gained great importance. In the light of this purpose, there are some criteria determined in location selection decision for a business firm which operates in the wedding sector. In this research, the criteria used in office location selection have been chosen by literature review and experts’ views. These criteria are weighted by fuzzy analytic hierarchy process (AHP). Then, using the weighted criteria, the best option among the alternative offices from different locations is chosen by Vise Kriterijumska Optimizacija I Kompromisno Resenje (VIKOR) technique. Keywords: office selection; location selection; wedding sector; fuzzy AHP; Vise Kriterijumska Optimizacija I Kompromisno Resenje; VIKOR. Reference to this paper should be made as follows: Arar, T., Karaoğlan, S. and Dirik, C. (2019) ‘Office location selection by fuzzy AHP and VIKOR’, Int. J. Information and Decision Sciences, Vol. 11, No. 1, pp.36–54. Biographical notes: Tayfun Arar is currently a Research Assistant in Business Department of Kirikkale University and keeps studying in managerial topics integrated with quantitative methods also as a PhD candidate. He received his Bachelor’s in Business Administration from the Hacettepe University and started his Master’s program in Production Management and Quantitative methods in the same university; but in the thesis part, he had to leave this program and started another Master program in Management and Organisation Program in the Kirikkale University which he has been working for more than three years. Serhat Karaoğlan is currently a Research Assistant and PhD candidate in the Department of Business Administration of Kirikkale University since 2014. He earned his BSc in Business Administration at the Gazi University, Ankara in 2011. He graduated from his Master’s program of Quantitative Methods in the Kirikkale University. Previously, he had worked as a civil servant for Minister Copyright © 2019 Inderscience Enterprises Ltd. Office location selection by fuzzy AHP and VIKOR 37 of Energy between 2006 and 2014. His studies are arts marketing and management, service marketing, marketing research, digital marketing and MCDM. Ceren Dirik is currently a Research Assistant in the Department of Business Administration of the Kirikkale University. She received her Bachelor’s in Business Administration from the Hacettepe University and graduated from the Master’s program of Production Management and Quantitative Methods in the Hacettepe University. She started her doctoral program in the Department of Business Administration in Kirikkale University which she has been working for approximately two years. Her areas of researches interest include MCDM, dynamic programming, data envelopment analysis and stochastic inventory control. 1 Introduction Deciding where to locate the building for a business company becomes more of an issue either it is a manufacturing or a service company (Önüt et al., 2010). This building can be either a facility to manufacture products, an office to serve customers, headquarter to manage businesses or public place such as a shopping centre, a hospital, a hotel or a university campus. This topic has been popular both in academic and business communities in last quarter (Chou et al., 2008). The background of this issue is cumulative developed with different models, methods and solutions (Chang and Lin, 2015). Location selection is one of the most important strategic decisions for business firms. Whether it is operating in manufacturing or service sector, a firm needs to establish new facilities to start up or expand (Govindan et al., 2016). The other most important reason why selecting a location needs to be planned very carefully at the beginning is the cost. Identifying and choosing the best location option not only saves money and resources, but also improves the environmental situation (Krylovas et al., 2016). The best location also brings the company an increased productivity and a good network (Athawale and Chakraborty, 2010). By a wisely made-location decision, especially business firms in service sector can response to their customers’ changing demands much faster while sustaining its service quality (Chakraborty et al., 2013). Throughout the literature on location selection, two important points are ostensible and these deficiencies need to be revised. First of them is, the structure to be located is mostly large sized and belong to corporate business firms. There are a few location selection studies made for small and medium sized enterprises (SMEs) in the literature such as Adnan et al. (2015), Wojcik et al. (2013) and Leishman et al. (2012)’s studies. The reason of why many location selection studies made for larger sized areas or structures is based on the type of investment that location decision is. Location selection is a long term investment decision that is so hard to reverse (Govindan et al., 2016). This means, this decision would affect the profitability of the company for years (Chou, 2009). Before deciding where to locate the facility, plant or other main structure, a firm needs to think laterally. A wrong location decision returns high costs to the firm in both short and long terms. The point is, while a large sized business firm can afford such a cost, it would be much more difficult for a SME to handle with it through its lower level budgets 38 T. Arar et al. respectively and may go bankruptcy much easily. Second is, as seen in Table 1, vast majority of the researches have been made for manufacturing firms. There is a minority of location selection for service sector firms; such as university campus (Özkan and Alp, 2014) and hotel (Chou et al., 2008). Today customers’ needs, expectations and wishes are changing constantly by being affected from the real and online environment. In such a ‘what customer says’ age, firms in service sector, by locating in the right place for customers would bring the loyalty and satisfaction (Chou et al., 2008). Along with the service industry’s increasing importance, weddings those are feeding many business lines have now become a sector itself and it is growing day by day. People, especially who live in developed cities, generally prefer to leave the issues of their wedding organisation to the professionals. These professional organisations can offer tailored services with different packages so that they can address different levels of customer budget. Generally speaking, what wedding organisation firms do can vary greatly ranging from serving a basic marriage decoration to the comprehensive and detailed wedding event. Audio system, photographer, place and table decoration, wedding consultancy, catering service, ceremony and reception hosting, transport, hair and make-up application, designer, florist, honeymoon tour organiser, jeweller, fireworks display and plenty of extras are some of the services offered by these companies. As such an important day planner and with wide range of services offered, selection of office location is very critical and needs to be considered carefully for a wedding organisation firm. According to Organisation for Economic Cooperation and Development (OECD, 2016)’s Family Database of 2014, crude marriage rates (CMRs), the number of marriages during the year per 1000 people, are very low at 3.5 or fewer in some countries such as Spain, Bulgaria, Italy, Luxembourg and Argentina. In most OECD countries, CMRs are somewhere between 4 and 5.5 marriages per 1,000, with the OECD average standing at 4.6. However, rates are twice that at around seven for China, Russian Federation, Turkey, Lithuania and the USA. The wedding industry has developed very quickly in Turkey and contributes significantly to the country’s economy. Turkey has become one of the preferred destinations for wedding tourism as a result of the increasing number of couples coming from abroad. In Turkey, an average of 600,000 couples is married every year since 2004 (Turkstat, 2016). For example, according to same database; with reference to 2015 data, 602,982 couples got married in Turkey, more than 30% in three major cities: İstanbul, Ankara (approximately 35,000) and İzmir. One of the reasons for this high marriage rate in Turkey is due to its historical and cultural attractiveness. The fact that it is a country where four seasons are experienced and that the cultural heritages of the respect for ‘marriage corporation’ and it is assertive in wedding shopping can be considered as other reasons. Considering the information obtained from the negotiations we have made with the Turkish sector authorities, the fee that the wedding organisation firms in Ankara demand per person range from 15 to 20 Turkish Liras (L) for a standard wedding package. These prices can change according to the number of invitees, wedding date, live flower usage, rented equipment and any other extra services. Wedding sector in Turkey reaches up to $23,000 (L 50,000). According to data from the Association for Prearrangement and Implementation of Creative Activities (YEPUD), wedding organising brings in between 250–450 million dollars in Turkey (Hurriyet, 2016). In this perspective the main aim of this research is to find the best office location for a wedding organisation company. For this purpose, first step is to clarify the criteria. 39 Office location selection by fuzzy AHP and VIKOR Throughout the literature the criteria mostly used in location selection by multi criteria decision models (MCDM) studies are listed below. Cost Availability of labour Business climate Development capability Accessibility Security Attractiveness Criteria mostly used in the location selection problems by MCDM methods Proximity to suppliers Proximity to market Transportation Table 1 ● ● ○ ● ● ○ ● ○ ○ ○ ● ● ○ ● ● ○ ● ○ ○ ○ Awasthi et al. (2011) ● ● ● ● ○ ○ ○ ● ● ○ Kuo (2011) ○ ● ● ● ○ ○ ○ ● ○ ○ Chakraborty et al. (2013) ○ ● ○ ○ ● ○ ○ ○ ○ ○ ○ ● ● ● ● ● ● ○ ○ ○ ○ ○ ● ○ ○ ● ● ○ ○ ○ Author(s) (year) Chu and Lai (2005) Anagnostopoulos et al. (2008) Athawale and Chakraborty (2010) Location Distribution centre Facility Kouchaksaraei et al. (2015) Tadic et al. (2014) Rao et al. (2015) Önüt et al. (2010) Zolfani et al. (2013) Devi and Yadav (2013) Logistics centre Shopping centre Plant Yong (2006) Özcan et al. (2011) Chatterjee and Bose (2013) Özkan and Alp (2014) Adnan et al. (2015) Kabir and Sumi (2014) Other locations (warehouse, windfarm, power stations, etc.) ○ ○ ● ● ● ● ● ○ ● ● ○ ○ ● ● ● ○ ● ○ ● ○ ○ ○ ○ ● ○ ○ ● ● ○ ● ○ ○ ● ● ○ ● ● ● ○ ● ● ○ ● ○ ● ● ● ○ ○ ○ ○ ○ ○ ● ● ○ ● ○ ○ ○ ● ● ○ ● ○ ○ ○ ○ ○ ○ ○ ○ ● ● ○ ● ○ ○ ○ ○ ○ ● ● ○ ○ ○ ● ● ○ ○ ○ ● ● ● ○ ○ ○ ● ● ○ ● ● ○ ● ○ ○ ○ ○ ○ ○ Note: ●That criterion exists; ○That criterion does not exist. As seen in Table 1, the black dots are the most used criteria in the studies. While some of those criteria which are contingent with the purpose of this study are chosen to examine, other criteria are identified by the experts’ views. Thus the main criteria chosen for location selection of a wedding organisation firm’s office are cost (C1), accessibility (C2), physical condition (C3) and regional features (C4). Sub-criteria are respectively start-up costs (C11), monthly costs (C12) and cost of labour (C13) for criterion cost (C1); parking lot availability (C21), traffic rush (C22) and public transportation (C23) for criterion 40 T. Arar et al. accessibility (C2); visibility of the office (C31), size of the office (C32), structural features (C33) and neighbour offices (C34) for criterion physical condition (C3); proximity to market (C41), proximity to business partners (C42), security condition (C43) and prestige (C44) for criterion regional features (C4). Figure 1 Hierarchical model of the study Second step is to identify the alternatives. This process is again made by an interview with an expert in this field. In this study, we address the office selection problem of firms which are operating in the wedding sector in Turkey. For ease of use, office location alternatives are determined only for one city of Turkey. Within this context, Ankara, which is the capital of Turkey and the second city where the most marriages take place, has been chosen. Third step is to clarify the method to analyse those criteria and alternatives. The methods which are used in the studies mentioned in Table 2 are shown. 41 Office location selection by fuzzy AHP and VIKOR ANP DEMATEL TOPSIS ELECTRE PROMETHEE GRA VIKOR MOORA COPRAS SWARA OTHER MCDM methods mostly used in location selection problems AHP Table 2 ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ●f Anagnostopoulos et al. (2008) ○ ○ ○ ●f ○ ○ ○ ○ ○ ○ ○ ●f Awasthi et al. (2011) ○ ○ ○ ●f ○ ○ ○ ○ ○ ○ ○ ○ Kuo (2011) ○ ● ●f ● ○ ○ ○ ○ ○ ○ ○ ○ Chakraborty et al. (2013) ● ○ ○ ○ ● ○ ● ○ ● ○ ○ ● ○ ○ ○ ○ ○ ● ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ● ● ○ Logistics centre ○ ●f ●f ○ ○ ○ ○ ●f ○ ○ ○ ○ ○ ○ ○ ● ○ ○ ○ ○ ○ ○ ○ ○ Shopping centre ●f ○ ○ ●f ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ● ● Plant ○ ○ ○ ○ ● ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ●f ○ ○ ○ ○ ○ ○ ● Other locations (warehouse, ○ windfarm, power ●f stations, etc.) ● ○ ○ ● ● ○ ● ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ● ○ ● ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ●f ○ ○ ○ ○ ● ○ ○ ○ ○ ○ ○ Author(s) (year) Chu and Lai (2005) Athawale and Chakraborty (2010) Location Distribution centre Facility Kouchaksaraei et al. (2015) Tadic et al. (2014) Rao et al. (2015) Önüt et al. (2010) Zolfani et al. (2013) Devi and Yadav (2013) Yong (2006) Özcan et al. (2011) Chatterjee and Bose (2013) Özkan and Alp (2014) Adnan et al. (2015) Kabir and Sumi (2014) Note: ●That method is used; ●f Fuzzy version of that method is used; ○That method is not used. Thus, there are four main criteria and 14 sub-criteria with five alternative offices at all. Though people could be counted as the most wisdom creatures on Earth, researches claim that humans do not have enough capacity for decision making in complex situations (Kahraman et al., 2003; Güneri et al., 2009). In any branches of life, decision maker would find an interval evaluation more trustworthy and prefer it rather than a 42 T. Arar et al. deterministic single valuation method (Göksu and Güngör, 2008). That is why, for weighting the criteria, fuzzy analytic hierarchy process (AHP) method is used. For choosing the best office based on the criteria, VIKOR technique is preferred due to the consideration of gap between alternatives (Opricovic and Tzeng, 2004) and its providing of an advantageous compromised solution (Amiri et al., 2011). 2 Method 2.1 Fuzzy logic Fuzzy logic has been introduced to literature first in 1965 by Zadeh (1965) by the idea that classical set theory based on binary logic (0–1) is not enough to integrate the mathematics into real life. Perception differences and subjective behaviours in humanitarian cognitive process can be explained by fuzzy logic (Şengül et al., 2012). In a fuzzy set, objects can range from 0 as being non-member to 1 as a full member (Onay et al., 2016). In this range, the values have continuity (Akman and Alkan, 2006). In Figure 2 which shows triangular numbers membership function, ‘l’, ‘m’ and ‘u’ indicates lower bound, middle value and upper bound respectively. Figure 2 Triangular fuzzy numbers membership function μΑ(x) 1 l m u x Basic arithmetic operations are made with given equations on fuzzy numbers as follows (Deng, 1999): Let X = (x1, x2, x3) and Y = (y1, y2, y3) be positive triangular fuzzy numbers. • Inverse: ⎛1 1 1⎞ X −1 = ⎜ , , ⎟ ⎝ x3 x2 x1 ⎠ • Addition: X ⊕ Y = ( x1 + y1 , x2 + y2 , x3 + y3 ) • (2) Subtraction: X (−)Y = ( x1 − y3 , x2 − y2 , x3 − y1 ) • (1) Scalar multiplication: (3) Office location selection by fuzzy AHP and VIKOR • ∀k > 0 k ∈ R, kX = ( kx1 , kx2 , kx3 ) (4) ∀k < k ∈ R, kX = ( kx3 , kx2 , kx1 ) (5) Multiplication: X ⊗ Y = ( x1 y1 , x2 y2 , x3 y3 ) • 43 (6) Division: X ⎛ x3 x2 x3 ⎞ , , = Y ⎜⎝ y3 y2 y1 ⎟⎠ (7) 2.2 Fuzzy AHP AHP technique which is developed by Thomas Saaty in the 1970s, one of the most well-known and most frequently used multi-criteria decision-making methods (Saaty, 1980; Vaidya and Kumar, 2006). The purpose of the method is to determine the importance and weights of each criterion in the hierarchical structure (Saaty, 1977). Besides being so popular, there are some deficiencies in the application of the method which are generally decision-maker originated. In order to overcome these problems, researchers used methods such as fuzzy logic. Van Laarhoven and Pedrycz (1983), Buckley (1985) and Chang (1996) have developed fuzzy AHP methods, based on the assumption that the AHP method contains deterministic logic and that pairwise comparisons are indeed uncertain and blurred. Fuzzy AHP become different at the first step of the method, which is pairwise comparison then use fuzzy numbers for calculations. The application steps of the fuzzy AHP according to the Buckley (1985) method are as follows: Step 1 The decision makers compare the criteria or alternatives according to Table 3. After the pairwise comparisons, the ‘fuzzy pairwise comparison matrix’ is created. If the number of decision makers is more than one, the geometric mean of the numerical values of the responses given by the decision makers is taken and the matrix A% is obtained. ⎡ d%11 d%12 L d%1n ⎤ ⎢ ⎥ d%22 L d%2 n ⎥ ⎢ d% A% = ⎢ 21 M M O M ⎥ ⎢ ⎥ ⎢⎣ d%m1 d%m 2 L d%mn ⎥⎦ Step 2 The geometric mean of the fuzzy values, r%i = (∏ d% ) 1/ n n j =1 ij , i = 1, 2, ...., n is calculated by equation. In this step, r%i still expresses triangular values. Step 3 (8) To obtain the fuzzy weights of each criterion, (9) 44 T. Arar et al. w% i = r%i ⊗ ( r%1 ⊕ r%2 ⊕ ... ⊕ r%n ) −1 (10) equation applied. Thus, the lwi, mwi and uwi values are calculated. Step 4 w% i = (lwi, mwi, uwi) values are still triangular fuzzy numbers. To defuzzify these numbers into crisp values, Mi = lwi + mwi + uwi 3 (11) Mi values are obtained with this equation and these values, Wi = Mi ∑ n i =1 (12) Mi are normalised by equation (12). As a result, weights of each criterion or alternative are calculated. Table 3 Linguistic expressions, scale (Saaty, 1977) and fuzzy equivalents Linguistic expressions Equal AHP Fuzzy AHP Scale Reciprocal scale Scale Reciprocal scale 1 1 1, 1, 1 1, 1, 1 Weakly more important 3 1/3 2, 3, 4 1/4, 1/3, 1/2 More important 5 1/5 4, 5, 6 1/6, 1/5, 1/4 Strongly more important 7 1/7 6, 7, 8 1/8, 1/7, 1/6 Absolutely important 9 1/9 9, 9, 9 1/9, 1/9, 1/9 2.3 VIKOR The VIKOR method was suggested by Opricovic in the year of 1998 and gained international recognition with the work of Opricovic and Tzeng (2004). This method was developed to optimise a decision problem consisting of criteria that are not related to each other (Opricovic and Tzeng, 2004). The VIKOR method, which is one of the multi-criteria decision-making methods, is a widely-used method to increase the quality of the decision making process (Lin et al., 2013). The compromise solution, founded by Yu (1973) and Zeleny (1982), means reaching agreement with a mutual concessions and providing closest alternative solution to the ideal. In this context, VIKOR method also aims to find compromise solution as illustrated in Figure 3. The VIKOR method aims to find a solution to the multi-criteria decision making problem with the highest group utility and the lowest individual regret (Opricovic and Tzeng, 2004). 45 Office location selection by fuzzy AHP and VIKOR Figure 3 Ideal and compromise solutions Source: Opricovic and Tzeng (2004) The method, which is being implemented with the aim of evaluating the alternatives, consists of the following steps respectively: Step 1 In the first step, fj* (represents the best value of a criterion) and fj– (represents the worst value of a criterion) values are determined (j = 1, 2, …, n). If the jth function represents a benefit then: f j* = max i fij and f j − = min i fij Step 2 (13) Si and Ri values (i = 1, 2, …, m) are computed for each alternative by the following equations: ∑ ⎡ w j ( f j* − fij ) / ( f j* − f j− ) ⎦⎤ (14) Ri = max j ⎣⎡ w j ( f j* − fij ) / ( f j* − f j− ) ⎦⎤ (15) Si = n j =1 ⎣ From the above equations, Si states the utility measure, Ri states the regret measure and wj are the weights which are expressing relative importance of scriteria. Step 3 Qi = (i = 1, 2, …, m) values are computed for each alternative by the relation: Qi = υ ( Si − S * ) (S − S ) − * + (1 − υ) ( Ri − R* ) ( R − − R* ) (16) In the equation (16), S* = mini, Si, S– = maxi, Si, R* = mini Ri, R– = maxi Ri and the parameter υ is the weight of maximum group utility, while (1 – υ) is the weight of the individual regret (Opricovic and Tzeng, 2007). The parameter υ can take any value between 0 and 1 although it is usually taken as 0.5 (San Cristóbal, 2011). In this study, we take the υ value equals to 0.5. Step 4 In this step, alternatives are ranked according to S and R values (calculated in Step 2) and Q values (calculated in step 3) in decreasing order. Thus, three ranking lists are obtained. 46 T. Arar et al. Step 5 As a result of the ranking process, in order to be able to identify the alternative with the smallest Q as compromise solution, it is necessary to satisfy the following two conditions: Condition 1: ‘Acceptable advantage’ Depends on following condition: Q(a ′′) − Q(a ′) ≥ DQ (17) In this inequality, a′ is the alternative with first, a″ is the alternative with second position on the ranking list by Q. Where m represents the number of alternatives, DQ = 1/(m – 1). Condition 1 indicates that best alternative should have an explicit advantage over its follower. Condition 2: ‘Acceptable stability in decision making’ The alternative with the smallest Q value (alternative a′ ) should also be the best ranked by S or/and R values. The realisation of condition 2 demonstrates that the compromise solution set is stable in the decision-making process. In case one of the above two conditions is not satisfied, the set of compromise solution is as follows: • If only ‘condition 2’ is not satisfied, alternatives a′ and a″ should be compromise solutions, • If only ‘condition 1’ is not satisfied, alternatives a′, a″, …, a(M) should be compromise solutions. a(M) is determined by the relation Q(a(M)) – Q(a′) < DQ for maximum M. 2.4 Application for a wedding organisation firm In this part of the study, 5 alternative offices will be compared under the decision criteria given in Figure 1. The decision criteria were evaluated by the decision makers and real estate experts and their weights were calculated by the fuzzy AHP. Afterwards, the data belonging to five offices were evaluated by VIKOR method and alternatives have sorted. 3 Results As a first step, the ‘fuzzy pairwise comparison matrix’ was obtained as a result of pairwise comparisons made by the decision makers and experts and is given in Table 4. Table 4 Fuzzy pairwise comparison matrix for main criteria Cost Cost Accessibility 1.00 2.00 Physical condition Regional features 3.13 0.76 0.84 1.00 1.00 0.35 0.44 0.59 0.90 1.16 1.41 2.28 2.83 1.00 1.00 1.00 0.20 0.26 0.35 1.11 0.71 0.86 1.11 1.00 1.00 1.00 1.00 1.00 2.59 Accessibility 1.00 1.14 1.32 1.00 Physical condition 0.32 0.39 0.50 1.68 Regional features 2.83 3.87 4.90 0.71 0.86 0.88 1.00 1.14 1.57 47 Office location selection by fuzzy AHP and VIKOR Four different pairwise comparison matrices were created as a result of pairwise comparisons of sub-criteria. When generating the pairwise comparison matrix, the geometric means of the responses of the decision makers (real estate experts and the office renter intended-buyer) are taken. According to the decision makers in comparing accessibility and cost. After the ‘fuzzy pairwise comparison matrix’ has been gained, the geometric mean of the fuzzy values is obtained by equation (9) and the r%i values are obtained. For example, the r%i value for the cost criterion is calculated as; ⎛ r%i = ⎜ ⎜ ⎝ n ∏ j =1 1/ n ⎞ d%ij ⎟ ⎟ ⎠ = [(1 ∗ 2 ∗ 0.76 ∗ 0.84)1/ 4 ;(1 ∗ 2.59 ∗ 0.88 ∗1.14);(1 ∗ 3.13 ∗1 ∗1.57)1/ 4 ] = [1.06;1.27;1.49] Then we obtain w% i values that show the fuzzy weights by equation (10); Mi values that show weights by equation (11) and wi values that indicate normalised weights by equation (12). The Wi values in given in Table 5 show the weights of each sub-criterion in the system and the sums are equal to 1. Table 5 Fuzzy and defuzzified weights of the criteria and sub-criteria Criteria lwi mwi ulwi Mi wi 0.21 0.29 0.41 0.30 0.29 Wi C1 Cost C2 Accessibility 0.08 0.11 0.16 0.11 0.11 C3 Physical condition 0.21 0.30 0.42 0.31 0.30 C4 Regional features 0.21 0.30 0.44 0.32 0.30 C11 Start-up costs 0.66 0.76 0.89 0.65 0.21 0.061 C12 Monthly costs 1.89 2.36 2.79 2.00 0.64 0.185 C13 Personnel costs 0.48 0.55 0.67 0.48 0.15 0.045 C21 Parking lot availability 1.74 2.02 2.27 3.05 0.57 0.061 C22 Traffic rush 0.42 0.48 0.59 0.76 0.14 0.015 C23 Public transportation 0.89 1.02 1.15 1.55 0.29 0.031 C31 Visibility of the office 1.09 1.31 1.55 0.94 0.30 0.089 C32 Size of the office 0.77 0.94 1.14 0.68 0.22 0.064 C33 Structural features 1.30 1.61 1.93 1.16 0.37 0.110 C34 Neighbour offices 0.42 0.51 0.65 0.38 0.12 0.036 C41 Proximity to market 1.06 1.24 1.42 0.73 0.23 0.070 C42 Proximity to business partners 0.32 0.37 0.45 0.22 0.07 0.022 C43 Security condition 0.61 0.74 0.92 0.44 0.14 0.043 C44 Prestige 2.40 2.96 3.46 1.73 0.55 0.168 In Table 5, lwi, mwi and uwi values are found by equations (9) and (10). Here Mi value is the defuzzified version of lwi, mwi and uwi values by equation (4) to obtain one value for easiness. In Table 5, while wi represents the local weights of the sub-criterion with regards of the main criterion, Wi indicates the global weights at total. Until this table, weights of criteria have been calculated by fuzzy AHP. After the calculation of the 48 T. Arar et al. criterion weights, alternatives were evaluated. First, decision matrix was established. Five alternative office places and 14 criteria for evaluating alternatives were given at this matrix (Table 6). In the decision matrix, alternatives have been evaluated by the real estate experts. Table 6 Decision matrix 0.061 0.185 0.045 0.061 0.015 0.031 0.089 Min Min Min Max Max Max Max C11 C12 C13 C21 C22 C23 C31 OI 12,000 2,250 2,000 4 3 5 5 OII 6,000 2,050 2,000 3 3 4 5 OIII 8,000 2,450 2,200 3 4 4 4 OIV 6,000 3,000 2,300 5 5 4 4 OV 4,000 1,750 1,750 3 3 5 5 fj * f j– 4,000 1,750 1,750 5 5 5 5 12,000 3,000 2,300 3 3 4 4 0.064 0.110 0.036 0.070 0.022 0.043 0.168 Max Max Max Max Max Max Max C32 C33 C34 C41 C42 C43 C44 OI 120 3 3 4 4 4 5 OII 110 4 4 5 5 4 4 OIII 155 4 3 4 4 4 5 OIV 185 5 3 3 2 5 5 OV 130 4 5 5 5 3 3 f j* 185 5 5 5 5 5 5 f j– 110 3 3 3 2 3 3 Note: O: office; min: cost (minimisation) criterion; max: benefit (maximisation) criterion. Table 7 S, R and Q values S R Q OI 0.466 0.110 0.381 OII 0.430 0.084 0.135 OIII 0.540 0.104 0.598 OIV 0.493 0.185 0.844 OV 0.389 0.168 0.413 In this table, while sub-criteria (C11, C12 and C13) represent relative costs those should be minimum; C32 indicates the m2 of alternatives. The other criteria’s scores have been determined by decision makers from 1 to 5 scale. Apart from criteria C11, C12, C13 whole criteria should be maximum rationally. While by equation (13), fj* indicates the maximum value among the alternatives for the rest of the criteria, because C1 is a cost criterion, here it means the minimum value; and the vice versa for fj–. After the decision matrix is obtained, S and R values are calculated by using equations (14) and (15). These values 49 Office location selection by fuzzy AHP and VIKOR indicate the average and worst group scores for each alternative and the Q values calculated by using equation (16) (v = 0.5) and result is given in Table 7. As written in step 2 and step 3 of VIKOR, S values state the utility and R values state the regret measure. Table 8 S*, S–, R* and R– values S* 0.389 S – 0.540 R* 0.084 R– 0.185 In Table 8, S* and R* represent the minimum S and R values of the offices respectively. Qi values in Table 7 are calculated via the values in both Table 7 (S and R values) and Table 8 by using equation (16). Following the calculation of S, R and Q, the alternatives are sorted by these values and the ranking results are shown below. Table 9 is built by Tables 7 and 8. According to Q values, the one having the minimum value is selected as the best alternative and the Office II is found as the best office place according to this order. Table 9 Ranking results S R Q Office-I 3 3 2 Office-II 2 1 1 Office-III 5 2 4 Office-IV 4 5 5 Office-V 1 4 3 The conditions have to be checked after the sorting step. In the case of five alternatives, DQ value (0.25) is not valid with the acceptable advantage condition since it is less than or equal to 0.246, which is the difference of office II and office I alternatives’ Q values those are in the first two places’. Office II provides the acceptable stability condition because it is the best alternative to the R value. If there is no acceptable advantage condition, differences between alternatives are examined in order. If difference is smaller than DQ value, alternatives is accepted as a compromise solution. When calculations are made according to the Q values in Table 7, it is possible to say that two alternatives which are office II and office I will take place in the compromise solution. 4 Conclusions and discussion In this research, location for an office to be used by a wedding organisation firm which has a considerable place in service sector that is growing day by day in such a country, where the ratio of young population is relatively high, is aimed to be chosen. For this purpose; first, main criteria and sub-criteria relatively those determine the office location have been gathered through the literature and experts’ views. Then for these four main 50 T. Arar et al. and 14 sub-criteria, five most popular locations in Ankara which is the capital city of Turkey have been chosen. To order criteria hierarchically, pairwise comparison of decision makers and real estate experts are analysed by fuzzy AHP. The results for main criteria showed that as approximate values, while physical condition (0.30), regional features (0.30) and cost (0.29) have similar importance on determining a location, accessibility has a relatively less importance with 0.11 weights. The reason that the priorities of office owners in service sector weight on costs, centralisation to the market and the physical situation of the building the office in is all about monetary. Especially in these days, the country is suffering from the cash shortage in market by several reasons such as US dollar’s unstoppable rising, political and geopolitical factors. Those all three factors have a direct impact on costs and profits in both short and long term. Business owners presume that, after reaching the maturity in the customers’ views, it should not be such important to be accessible. Their loyal customers would trigger the buzz marketing and these customers shall desire to reach high quality service wherever it is provided. After finding the weights of main criteria, sub-criteria’s weights have been calculated. Results show that monthly costs are the most important factor by 0.185. In such a dynamic environment both politically and economically, expenditures may show differences from time to time. For SMEs, any investment or expenditure plays significant roles which have considerable effects on workflows. Depending on session of year, variable monthly costs from employee wages to other office related expenditures have effects on work related decisions. All those costs may also show differences by location. For example, while rents are stable in one place, it may change rapidly due to attractiveness of another place. Prestige follows it with 0.168. Today, the prestige is very important in the perceptions of customers in services sector. Even a company that providing relatively low quality services could boost the customers’ attention in a prestigious location. Thus by placing in such a location, wedding organisations would reach more customers. Third important factor is structural features by 0.11. As mentioned before, after starting up the business, owner should adore making other investments. But one of the determining factors for these investments would be the structural features of the building as whether it is worth for it or not. Until here, we tried to summarise the criteria weighting part of the study in which fuzzy AHP is used. Then for choosing the best option in terms of an office for a wedding organisation, VIKOR method is used. As a result, despite the fact that Office II is chosen to be the best option; by the compromised solution of VIKOR, Office I and II would be two alternatives a decision maker may make a choice. In addition to this result, other MCDM methods, such as frequently used TOPSIS, relatively new MOORA and well-known and easy SAW could be used for evaluating alternatives. The alternatives are evaluated using these three methods as well and the results are shown in Table 10. Table 10 Ranking results with other MCDM methods TOPSIS SAW MOORA Office-I 5 4 5 Office-II 1 2 2 Office-III 3 5 4 Office-IV 4 3 3 Office-V 2 1 1 51 Office location selection by fuzzy AHP and VIKOR As seen in Table 10, different MCDM methods may give different results. While office V is at the first place for SAW and MOORA, it is at the second place in TOPSIS and the third place in VIKOR. The differences are caused by the nature of different algorithms of the techniques. For this reason Spearman’s rank correlation coefficients are examined. Table 11 Spearman’s rank correlation results VIKOR TOPSIS SAW MOORA VIKOR 1 0.4 0.3 0.1 TOPSIS 0.4 1 0.6 0.8 SAW 0.3 0.6 1 0.9* MOORA 0.1 0.8 0.9* 1 Note: *Correlation is significant at the 0.05 level (two tailed). Based on Table 11, it is clearly seen that there is a high correlation between the methods of SAW and MOORA since these both methods use ideal values. On the other hand, in TOPSIS calculations both ideal and anti-ideal values are considered. Furthermore, VIKOR is not correlated with any other MCDM methods as seen in Table 11. Due to anti-ideal values are not the goal as other MCDM methods such as TOPSIS suggests; VIKOR would give more effective results to decision makers considering only ideal value as SAW and MOORA but this time by providing compromised solution and advantage rate as it is presenting the decision maker elasticity (Brifcani et al., 2012). There are also some other distinctive reasons those make VIKOR method inevitable and superior to be chosen for this problem as follows (Opricovic and Tzeng, 2007): • In case the occurrence of any conflict, this method provides decision makers a compromised solution while the decision makers are willing to confirm a solution which is the closest to the ideal. • It is convenient to use this method not only when each criterion function and decision maker’s utility are related linearly, but also when the criteria are conflicting and non-commensurable. • Despite the fact that this method could be initiated in the case there is no participation of decision makers, they are responsible for approving the ultimate solution by whom preferences must be considered. • The method provides compromised solution based on the comparative advantage rate of alternatives. • The compromised/ideal solution is supported by stability analysis. Because of all those reasons above, VIKOR method is preferred. 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