A hybrid approach based on the BWM-VIKOR and GRA for ranking facility location in construction site layout for Mehr project in Tehran

. Science, Canada 2018 by the authors; licensee Growing ©


Introduction
Heavy costs are spent on safety and suitable layout of facilities in some applications such as civil projects and non-civil projects performed by government and private or public sectors respectively; hence, the most important goal of such problems is to minimize system costs and maximizing safety level (Kumar & Cheng, 2015;Said & El-Rayes, 2013).Many studies examined this problem only by consideration of minimizing costs while managers tend to optimize more objectives like safety level maximization in the real world.On the other hand, changing a facility layout after implementation of a project is difficult or infeasible; accordingly, it is essential to consider all of the criteria affecting the final decision-making (Yahya & Saka, 2014).Another important point for the implementation of all industrial and construction projects is the safety level and factors affecting it.This is a vital issue because endangered safety of workers, managers and equipment may lead to costly postponements and heavy private or public fines when workers' safety is at risk (Kaveh et al., 2018).Therefore, a suitable model should be proposed for proper facilities layout in construction projects efficiently by considering all of the effective factors.
In this research, a hybrid method based on the BWM, VIKOR and GRA is presented to prioritize the potential locations for construction site layout.This subject has been less considered by the researchers.Jozi et al. (2015) employed the hybrid analytical hierarchy (AHP) process (Saaty, 2003) with data envelopment analysis (DEA) (Banker et al., 1984) in order to rank layout design patterns.They applied AHP method to determine functional values of qualitative criteria in order to use them in the DEA model.Durmusoglu (2018) used a similar approach to prioritize layout design patterns with the different method in which, two fuzzy variables of information flow and environmental condition were used to determine the relationships between activities and closeness ratings based on the fuzzy decision system.Ardeshir et al. (2014) used the searching GA approach and the ELECTRE multi-criteria decision-making method (Jain & Ajmera, 2019) in order to rank the patterns.In this research, Paretooptimal solution was determined using boundary multi-objective genetic algorithms then the optimal solution was selected using the ELECTRE method.Nguyen et al. (2016) employed the TOPSIS approach (Biswas & Saha, 2019) in order to prioritize site layout designs then compared the obtained results to the results of TOPSIS.The proposed approach dramatically depends on the subjective judgments of the designers.Marzouk and Al Daour (2018) presented a decision-making system, which consists of input, design, evaluation, selection and output steps in order to solve the construction site layout planning multiobjective dynamic problem.Various objectives, scheduling plan and sites conditions were determined at the input step.At the design step, two mathematical optimization models of Max-Min ant system (MMAS) and the corrected algorithm based on the Pareto Ant Colony Optimization were presented to solve single-objective and multi-objective optimization problems, respectively.Ultimately, The Fuzzy TOPSIS (Aikhuele, 2019) method was used at evaluation and selection steps in order to evaluate and select the best layout design among other generated designs at the design step.Mytilinou et al. (2018) carried out a study in which, construction site criteria were ranked using quality management, cost, and safety approach in construction projects using TOPSIS method.This study was conducted to be beneficial for project managers' success.Analyzing sub-criteria based on the above-mentioned method, projection type, safety, project programming, work time and building dimensions were selected as prior cases, respectively.Abune'Meh (2017) carried out a study where the criteria affecting the evaluation of layout designs were identified at first step and a hybrid fuzzy multi-criteria decision-making method was presented to select the optimum layout design.In this method, Fuzzy Group AHP, Shannon entropy (Vatansever & Akgűl, 2018), and TOPSIS were utilized to determine the functional values of layout designs by consideration of qualitative criteria, to calculate criteria's weights and to rank final layout designs, respectively.Moreover, qualitative and quantitative criteria were taken into account simultaneously so that the function of layout designs was considered for qualitative criteria within a fuzzy method.In addition, the optimal design was selected proportionally without considering the relative importance between criteria based on the opinions of experts.Esfahani and Nik (2016) carried out a study in order to address the layout of some facilities like Tower Crane in construction site and effective factors of these facilities in construction site safety and proposed an appropriate solution to increase safety within design step.Ning et al. (2016) conducted a study where AHP approach was used to determine functional values of qualitative criteria.They employed a commercial software to create layout patterns and functional quantitative values and finally used a non-linear weighted optimization model for order of layout design patterns in presence of two groups of criteria considering the order of criteria based on the designers' ideas.This study implemented the obtained model in a real case study in order to show the model applicability then presented the results.Table 1 reports a classification of multi-criteria decision-making methods that have been used in previous studies.According to Table 1, most of the studies have utilized AHP method.In fact, AHP is one of the widely used decision-making methods in this area (Kumar et al, 2017).Some of decision-making methods like TOPSIS and VIKOR have been also employed with AHP in a hybrid method.However, the interesting point is that the new decision-making methods such as BWM and GRA have not been considered by the researchers in this field while BWM is a more powerful approach used to determine weight of criteria compared to the other decision-making methods (Rezaei, 2016).This method can find the weight of criteria precisely by using a linear optimization model.Except the questionnaires that have been filled out with the experts and there is not any user interference in determining weight of these criteria (Rezaei, 2015).Hence, the obtained weights have an acceptable reliability.Furthermore, GRA method is highly robust in final ranking of alternatives based on the criteria (Zhang et al., 2011).Therefore, the present study uses a hybrid approach based on BWM, GRA and VIKOR methods in order to expand the application of these methods in finding suitable locations for construction site layout.This paper has been organized as follows: section 2 explains the research problem and introduces the taken alternatives and criteria.Section 3 describes the applied multi-criteria decisionmaking methods.Section 4 presents the computational results.Finally, section 5 presents a summary of research results.

Definitions and Concepts of BWM, VIKOR and GRA Technics
This section introduces the definitions related to BWM and VIKOR and GRA technics as well as the Monte Carlo Simulation Method.The hybrid model of MCDM is suggested based on the basic concept.

The Best Wordt-Method
BWM is a robust method proposed to solve MCDM problems and is used to calculate the weights of alternatives and criteria (Rezaei, 2015(Rezaei, , 2016)).This method removes weaknesses such as incompatibility of pairwise comparison-based methods (e.g AHP and ANP).In recent years, BWM has been employed by many researchers to determine weights and rank alternatives in different fields.In general, structure of BWM method steps is as follows: Step 1: creation of decision criterion system: decision criterion system comprises a set of identified criteria by reviewing literature and experts' opinions as a set of {c1,c2,…,cn} .Values of decision criteria reflect function of different alternatives.
Step 2: determining the best and the worst criteria among the main criteria and sub-criteria; according to decision criterion system, the best and worst criteria should be identified by decision makers.The best criterion is indicated by CB and the worst criterion is shown by WB.
Step 3: Reference comparisons for the best criterion: This step determines the priority of the best criterion compared with other criteria using values between 1 and 9 based on the verbal comparison scale, which is presented in Table 5. Results are indicated in a vector: (1) where, is the priority related to the best-selected criterion of B compared to each criterion of j.So,

1.
Step 4: Reference comparisons for the worst criterion: priority of all of the criteria related to worst selected criterion is calculated using values 1-9 in the same way.Results of this vector shown as follows: (2) where, indicates the priority of each criterion j relative to the worst selected criterion of W. obviously, 1 Step 5: Determine the optimal weights * , * , … , * : to achieve the optimal weights of the criteria at this step, the highest absolute difference , should be minimized for all of js values.This is formulated as following optimization problem: (3) Model ( 4) is linear with exclusive solution.Hence, optimal weights * , * , … , * and optimal value of * are obtained with solving this model.Values near to zero ( * ) in this model indicate high compatibility level (Rezaei, 2016).

Grey Relational Analysis Technique
Grey Relational Analysis (GRA) was developed by Deng (1982).Grey system theory is an algorithm that analyzes the indefinite relations between members of a system.This algorithm can be used in multicriteria decision-making problems.This approach is able to identify both qualitative and quantitative relationships between sophisticated factors within a system.The approach can examine the relationship between two alternatives by measuring the distance between them.It is assumed that the multi-criteria decision-making problem consists of m alternatives A1, A2,….,Am and n criteria C1, C2,…,Cn so that each alternative is evaluated based on the n criteria and all of the measured values are assigned to the alternatives and shown based on the decision matrix .GRA steps are as follows: Step 1: Calculate the normal decision matrix and normalized value using Eq. ( 5) and Eq. ( 6).
) 5 ( where, i represents the sequence of benefit criteria and J is the sequence of costs.
, and is the fix coefficient 0,1 , which equals 0.5 in this research.
Step 4: The gray relational rate between and is calculated using Eq. ( 9) by calculating all of gray relational degrees.
Step 5: ranking the alternatives based on the gray relational value in a way that the greater value of , shows the optimality of alternative .

VIKOR Technique
VIKOR technique is a customized ordering method, which is mostly used in presence of different conflicting criteria (Opricovic, 1998).This is a compromise solution based on the closeness to the ideal solution and an agreement established by mutual concessions.This method has been widely used by researchers to rank the alternatives.VIKOR Method has the following steps (Gupta, 2018): Step 1: Calculate the pairwise matrix for each alternative so that each criterion is evaluated using the verbal scale, which is presented in Table 4.
where, is the value of alternative i relative to the criterion j given by the expert t.
Step 3: Calculate the best * and the worst of all criteria using Eq. ( 11) and Eq. ( 12).
where, * represents the positive ideal solution and represents the negative ideal solution for criterion j.
, where, represent the distance between the positive ideal solution and alternative i; represents the distance between the negative ideal solution and alternative i, indicates the weights of factors obtained from fuzzy BWM analysis.
where, , * and , * and parameter is introduced as a weight for the strategy of "the majority of criteria", which equals 0.5 in this research.
Step 6: Rank the alternatives using values.
Step 7: The alternatives are ranked based on the minimum if the following two conditions are satisfied: C1. "Acceptable Advantage": the alternative A 1 is chosen if 1/ 1 where, is the alternative with the second position and represents the total alternatives.C2. "Acceptable stability in decision making": The alternative must also be the best ranked by and or values.
Step 8: The alternative with the minimum value in should be ranked at the first position.

Computational Results
This section examines the results obtained from the case study, which in the Mehra Housing construction project in Tehran, Iran using the proposal method.Some information were randomly generated based on the problem structure due to inaccessibility to all data of the project.In this project, 40 potential locations have been selected to establish 20 facilities by the experts.Methodology steps to achieve the results have been presented in following sections.

Determining the weights of the criteria affecting the increasing safety level and ranking the potential locations for site layout
Data analysis is a multistep process in which, the data that have been collected by using the data collecting tools in the statistical sample (society) are summarized, coded, classified and processed in order to provide the field for analyses and relationships between the data to achieve the research goals.
In this process, the data are refined conceptually and empirically.

Validation of safety criteria
Lawshe's Validation was used in this section by distributing and collecting the questionnaire (1) in order to determine safety criteria affecting the site layout.In this case, 30 experts were interviewed to determine validity of the identified criteria, which the results are reported in Table 1.As there are 30 evaluators, the minimum CVR equals to 0.33 according to the table 1.Therefore, the finalized safety criteria affecting the site layout are indicated in Table 2:

Weights of safety criteria
This section presents the results of the most important (best) and unimportant (worst) criteria using the BWM questionnaire.To valuate criteria, the opinions of an expert committee in the area of HS were used.The best and worst criteria identified by each respondent were the most important and unimportant criteria affecting site layout, respectively based on the experts' opinions.The best and worst criteria, which are identified by experts, can be seen in Table 3.

Table 3
The best and worst identified criterion by the experts

The most unimportant criterion
The most important criterion Relevant criterion This part of study determines the preferences of the the best criterion among all of the criteria.This information is obtained from distributing and collecting the BWM questionnaire so that the respondents are asked to identify the preference of the best criterion relative to other criteria.Therefore, the bestother criteria vectors are indicated in Table 4.

Table 4
The best-other criteria vectors The best criterion Experts Preferences of other criteria relative to the worst criterion are determined in a same way.This information is obtained from distributing and collecting the BWM questionnaire so that the respondents are asked to identify the preference of the worst criterion relative to other criteria.Therefore, the worstother criteria vectors are indicated in Table 5.
Ultimately, the best-worst method is employed to determine the results of consistency coefficient of pairwise comparisons as well as the weights of the criteria affecting site layout.The weights of safety criteria are calculated by solving the linear WBM technique among eight experts and using GAMS24.3Software and BARON solver.These weights are the average weights for each criterion, which are demonstrated in a unit weigh vector in Table 6.6, comparisons are highly compatible due to their proximity to zero.It is concluded from the pairwise comparisons between the criteria that the obtained weights for criteria of light shortage, access to standard equipment and safety flexibility of equipment had the highest values respectively relative to the other criteria.Table 6 shows that the final value of CR is lower than 0.1 indicating the proper criteria selection to achieve the result.
In fact, it can be stated based on the opinions of experts that the introduced criteria had an appropriate consistency and could affect the final responses.

Evaluation of potential locations
At this step, 40 potential locations are evaluated for site layout.To facilitate this process, the locations are assessed by the verbal variables including very good, good, moderate, poor, very poor, which are scored from one to five.Very good variable for each criterion indicates the best evaluation value per all of the criteria.Locations evaluation values are reported in following tables.

Ranking the potential locations
At this section, verbal variables are converted to quantitative ones then functional weights of the locations are measured using VIKOR and GRA techniques.The functional weights of locations have been shown in following tables by consideration on safety criteria.

VIKOR ranking results
At this section, the 40 initial locations are ranked for site layout by distributing and collecting the questionnaire 3 as well as stepwise implementation of VIKOR method.This process is accomplished through following steps: Step 1: creating the decision matrix: decision matrix is created as indicated in table 7 based on the number of criteria, alternatives and evaluation of all alternatives for different criteria.

Table 7
Values for evaluation of initial locations for site layout Step 2: Normalization of the decision matrix: the alternative-criterion decision-making matrix should be normalized.For example, fij is calculated as follows: (16) and other f values are calculated then the obtained values up to three decimal places are shown as a matrix in Table 8.Step 3: determining the best and worst value.The best and worst values of each criterion are determined as indicated in Table 9.  Step 4: calculating the advantage, regret and VIKOR indicators besides determining the potential locations: The considered initial locations are sorted at this step by considering the VIKOR index, where the alternatives with lower Qi have lower preferences.As it is shown, the selected locations 7, 36 and 30 have ranked at the 1 to 3 positions, respectively.

Results of GRA ranking
At this section, the 40 initial locations are ranked for site layout by distributing and collecting the questionnaire 3 as well as stepwise implementation of VIKOR method.This process is done through following steps: Step 1: forming decision-making matrix: at this step, the opinions collected from the questionnaire and then the criterion-alternative matrix is formed based on the averaged opinions indicated in Table 12.

Table 12
The values of evaluating initial locations for site layout Step 2: forming the normal decision-making matrix: at this step, the matrix is normalized; accordingly, the normal alternative-criterion matrix is indicated in Table 13.
Step 3: calculating the gray relational degree matrix: at this step, gray relational degree is calculated for each alternative and the results are indicated in Table 14.Step 4: calculating the gray relational rank: the gray relational rank of each alternative is calculated at this step.The results are reported in Table 15.According to the gray relational analysis, an alternative with the highest gray relational degree is the preferred alternative; therefore, priority of bank branches is determined based on the gray relational degree.The results obtained from the gray relational degree computations imply that the selected locations 9, 29 and 7 are ranked at positions 1 to 3.

Sensitivity Analysis of GRA and VIKOR Techniques
To analyze sensitivity and reliability of the results obtained from the VIKOR method, the effect of various v values on the VIKOR results were examined.The obtained findings are illustrated in the Fig. 1.As it can be seen in this figure, changing alternatives' preferences have minor difference based on the values of the strategy of the majority of group utility (v).Nevertheless, the selected locations 7, 9, 30 and 36 are the highest ranks.
Therefore, VIKOR technique does not have an acceptable compatibility with changes in v parameter.To examine the effect of different determination coefficients on the results of gray relational analysis, the gray relational degree was calculated for each location by consideration of various determination coefficients.Different determination coefficients were taken in this analysis and the obtained results are shown in Fig. 2. As it is seen, the preferences related to the options have not changed when determination coefficient (ξ) varies and the results obtained from the GRA method are more stable relative to the VIKOR method.Ultimately, the potential locations for site layout were determined as indicated in Table 16.It should be noted that the alternatives, which their gray relational degrees were greater than 0.555 were selected as the potential locations based on the consensus of decision makers.As it is seen in Fig. 3, almost all of the selected site layout locations are located at the central parts of the site; this may be related to the scores of safety criteria provided by the BWM technique.In fact, the experts believe that safety level at the central part of the site is higher that the marginal space.Moreover, some facilities should be located close to the main street in order to achieve an appropriate transportation system and this can be seen in the obtained results of research.

Fig. 1 .
Fig.1demonstrates the initial site of the studied construction workshop.

Fig. 3
Fig.3represents the structure of selected potential locations.

Fig. 3 .
Fig. 3.The selected potential locations for facilities site layout

Table 1
Different types of decision-making methods for energy sites selection

Table 1
Results of validating the safety criteria affecting site layout

Table 2
Final criteria for site layout

Table 5
The worst-other criteria vectors

Table 6
Weights of safety criteria for site layout *Here ξ * represents consistency of comparisons.According to the Table

Table 8
Normalized matrix of evaluation values of initial locations for site layout

Table 9
The best and worst criteria

Table 10
Maximum and minimum distance between alternatives and the ideal solution

Table 11
Results of the advantage (Si), regret (Ri) and VIKOR (Qi) indicators and the proposal alternatives ranking

Table 14
Gray relational degree matrix

Table 15
Gray relational rank matrix

Table 16
The selected potential locations