Studying the application of a multiple-criteria decision-making method in construction management based on visual basic programming language

This study presents a supporting tool for the decision-making process based on the Analytic Hierarchy Process (AHP) in construction management. This tool is built in Visual Basic for Applications (VBA) language and run in Microsoft Excel spreadsheet software.

ISSN 1859-1531 - THE UNIVERSITY OF DANANG, JOURNAL OF SCIENCE AND TECHNOLOGY, NO 6(115).2017 55 STUDYING THE APPLICATION OF A MULTIPLE-CRITERIA DECISIONMAKING METHOD IN CONSTRUCTION MANAGEMENT BASED ON VISUAL BASIC PROGRAMMING LANGUAGE Pham Anh Duc, Truong Ngoc Son, Vo Van Thuan, Ho Thi Ngoc Nhung, Doan Thi Thu Oanh University of Science and Technology - The University of Danang; paduc@dut.udn.vn; tnson@dut.udn.vn; vanthuan0609@gmail.com Abstract - Making decision under multiple criteria is a fertile research area with lots of scope for real-life applications However, the decision-making process is limited on subjective assessments and it has not been balanced between costs and benefits This study presents a supporting tool for the decision-making process based on the Analytic Hierarchy Process (AHP) in construction management This tool is built in Visual Basic for Applications (VBA) language and run in Microsoft Excel spreadsheet software It will provide a convenient, reliable and faster way for the user to make a decision and get the final result of the decision by showing the best alternative based on the most important criteria This tool is time-saving and reduces errors in decision-making process in many fields, especially in construction management Key words - decision-making; multiple-criteria; AHP; construction management; VBA Introduction Decision-making is an important part of most human activities, whether we are performing daily activities, professional or political work Some decisions may be relatively simple, especially if the consequences of a bad decision are small, while others can be very complex and have significant effects Real-life decision problems will, in general, involve several conflicting points of view (criteria) that should be taken into account conjointly, in order to achieve a reasonable solution [1] In the construction management field, making decisions based on multiple criteria is an integral part including selections of contractors, suppliers, consultants, and so forth The decision-making process may cause conflicts among criteria For example, making decision based only on the lowest cost or the largest profit may lead to an unrealistic decision due to lack of quantitative factors [2] Therefore, a decision making process needs comprehensive consideration for multiple criteria to improve the accuracy and figure out optimal choices To tackle this issue, in recent years, various researchers have applied the theories ofmultiple-criteriaapproach to assess the comprehensive impacts of the factors on the decision-making process The Analytic Hierarchy Process (AHP) is one of the methods supporting the decision-making process that is utilized in various fields such as science, economics, healthcare, education, and especially in the construction industry The accuracy in making decisions is increasingly required and technologies have been developing towards the trend of automation Therefore, the researchers have decided to develop a tool supporting multiple-criteria decision-making activities This tool adopted the Visual Basic for Applications (VBA) programming language which was integrated in Excel spreadsheet software VBA is a programming language which is developed for office applications and VBA has been supporting Excel software with high customization capability beyond ordinary spreadsheet limits as well as the capability of solving complex problems and higher automation This tool can help users make decisions quickly and relevantly based on logical calculations Besides, this study provides readers with comprehensive understanding of the AHP method and its applications in the aspects of life Theoretical background Analytical Hierarchical Process (AHP) is one of the multi -criteria decision making tools that have been used widely in assisting people and organization in their decision making process The AHP was developed by Saaty (1980) to deal with multiple-criteria problems [3] It is designed to solve complex multi-criteria decision problems AHP requires the decision maker to provide judgements about the relative importance of each criterion and then to specify a preference for each decision alternative using each criterion AHP allows better, easier and more efficient identification of selection criteria, their weighting and analysis AHP allows a logical mixture of data, which could be quantitative, qualitative, experience, insight, and intuition in its algorithmic framework It enables decision makers to find the weight of each criterion [4] Subsequently, Saaty and Vargas (1994) introduced the applications of AHP to solve economic, political, and social problems as well as those related to technical designs [5] AHP’s applications for selecting suppliers: Al-Harbi (2001) introduced the application of AHP as a potential method for selecting the optimal contractor in project management [6] He constructed a hierarchical structure for the prequalified criteria and the contractors wishing to take part in the prequalifying stage Besides, Tam and Tummala (2001) applied the AHP for selecting telecom system providers [7], which was a complex and multiple-criteria process AHP’s applications for selecting construction site: Korpela and Tuominen (1996) presented an integrated approach in selecting warehouse’s location, in which both quantitative and qualitative factors are considered [8] Besides, Badri (1999) utilized the AHP for site selection [9] He confirmed that the AHP could help the staff in making plan for building strategies AHP’s applicationsin forecasting: Korpela and Tuominen (1997) used the AHP to forecast the inventory demand [10] Some of the AHP’s applications in different fields are shown in Table 56 Pham Anh Duc, Truong Ngoc Son, Vo Van Thuan, Ho Thi Ngoc Nhung, Doan Thi Thu Oanh Recently, the AHP method has been studied in Viet Nam Dang The Ba and Pham Thi Minh Hanh (2013) applied decision support system in water resource management for the Dakmi dam [11] Table Applications of AHP in making decisions Description Dweiri, F., et al.,, (2016) [1] Supplier selection in automobile industry G Bỹyỹkửzkan, and G ầifỗi, (2012) [12] A combined fuzzy AHP and fuzzy TOPSIS based strategic analysis of electronic service quality in healthcare industry J.-F Chen, H.-N Hsieh, and Q H Do (2015) [13] Evaluating teaching performance based on fuzzy AHP Educa tion Assess and select supplier Author Health Field The works mentioned previously show that AHP is a very useful and beneficial method as an aiding tool in decision making process However, there are very few tools where AHP process is supported automatically This study builds a tool based on multiple-criteria decision-making method with fast calculating process and easily applied in order to tackle issues in management, learning, and research, compared to previous studies This study also uses the proposed tool for selecting appropriate type of bridge in construction management Thereby, the high applicability of the proposed tool in the construction industry is obvious The proposed method 3.1 Multiple-criteria decision analysis Multiple-criteria decision making (MCDM) is a sub-field of operations research or management science and has attracted an increasing attention of researchers for decades A considerable amount of literature has been published on various MCDM methods and their applications [14] The general objective of MCDM is to assist the decision-maker (DM) in selecting the 'best' alternative from the number of feasible choice-alternatives under the presence of multiple choice criteria and diverse criterion priorities MCDM method manages the complexity of criteria by converting from the qualitative assessment into scoring In recent years, researchers have improved and developed the MCDM method into various methods which was divided into families [15]: the Multi-attribute utility theory– MAUT,the Multi-criteria decision analysis methods– ELECTRE, the Preference Ranking Organization Method for Enrichment of Evaluations - PROMETHEE, and the AHP The advance of the AHP method is not only capable of controlling the consistency of the judgments from experts but also the evaluation process of this method is conducted independently from any arising issues and experts, ensuring the objectivity of assessment The AHP method has proven its efficiency through the successful application in many fields 3.2 AHP method AHP is a method of multi-criteria decision developed by Saaty (1980) [3] The AHP is based on three principles: a Analyzing data: First, AHP analyzes a multiplecriteria problem based ona hierarchical structure The hierarchical structure diagrams start with the target analyzed through the major criteria and the componential criteria, and the final rank usually includes relevant options b Comparing elements in the corresponding level: Based on their own knowledge and experience, the interviewees will express their opinions on each pair of elements by answering questions To assess the level of importance or superiority of this element compared to the other elements, the scale (Table 2) is made with the values from to (pair-wise comparisons) Table Pair-wise comparison scale for AHP preferences [3] No Numerical rating Verbal judgments of preferences Equally preferred Moderately preferred Strongly preferred Very strongly preferred Extremely preferred The average values 2,4,6,8 The final result is a set of pair-wise comparison matrices (size n x n) for each of the lower levels with one matrix for each element in the level immediately above (Table 3) If the element A is more important than element B and rated at 9, B will be rated as less important than A with a value of 1/9 Table The judgment matrix A1 A2 A3 … An A1 A2 A3 … An 1/a12 1/a13 … 1/a1n a12 1/a23 … 1/a2n a13 a23 … 1/a3n … … … … a1n a2n a3n … c Synthesis of priorities: The method aggregate the pairwise comparison data to have common values of priority Saaty used the method of least squares to obtain weights from the pair-wise comparison Summation method is used to solve the maximum eigenvalue of the matrix: - Calculating the total of each column in the matrix ∑aij (Table 4) - Synthesizing the pair-wise comparison matrix is performed by dividing each element of the matrix by its column total Wij= aij/∑aij, The priority vector can be obtained by finding the row averages (Table 5) Table Comparison matrix of factors A1 A2 A3 … An ∑ A1 A2 A3 … An 1/a12 1/a13 … 1/a1n ∑ai1 a12 1/a23 … 1/a2n ∑ai2 a13 a23 … 1/a3n ∑ai3 … … … … … a1n a2n a3n … ∑ain ISSN 1859-1531 - THE UNIVERSITY OF DANANG, JOURNAL OF SCIENCE AND TECHNOLOGY, NO 6(115).2017 57 Table Matrix of consistent index(w) A1 A2 A3 … An ∑ A1 A2 A3 … An w W11 W21 W31 … Wn1 W12 W22 W32 … Wn2 W13 W23 W33 … Wn3 … … … W44 … W1n W2n W3n … Wnn w1 w2 w3 … wn - Checking the consistency: Saaty (1990) used a consistency ratio CR [16] to check the consistency of the priority elements, if consistency ratio CR  0.1 then the assessment is fairly consistent, on the contrary, the assessment is inaccurate Consistency index (CI) is determined as follows: Weighted sum matrix = Pairwise comparison matrix x Priority vector (1)  X1   X 2        Xn   a1  a2        an  x  w1   w 2        wn  = Consistency vector = Weighted sum matrix/ Priority vector (2) Y  Y        Yn   X1   X 2        Xn  Figure AHP application module  w1   w2         wn  = / The method then computes the average of these values to obtain ƛmax (3) Consistency index CI = (ƛmax - n)/(n - 1) (4) Consistency ratio: CR = CI/RI (5) RI (Average random consistency) is a function of the level of the matrix (N), shown in Table Table Average random consistency RI [3] n 10 RI 0.0 0.0 0.9 1.1 1.2 1.3 1.4 1.4 1.5 3.3 Decision-making tool This study uses the VBA programming language integrated in Excel to build the supporting tool based on the AHP method The tool is an application that can run directly on Microsoft Windows versions with simple module and usage Users run spreadsheet file AHP.xlsx to start the tool with the main module presented in Figure Users enter alternatives and the related criteria on "Import Module" in Figure After entering the data, the tool will calculate automatically and offer the optimal selection in form of diagrams (Figure 3) Figure Importmodule 3.4 Case study: Type of bridge selection In this case study, the topic of a bridge construction project in Quang Nam province is selected The site location already consists of two existing bridges over the river, but due to increased vehicle population and traffic load resulting in frequent traffic congestions the need for another bridge was necessary Proposed bridge should solve the problem of traffic congestion in the area along with the elegant aesthetical appearance First step of the proposed methodology is to identify important criteria affecting the choice of superstructure and develop best possible alternatives for the project For the identification of criteria Delphi technique is used Eleven top rated criteria were selected which included Cost (C.), Traffic data (T.D), Hydraulic data (H.D), Environmental impact (E.I), Site selection (S.S) For the development of alternatives for type of bridge, extensive study of decision problem is required Local authority had done the study through various consultancies and considered three alternatives regarding type of bridge For the study the same alternatives are taken under consideration The six alternatives are considered namely Segmental bridge (S.B.), Cantilever bridge(C.B.), Cable Stayed Bridge (C.S.), Extradosed bridge (E.B.), Box girder bridge (B.G.), and Arch Bridge (A.B.) for the study The criteria for evaluating type of bridge are structured in hierarchy as shown in Figure Based on their own knowledge and experiences, the experts evaluated the types Table and Table show the opinions of the assessments for six types of brigdes for Cost Each element in the Weighted sum matrix in Table is calculated in three steps: Calculate the sum of each column in the pair wise comparison matrix (Table 7),the priority 58 Pham Anh Duc, Truong Ngoc Son, Vo Van Thuan, Ho Thi Ngoc Nhung, Doan Thi Thu Oanh can be obtained by calculating the ratio of the components and standardizing values for priority vector Level 1: Goal Type of bridge selection Level 2: Criteria Level 3: Types of bridge S.B C.B C.S Cost Traffic data Hydraulic data Enviromenmental impact Site selection S.B S.B S.B S.B S.B C.B C.B C.B C.B C.B C.S C.S C.S C.S C.S E.B E.B E.B E.B E.B B.G B.G B.G B.G B.G A.B A.B A.B A.B A.B = Segmental bridge = Cantilever bridge = Cable Stayed Bridge E.B B.G C.P = Extradosed bridge = Box girder bridge = Arch Bridge Figure The structure type of bridge criteria We calculate the consistency ratio, CR, as follows: - Weighted sum matrix = Pairwise comparison matrix x Priority vector 1/  3     1/    1 /    1    0.145   + 0.096 + 0.146   + 0.349 1/  + 1                3     1/  2             1/  1  1 /  1/  1/     0.916  1/  1   0.587        0.168   + 0.098   =  0.924             2.303    1  1.153          1   0.623  - Consistency vector = Weighted sum matrix/ Priority vector 0.916 = 6.317; 0.587 = 6.115; 0.924 = 6.329; 0.145 0.096 0.146 2.303 = 6.599; 1.153 =6.863; 0.623 =6.357 0.349 0.168 0.098 We compute the average of these values to obtain ƛmax Figure OutputModule Table Pair-wise comparison matrix for Cost Cost S.B C.B C.S E.B B.G A.B S.B C.B C.S E.B B.G A.B 1/3 1/2 1 1 1 1/2 1/4 1/3 1/2 1/3 1/3 1/3 1/2 1 ƛ max = Priority vector 2 1 0.145 0.096 0.146 0.349 0.168 0.098 Cost S.B C.B C.S E.B B.G A.B S.B C.B C.S E.B B.G A.B 0.102 0.034 0.102 0.407 0.305 0.051 0.273 0.091 0.091 0.273 0.182 0.091 0.154 0.154 0.154 0.308 0.154 0.077 0.091 0.121 0.182 0.364 0.121 0.121 0.049 0.073 0.146 0.439 0.146 0.146 0.200 0.100 0.200 0.300 0.100 0.100 Priorityvalue of A for experienceis as follows: ∑a11 = + 1/3 + + + + 1/2 = 9.83 W11 = = 0,102 9.83 w1 = 0.102  0.273  0.154  0.091  0.049  0.2 = 0.45 Calculating similarly for the remaining elements, we obtain weighted sum vector for Experience = 6.437 - Consistency index: CI = max  n = 6.437  = 0.0874 n 1 1 RI=1.24 with n=6 - Consistency ratio: CR = Table Weighted sum matrix for Cost 6.317  6.155  6.329  6.599  6.863  6.357 CI = 0, 00874 = 0,07< 0,1 (satisfied) RI 1, 24 λmax=6.437; CI=0.0874; CR=0.07 < 0,1 The remaining criteria are estimated for weight sum vector by the same as Cost: Traffic data (T.D), Hydraulic data (H.D), Environmental impact (E.I), Site selection (S.S) (Table – Table 16) Table 17 and Table 18 show evaluation and priority between criteria Table Pair-wise comparison matrix for Traffic data Traffic data S.B C.B C.S E.B B.G A.B S.B C.B C.S E.B B.G A.B 1/2 1/3 1/2 1/2 1/5 2 1/3 1/2 1/3 1/5 1/2 1/3 1/2 1/5 5 Priority vector 0.087 0.241 0.084 0.175 0.348 0.067 ISSN 1859-1531 - THE UNIVERSITY OF DANANG, JOURNAL OF SCIENCE AND TECHNOLOGY, NO 6(115).2017 Table 10 Weighted sum matrix for Traffic data Table 15 Pair-wise comparison matrix for Site selection Traffic data S.B C.B C.S E.B B.G A.B Site selection S.B C.B C.S E.B B.G A.B 0.074 0.222 0.037 0.222 0.370 0.074 0.074 0.221 0.110 0.110 0.441 0.044 0.182 0.182 0.091 0.182 0.273 0.091 0.054 0.324 0.081 0.162 0.324 0.054 0.073 0.183 0.122 0.183 0.366 0.073 0.063 0.313 0.063 0.188 0.313 0.063 S.B C.B C.S E.B B.G A.B λmax=6.23; CI=0.05; CR=0.04 < 0,1 Hydraulic S.B C.B C.S E.B B.G A.B data 3 1/4 1/3 1/3 1/6 1/3 1/4 1/7 1/3 1/9 1/3 1/5 1/3 1/5 1/7 Priority vector 0.083 0.149 0.410 0.063 0.266 0.028 1/3 1/6 1/2 1/6 1/5 1/4 1/4 1/3 6 1/3 1/6 1/6 1/5 1/2 1/4 1/2 0.372 0.156 0.039 0.294 0.053 0.088 Site selection S.B C.B C.S E.B B.G A.B S.B C.B C.S E.B B.G A.B 0.423 0.141 0.070 0.211 0.070 0.085 0.383 0.128 0.032 0.383 0.032 0.043 0.261 0.174 0.043 0.261 0.087 0.174 0.517 0.086 0.043 0.259 0.043 0.052 0.308 0.205 0.026 0.308 0.051 0.103 0.339 0.203 0.017 0.339 0.034 0.068 λmax=6.31; CI=0.06; CR=0.05 < 0,1 Table 17 Pair-wise comparison matrix for criteria Table 12 Weighted sum matrix for Hydraulic data Hydraulic data S.B C.B C.S E.B B.G A.B S.B C.B C.S E.B B.G A.B 0.075 0.226 0.226 0.075 0.377 0.019 0.038 0.113 0.453 0.038 0.340 0.019 0.154 0.115 0.461 0.066 0.154 0.051 0.058 0.173 0.404 0.058 0.288 0.019 0.041 0.068 0.615 0.041 0.205 0.029 0.133 0.200 0.300 0.100 0.233 0.033 C T.D H.D E.I S.S Table 13 Pair-wise comparison matrix for Environmental impact E.impact S.B C.B C.S E.B B.G A.B Priority vector S.B C.B C.S E.B B.G A.B 1/5 1/3 1/7 1/6 1/6 1/5 1/3 1/3 1/3 1/6 1/3 1/4 6 3 1/3 1/4 1/2 0.444 0.143 0.228 0.034 0.066 0.086 Table 14 Weighted sum matrix for Environmental impact E.impact S.B C.B C.S E.B B.G A.B S.B C.B C.S E.B B.G A.B 0.498 0.100 0.166 0.071 0.083 0.083 0.507 0.101 0.304 0.020 0.034 0.034 0.590 0.066 0.197 0.033 0.066 0.049 0.269 0.192 0.231 0.038 0.115 0.154 0.391 0.196 0.196 0.022 0.065 0.130 0.407 0.203 0.271 0.017 0.034 0.068 C T.D 1/5 1/7 1/2 1/3 1 3 H.D E.I S.S Priority vector 1 5 1/3 1/5 1 1/3 1/5 1 0.439 0.071 0.055 0.225 0.210 Table 18 Weighted sum matrix for criteria λmax=6.38; CI=0.08; CR=0.06 < 0,1 λmax=6.43; CI=0.09; CR=0.07 < 0,1 Priority vector S.B C.B C.S E.B B.G A.B Table 16 Weighted sum matrix for Site selection Table 11 Pair-wise comparison matrix for Hydraulic data S.B C.B C.S E.B B.G A.B 59 C T.D H.D E.I S.S C T.D H.D E.I S.S 0.460 0.092 0.066 0.230 0.153 0.385 0.077 0.077 0.231 0.231 0.368 0.053 0.053 0.263 0.263 0.441 0.074 0.044 0.221 0.221 0.542 0.060 0.036 0.181 0.181 As the value of CR is less than 0.1, the judgments are Acceptable According to values calculated above, we can obtain the overall priority of contractors (Table 13) - Overall priority of contractor S.B = 0.439(0.145) + 0.071(0.087) + 0.055(0.083) + 0,225(0.444) + 0,21(0.372) = 0,252 - Overall priority of contractor C.B = 0.439(0.096) + 0.071(0.241) + 0.055(0.149) + 0.225(0.143) + 0.21(0.156) = 0.132 - Overall priority of contractor C.S = 0.439(0.146) + 0.071(0.084) + 0.055(0.410) + 0.225(0.228) + 0.21(0.039) = 0.152 - Overall priority of contractor E.B = 0.439(0.349) + 0.071(0.175) + 0.055(0.063) + 0.225(0.034) + 0.21(0.294) = 0.238 60 Pham Anh Duc, Truong Ngoc Son, Vo Van Thuan, Ho Thi Ngoc Nhung, Doan Thi Thu Oanh - Overall priority of contractor B.G = 0.439(0.168) + 0.071(0.348) + 0.055(0.266) + 0.225(0.066) + 0.21(0.053) = 0.139 - Overall priority of contractor A.B = 0.439(0.098) + 0.071(0.067) + 0.055(0.028) + 0.225(0.086) + 0.21(0.088) = 0.087 Table 19 Priority matrix for prequalified types of bridges Cost Overall Traffic Hydraulic Site E.impact data data selection Priority vector 0.439 0.071 0.055 0.225 0.210 S.B 0.145 0.087 0.083 0.444 0.372 0.252 C.B 0.096 0.241 0.149 0.143 0.156 0.132 C.S 0.146 0.084 0.410 0.228 0.039 0.152 E.B 0.349 0.175 0.063 0.034 0.294 0.238 B.G 0.168 0.348 0.266 0.066 0.053 0.139 A.B 0.098 0.067 0.028 0.086 0.088 0.087 As the results of the evaluation by experts and with the aid of decision-making tool, the analysis results are shown in Table 19 According to the results of the ranking in Table 20, the types of bridge are now ranked based on their overall priorities Table 20 Ranking table Types of Bridge Segmental bridge (S.B.) Cantilever bridge(C.B.) Cable Stayed Bridge (C.S.) Extradosed bridge (E.B.) Box girder bridge (B.G.) Arch Bridge (A.B.) Ranking According to the results of the ranking table, the Segmental bridgeis selected Accurately choosing the most suitable bridge construction operation is vital for the success of a bridge project The result demonstrates the capability and effectiveness of the model that can assist project contractors to better evaluate bridge construction methods Notably, the use of the proposed model is not restricted to the types and numbers of bridge construction methods The model provides a structured and systematic approach for effectively identifying the preferred bridge construction technique It may be applied for different areas of construction management and solving a large scale decision-making problem Conclusions and recommendation Although the AHP method is not unfamiliar, its application has not been popular in Vietnam This study has figured out the method of decision-making support through the AHP and proposed a tool written in VBA programming language and run in Microsoft Excel spreadsheet software This study has applied the AHP method combined with decision support tool to solve a problem in construction management: selecting the type of bridge For construction projects with open tendering that includes many types of bridge and various criteria, the study has found out the type of bridge with the highest weighting that met the requirements from the projects and investors This helps managers make an effective and quick decision of selecting types of bridge This tool could be applied in a wide variety of fields such as Forecasting Finance, Education, Technology, Risk Analysis, Sports, Transportation, Resource Allocation, and many other fields The study supports users in approaching the AHP method and making decisions quickly with the sciencebased combination of qualitative and quantitative factors so that users can get best decisions The implementation of AHP model in the case study has been discussed in the paper, illustrating a successful process conducted by the tool Based on testing, the result figured out by the tool was the same as the result from manual calculation The only difference is that manual calculation is time-consuming, compared to the fast processing speed of the tool Moreover, every user even those who not have any idea about the AHP concept can use the tool because it processes the data automatically The manual method requires knowledge of formulas, concept as well as AHPbased approach, which not all users can handle In contrast, developing the tool enables users from any background to find accurate and effective solution in a short time Due to time constraints, this proposed tool has not been totally completed, it just ensures the basic functions of an automated decision support tool Therefore, in the future, the tool needs to be improved about criteria-assessing method and needs an increase of more than two ranks so that it can meet more complex demands of decisionmaking as well as surveys of opinions and feedback from experts more quickly and accurately The tool can be developed in this proposed way: combined with other methods such as the fuzzy sets, TOPSIS combined with VIKOR and AHP can improve the capability of supporting decision-making The researchers are planning to create a web-based model assisting users in updating online criteria in many different fields as well as getting opinions and feedback from professionals immediately This will help the support process become faster The web-based tool and calculating tools developed in the future will help users find out decisions in the most accurately, objectively and fastest way REFERENCES [1] F Dweiri, S Kumar, S A Khan et al., “Designing an integrated AHP based decision support system for supplier selection in automotive industry,” Expert Systems with Applications, vol 62, pp 273-283, 11/15/, 2016 [2] Trần Thị Mỹ Dung, “Tổng quan ứng dụng phương pháp phân tích thứ bậc quản lý chuỗi cung ứng,” Tạp chí Khoa học, vol 21a, pp 180-189, 2012 [3] Saaty TL, “The analytic hierarchy process,” New York: McGrawHill, 1980 [4] A.-A Fadwa Gamal Mohammed, and M A Ayu, "Web based multi criteria decision making using AHP method." pp A6-A12 [5] Saaty TL and Vargas LG, “Decision Making in Economic, Political, Social, and Technologycal Environments with the Analytic Hierarchy Process,” RWS Publication, Pittsburgh, PA, USA, 1994 [6] K.M Al Harbi, “Application of AHP in project management,” ISSN 1859-1531 - THE UNIVERSITY OF DANANG, JOURNAL OF SCIENCE AND TECHNOLOGY, NO 6(115).2017 [7] [8] [9] [10] [11] International Journal of Project Management vol 19, no 4, pp 1927, 2001 M.C.Y Tam and V.M.R Tummala, “An Application of the AHP in vendor selection of a telecommunications system,” Omega, vol 29, no 2, pp 171–182, 2001 J Korpela and M Tuominen, “A decision aid in warehouse site selection,” International Journal of Production Economics, vol 45, no 1–3, pp 169–180, 1996 M Badri, “Combining the AHP and GP for global facility location– allocation problem,” International Journal of Production Economics, vol 62, no 3, pp 237–248, 1999 J Korpela and M Tuominen, “Inventory forecasting with a multiple criteria decision tool,” International Journal of Production Economics, vol 45, no 1-3, pp 159–168, 1997 Đặng Thế Ba Phạm Thị Minh Hạnh, “Hệ thống hỗ trợ định quản lý tổng hợp tài nguyên nước: Thử nghiệm phân tích quản lý đập Đakmi 4,” Tạp chí khoa học ĐHQGHN, Các Khoa học Trái Đất Môi Trường, vol 29, no 2, pp 1-10, 2013 61 [12] G Bỹyỹkửzkan, and G ầifỗi, A combined fuzzy AHP and fuzzy TOPSIS based strategic analysis of electronic service quality in healthcare industry,” Expert Systems with Applications, vol 39, no 3, pp 2341-2354, 2/15/, 2012 [13] J.-F Chen, H.-N Hsieh, and Q H Do, “Evaluating teaching performance based on fuzzy AHP and comprehensive evaluation approach,” Applied Soft Computing, vol 28, pp 100-108, 3//, 2015 [14] J W M Köksalan, S Zionts, “Multiple criteria decision making From early history to the 21st century,” World Scientific Publishing Co Pte Ltd, Singapore 2011 [15] C Musingwini and R.C.A Minnitt, “Ranking the efficiency of selected platinum mining methods using the analytic hierarchy process (AHP),” Third International Platinum Conference ‘Platinum in Transformation, The Southern African Institute of Mining and Metallurgy, 2008 [16] Saaty TL, “How to make a decision: the analytic hierarchy process,” European Journal of Operational Research, North-Holland, vol 48, pp 9-26, 1990 (The Board of Editors received the paper on 21/03/2017, its review was completed on 26/06/2017) ... A. -A Fadwa Gamal Mohammed, and M A Ayu, "Web based multi criteria decision making using AHP method. " pp A6 -A1 2 [5] Saaty TL and Vargas LG, “Decision Making in Economic, Political, Social, and... platinum mining methods using the analytic hierarchy process (AHP),” Third International Platinum Conference ‘Platinum in Transformation, The Southern African Institute of Mining and Metallurgy,... Comparison matrix of factors A1 A2 A3 … An ∑ A1 A2 A3 … An 1 /a1 2 1 /a1 3 … 1 /a1 n ∑ai1 a1 2 1 /a2 3 … 1 /a2 n ∑ai2 a1 3 a2 3 … 1 /a3 n ∑ai3 … … … … … a1 n a2 n a3 n … ∑ain ISSN 1859-1531 - THE UNIVERSITY OF DANANG,