Microsoft Word - ETASR_V12_N5_pp9087-9091 Engineering, Technology & Applied Science Research Vol. 12, No. 5, 2022, 9087-9091 9087 www.etasr.com Pham et al.: Application of the Grey System Theory in Construction Management Application of the Grey System Theory in Construction Management A Case Study of Construction Paint Supplier Evaluation and Selection Criteria Cuong Phu Pham Faculty of Transport and Economics, Campus in Ho Chi Minh City, University of Transport and Communications, Vietnam cuongpp_ph@utc.edu.vn Phong Thanh Nguyen Department of Project Management Ho Chi Minh City Open University Ho Chi Minh City, Vietnam phong.nt@ou.edu.vn Phuong Thanh Phan Department of Project Management Ho Chi Minh City Open University Ho Chi Minh City, Vietnam phuong.pthanh@ou.edu.vn Received: 18 June 2022 | Revised: 6 July 2022 | Accepted: 20 July 2022 Abstract-Material management is an important task in building construction. They account for a substantial proportion of investment capital and construction volume. However, as material prices are often affected by the market, choosing the right construction supplier is not an easy decision for contractors, especially for those materials required during the finishing phase of the construction. As one of these finishing materials is paint, identifying core criteria for evaluating and selecting the best construction paint supplier is a crucial economic choice for construction contractors. Assessing the importance of these criteria is a complex multi-criteria decision-making problem. To reflect the risks and uncertainties in this problem, the current paper presents a grey system theory approach to prioritize important criteria for selecting paint material suppliers in construction projects. Keywords-construction management; project management; evaluation and selection criteria; material management; paint supplier; grey theory I. INTRODUCTION Material management is an essential task in the construction management of any civil engineering project because construction materials account for a high proportion of the total construction cost [1, 2]. In this regard, evaluating and selecting an efficient supplier of construction materials is a very important economic decision and helps the contractor manage materials effectively [3]. One definition of an efficient supplier is a company that specializes in distributing high- quality products in the proper quantity, at the proper time, for a fair price [4]. In a construction project, one commonly required and evaluated material is construction paint. Determining the critical criteria in selecting the construction paint supplier is essential to choosing the material supplier. However, traditional assessment methods (e.g. scoring methods) are often based on the subjective opinions of construction experts, which often do not consider uncertainty in their expert judgments or opinions. This results in a final decision that is often irrational and sometimes inconsistent with reality. To improve this issue, this paper proposes a new quantitative model for prioritizing paint supplier evaluation and selection criteria based on the grey system theory. II. RESEARCH BACKGROUND Construction paint in civil engineering projects is available in liquid, paste, or powder form. The effect of construction paint is to create a solid film that adheres firmly to the building surface for building structure protection and esthetics. Choosing an efficient construction paint supplier is crucial for construction managers. In addition to helping the construction project attain the highest quality, it also helps reduce project cost and shorten the project implementation time. This study identifies the eight most important factors to consider when selecting the construction paint supplier in civil engineering projects based on a literature review of research papers and in- depth interviews with experts [5-21]. These criteria are: (F1) the reputation of the paint supplier, (F2) the quality management system certification of the paint supplier, (F3) the quality of construction paint materials, (F4) the number of paint categories and products, (F5) delivery time, (F6) terms and conditions of payment, (F7) price of the paint product, and (F8) the warranty period. III. RESEARCH METHODOLOGY One approach in studying uncertainty is the grey theory, introduced by Deng in [22-24]. It excels at analyzing mathematical systems with uncertain knowledge. When Corresponding author: Phong Thanh Nguyen Engineering, Technology & Applied Science Research Vol. 12, No. 5, 2022, 9087-9091 9088 www.etasr.com Pham et al.: Application of the Grey System Theory in Construction Management working with discrete data and insufficient knowledge, grey system theory can be utilized to handle uncertainty or indeterminate problems. A grey system is defined as a system that includes grey variables and a grey number to provide ambiguous information [25]. Figure 1 illustrates the grey system theory. Fig. 1. Grey system theory. The degree of information and connections between black and white systems are also explained by grey systems, in which grey numbers represent numbers with unknown precise values. Information that is partial, incomplete, or missing can take many different forms. This study uses grey numbers to reflect subjective judgments and reduce evaluation variance among construction experts. Table I [26] compares black, grey, and white systems. TABLE I. COMPARISON OF BLACK, GREY, AND WHITE SYSTEMS Parameter Black system Grey system White system Information Unknown Incomplete Completely known Appearance Dark Blurred Clear Processes New Changing Old Properties Chaotic Multivariate Order Methods Negation Change for better Confirmation Attitude Letting go Tolerant Rigorous Outcomes No solution Multi-solutions Unique solution TABLE II. LINGUISTIC SCALES WITH GREY NUMBERS Level of importance Linguistics scale Grey numbers 1 EI = Equivalent Importance [1, 2] 3 MI = Medium Importance [2, 4] 5 SI= Strong Importance [4, 6] 7 VSI = Very Strong Importance [6, 8] 9 EMI = Extreme Importance [8, 10] Let x denote a closed and bounded set of real numbers. A grey number, denoted as ⊗x, is a number with an unknown exact value but within a known range. These grey numbers represent uncertain and ambiguous data. In this study, we propose a combination of grey system theory and the Analytical Hierarchy Process (AHP) decision-making method to reduce subjective judgments in prioritizing weights of important criteria in evaluating and selecting paint suppliers for a construction project. In the grey AHP approach, grey numbers are used instead of crisp sets and crisp numbers. The grey AHP method uses pairwise comparisons with linguistic scales and gray scales. The main computational steps to use grey AHP in this study are [27-47]: Step 1. Define the research problem using traditional AHP. In this step, we identify the research problem, create the hierarchical structure, and construct the pairwise comparison matrix using construction experts’ evaluations with linguistic scales containing grey numbers in Table II. The grey comparison matrix using the geometrical mean formulation is constructed as follows: 11 12 1 21 22 2 1 2 n n m m mn x x x x x x D x x x ⊗ ⊗ ⊗    ⊗ ⊗ ⊗  =     ⊗ ⊗ ⊗  ⋯ ⋯ ⋮ ⋮ ⋮ ⋮ ⋯ (1) where ij x⊗ is the pairwise comparison concerning the i th criterion over the j th criterion. Step 2. Calculate the normalized grey comparison matrix. The normalization for the grey numbers is given in (2)-(4). * * ** * * 11 11 12 12 1 1 * * ** * * 21 21 22 22 2 2* * * ** * * 1 1 2 2 , , , , , , , , , n n n n m m m m mn mn x x x x x x x x x x x x D x x x x x x                            =                   ⋯ ⋯ ⋮ ⋮ ⋮ ⋮ ⋯ (2) * 1 11 1 2 1 2 ij ij ij m mm m ij ijij ij i ii i x x x x xx x = == = = =   ++       (3) * 1 11 1 2 1 2 ij ij ij m mm m ij ijij ij i ii i x x x x xx x = == = = =   ++       (4) Step 3. Calculate the grey weight of each criterion by determining the averages of the rows using (5): ** * 1 1 , n n ij ij ij j j i x x x w n n = =  ⊗   ⊗ = =   (5) where n = {1, 2, . . . , N} is the criterion set. Step 4. Calculate the whitenization of the grey weights. The whited value of an interval grey weight is a crisp number with a potential value between the interval grey weight’s upper and lower bounds, as follows: (1 ) i i i M w wλ λ= − + (6) where λ is the whitening coefficient and [0,1]λ ∈ . Step 5. Calculate the Consistency Ratio (CR): To determine whether the decision-comparison preparers were consistent, this step involves examining the CR of the pairwise comparison matrix. The calculation of the CR from construction experts is [48-52]: max 1 1 nCI CR RI n RI λ − = = × − (7) where CI is the consistency index, RI is the random index, and max λ is the largest eigenvalue. Engineering, Technology & Applied Science Research Vol. 12, No. 5, 2022, 9087-9091 9089 www.etasr.com Pham et al.: Application of the Grey System Theory in Construction Management IV. RESULTS AND DISCUSSION For calculation simplicity, Table III presents the integrated grey comparison matrix, developed based on the synthesis of construction expert opinions using the geometrical mean formulation for grey numbers given in Table II. Next, we calculated the normalized grey comparison matrix using (2)- (4), as shown in Table IV. After obtaining the normalized grey comparison matrix, we calculate the grey weight of each criterion for evaluating and selecting the construction paint supplier by determining the row averages using (5). The whitenization of the grey weights, obtained by applying (6), is shown in Table V. We choose the value of λ to be 0.5 [52, 53]. Finally, we applied (7). The CR of this pairwise comparison matrix is CR = 2.02% < 10%, so the evaluation result is reliable because the pairwise comparison matrix is consistent. The top 5 most important criteria for evaluating and selecting the paint supplier in construction projects were determined to be F7, F1, F3, F2, and F6. Currently, the price of fuel (F7), especially gasoline, is quite high due to scarcity resulting from the conflict between Russia and Ukraine. This causes the paint prices on the market to increase. Therefore, construction contractors are more interested in the price than other criteria. Related to the second most important criterion, the reputation and branding of a paint supplier (F1): some large suppliers spend much money promoting their brands and products on all kinds of media, gaining notoriety in the business world, industry associations, and business partners. In contrast, some suppliers do not choose aggressive advertising methods but rely on their positive reputation to help them promote their branding. Terms and conditions of payment (F6) are usually provided in the purchase contract. Contracts are documents that detail agreements between transaction objects created to achieve the needs of all parties. There are many forms of payment, including one-time payments or partial payments. The ability of the supplier to permit customers to owe money with attractive conditions will make the method of partial payment very popular because the contractor’s cash flow is rarely consistent. In addition, to assist customers, the payment process needs to include whether the currency of the transaction is local (VND) or foreign (USD). The variety of options and convenience in financial transactions by the supplier will provide the contractor with more payment options. Because each contractor has its own form of currency storage and its own trading methods, some businesses pay in cash. Others pay through bank transfers, and foreign-owned companies use USD in their projects. V. CONCLUSION Applying a grey AHP, a new quantitative method, by integrating grey system theory with the AHP, we prioritize the critical criteria in the evaluation and selection process of building paint suppliers in construction projects. This new method has an advantage over traditional methods because it supports group decision-making. In addition, it also accounts for uncertainty in the judgments of construction professionals and data incompleteness. The 5 most important criteria for evaluating and selecting the paint supplier in construction projects are (F7) the price of the paint product, (F1) the reputation of the paint supplier, (F3) the quality of construction paint materials, (F2) the quality management system certification of the paint supplier, and (F6) the terms and conditions of payment. TABLE III. INTEGRATED GREY COMPARISON MATRIX [1.0000, 1.0000] [1.5874, 3.1748] [1.2599, 2.5198] [4.5789, 6.6039] [3.1748, 5.2415] [2.5198 4.5789] [0.6300, 1.2599] [5.2415, 7.2685] [0.3150, 0.6300] [1.0000, 1.0000] [0.7937, 1.5874] [2.0000, 3.6342] [1.2599, 2.5198] [1.2599, 2.5198] [0.1733, 0.2752] [5.2415, 7.2685] [0.3969, 0.7937] [0.6300, 1.2599] [1.0000, 1.0000] [3.1748, 5.2415] [2.0000, 3.6342] [1.5874, 3.1748] [0.3969, 0.7937] [3.6342, 5.7690] [0.1514, 0.2184] [0.2752, 0.5000] [0.1908, 0.3150] [1.0000, 1.0000] [0.7937, 1.5874] [0.3467, 0.6300] [0.1376, 0.1908] [0.7937, 1.5874] [0.1908, 0.3150] [0.3969, 0.7937] [0.2752, 0.5000] [0.6300, 1.2599] [1.0000, 1.0000] [0.6300, 1.2599] [0.1733, 0.2752] [0.7937, 1.5874] [0.2184, 0.3969] [0.3969, 0.7937] [0.3150, 0.6300] [1.5874, 2.8845] [0.7937, 1.5874] [1.0000, 1.0000] [0.1733, 0.2752] [2.0000, 3.6342] [0.7937, 1.5874] [3.6342, 5.7690] [1.2599, 2.5198] [5.2415, 7.2685] [,3.6342 5.7690] [3.6342, 5.7690] [1.0000, 1.0000] [6.6039, 8.6177] [0.1376, 0.1908] [0.1376, 0.1908] [0.1733, 0.2752] [0.6300, 1.2599] [0.6300, 1.2599] [0.2752, 0.5000] [0.1160, 0.1514] [1.0000, 1.0000] TABLE IV. INTEGRATED GREY COMPARISON MATRIX [0.2399, 0.2399] [0.1474, 0.2948] [0.1724, 0.3448] [0.1908, 0.2752] [0.1769, 0.2921] [0.1642, 0.2984] [0.1794, 0.3589] [0.1690, 0.2343] [0.0756, 0.1511] [0.0929, 0.0929] [0.1086, 0.2172] [0.0833, 0.1514] [0.0702, 0.1404] [0.0821, 0.1642] [0.0494, 0.0784] [0.1690, 0.2343] [0.0952, 0.1904] [0.0585, 0.1170] [0.1368, 0.1368] [0.1323, 0.2184] [0.1115, 0.2025] [0.1035, 0.2069] [0.1130, 0.2261] [0.1172, 0.1860] [0.0363, 0.0524] [0.0255, 0.0464] [0.0261, 0.0431] [0.0417, 0.0417] [0.0442, 0.0885] [0.0226, 0.0411] [0.0392, 0.0543] [0.0256, 0.0512] [0.0458, 0.0756] [0.0368, 0.0737] [0.0377, 0.0684] [0.0260, 0.0530] [0.0557, 0.0557] [0.0411, 0.0821] [0.0494, 0.0784] [0.0256, 0.0512] [0.0524, 0.0952] [0.0368, 0.0737] [0.0431, 0.0862] [0.0660, 0.1200] [0.0440, 0.0880] [0.0652, 0.0652] [0.0494, 0.0784] [0.0645, 0.1172] [0.1904, 0.3809] [0.3374, 0.5357] [0.1724, 0.3448] [0.2184, 0.3029] [0.2025, 0.3215] [0.2369, 0.3760] [0.2848, 0.2848] [0.2129, 0.2778] [0.0330, 0.0458] [0.0128, 0.0177] [0.0237, 0.0377] [0.0263, 0.0525] [0.0351, 0.0702] [0.0179, 0.0326] [0.0331, 0.0431] [0.0322, 0.0322] TABLE V. WHITENIZATION OF THE GREY WEIGHTS (F1) The reputation of the paint supplier 0.2362 (F2) The quality management system certification of the paint supplier 0.1226 (F3) Quality of construction paint materials 0.1470 (F4) Number of paint categories and products 0.0425 (F5) Delivery time 0.0535 (F6) Terms and conditions of payment 0.0716 (F7) Price of the paint product 0.2925 (F8) Warranty period. 0.0341 Engineering, Technology & Applied Science Research Vol. 12, No. 5, 2022, 9087-9091 9090 www.etasr.com Pham et al.: Application of the Grey System Theory in Construction Management ACKNOWLEDGMENT The authors would like to thank the Professional Knowledge & Project Management Research Team (K2P), Ho Chi Minh City Open University, Vietnam for supporting this research. REFERENCES [1] B. Abdzadeh, S. Noori, and S. F. 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