Applied Science, Faculty of
Engineering, School of (Okanagan)
DSpace
UBCO
Muhammad, Usamah Inam
Master of Applied Science - MASc
University of British Columbia
This research develops a multi-stage multiple criteria decision making (MCDM) approach for combined supplier-selection, material selection problems. The method has been exemplified through an industrial case study on the development of insulated skirting products. Namely, a Canadian distribution company has been long supplying the Canadian market with skirting products for manufactured homes, but recently has had issues with their overseas material supplier, particularly due to increased exchange rates. Hence, it has desired to shift their supply stream to a local manufacturer. There exist a large number of potential manufacturers that would be suitable for this new partnership. It has been crucial to scrutinize the decision alternatives systematically in order to rank and allow for the optimal selection of the supplier(s) and their skirting products. When manufacturing suppliers are changed for a business, a natural consequence is that the end product’s material properties would also change, hence the need for a rigorous material testing as part of a multiple criteria decision making process. A step-by-step procedure has been developed here that combines supplier and material selection sub-decisions in order to find the most suitable alternative, using a hybrid of multiple criteria optimization techniques. The procedure accounts for the required decision accuracy and time-sensitivity measures that a production manager would face under different decision scenarios. The case study shows that if the company’s business situation is time-critical and the decision accuracy may not be of primary concern, a simple non-compensatory MCDM method would suffice. Otherwise, more structured compensatory methods should be employed. The criteria proposed for the case study have been selected based on the company staff feedback. The presented methodology is customizable and may be applied to other similar supplier decision making problems. Correlation analysis has also performed to ensure the independence of the quantitative material criteria, as required per assumptions of the standard MCDM methods.
A Customizable, Multi-stage Multi-criteria Decision Analysis Approach for Material-Supplier Selection Problem in SMEs: A Case Study of Insulated Housing Products by Usamah Inam Muhammad BSc. Mechanical Engineering, King Fahd University of Petroleum and Minerals A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE COLLEGE OF GRADUATE STUDIES (Mechanical Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Okanagan) April 2019 © Usamah Inam Muhammad, 2019 ii The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, a thesis/dissertation entitled: A Customizable, Multi-stage Multi-criteria Decision Analysis Approach for Material-Supplier Selection Problem in SMEs: A Case Study of Insulated Housing Products submitted by Usamah Inam Muhammad in partial fulfillment of the requirements for the degree of MASTER OF APPLIED SCIENCE in Mechanical Engineering Examining Committee: Dr. Abbas S. Milani, School of Engineering, UBCO Co-supervisor Dr. Rehan Sadiq, School of Engineering, UBCO Co-supervisor Dr. Kasun Hewage, School of Engineering, UBCO Supervisory Committee Member Dr. Eric Li, Faculty of Management, UBCO University Examiner Additional Supervisory Committee Members: Dr. Ray Taheri, School of Engineering, UBCO Supervisory Committee Member iii Abstract This research develops a multi-stage multiple criteria decision making (MCDM) approach for combined supplier-selection, material selection problems. The method has been exemplified through an industrial case study on the development of insulated skirting products. Namely, a Canadian distribution company has been long supplying the Canadian market with skirting products for manufactured homes, but recently has had issues with their overseas material supplier, particularly due to increased exchange rates. Hence, it has desired to shift their supply stream to a local manufacturer. There exist a large number of potential manufacturers that would be suitable for this new partnership. It has been crucial to scrutinize the decision alternatives systematically in order to rank and allow for the optimal selection of the supplier(s) and their skirting products. When manufacturing suppliers are changed for a business, a natural consequence is that the end product’s material properties would also change, hence the need for a rigorous material testing as part of a multiple criteria decision making process. A step-by-step procedure has been developed here that combines supplier and material selection sub-decisions in order to find the most suitable alternative, using a hybrid of multiple criteria optimization techniques. The procedure accounts for the required decision accuracy and time-sensitivity measures that a production manager would face under different decision scenarios. The case study shows that if the company’s business situation is time-critical and the decision accuracy may not be of primary concern, a simple non-compensatory MCDM method would suffice. Otherwise, more structured compensatory methods should be employed. The criteria proposed for the case study have been selected based on the company staff feedback. The presented methodology is customizable and may be applied to other similar supplier decision making problems. Correlation analysis has also iv performed to ensure the independence of the quantitative material criteria, as required per assumptions of the standard MCDM methods. v Lay Summary Supplier selection for companies usually occurs when a new product must be made or an older supplier has to be changed for various reasons, including budgetary considerations. As suppliers change, however, the materials that are provided also often change. It is important to consider the qualities of the suppliers as well as the materials they carry concurrently. This MASc research presents a methodology for the screening and selection of an optimal supplier by combining supplier and material selection contexts, using a hybrid of multiple criteria decision making (MCDM) techniques. The methodology is scenario dependent, as it uses different mathematical techniques of varying complexity depending on the decision situation surrounding the given industrial application. It further uses a real-world case study to demonstrate the application of the method. vi Preface This research is based on an industrial project supported by an anonymous Canadian company, and awarded by the Mathematics of Information Technology and Complex Systems (MITACS) research organization. vii Table of Contents Abstract ......................................................................................................................................... iii Lay Summary .................................................................................................................................v Preface ........................................................................................................................................... vi Table of Contents ........................................................................................................................ vii List of Tables ..................................................................................................................................x List of Figures .............................................................................................................................. xii List of Abbreviations ................................................................................................................. xiv Acknowledgements ......................................................................................................................xv Dedication ................................................................................................................................... xvi Introduction ................................................................................................................1 1.1 Background ..................................................................................................................... 1 1.2 Objectives and Scope ...................................................................................................... 2 1.3 Thesis Organization ........................................................................................................ 4 Literature Review .......................................................................................................5 2.1 Multiple Criteria Decision Making ................................................................................. 5 2.2 Considerations of Select MCDM Techniques ................................................................ 8 2.2.1 Dominance .................................................................................................................. 8 2.2.2 Maximin ...................................................................................................................... 9 2.2.3 Maximax ..................................................................................................................... 9 2.2.4 Elimination By Aspects ............................................................................................ 10 2.2.5 Conjunctive Method.................................................................................................. 11 viii 2.2.6 Disjunctive Method ................................................................................................... 11 2.2.7 Lexicographic Method .............................................................................................. 12 2.2.8 Simple Additive Weighting ...................................................................................... 13 2.2.9 Weighted Product Method ........................................................................................ 14 2.2.10 TOPSIS ..................................................................................................................... 14 2.2.11 Median Ranking Method .......................................................................................... 15 2.2.12 Best-Worst Method .................................................................................................. 16 2.2.13 AHP .......................................................................................................................... 17 2.2.14 Modified Digital Logic ............................................................................................. 18 2.3 Supplier Selection as an MCDM Problem .................................................................... 18 2.4 Material Selection as an MCDM Problem .................................................................... 26 Methodology..............................................................................................................33 3.1 Background ................................................................................................................... 33 3.2 Step-by-Step Procedure ................................................................................................ 35 3.2.1 Step 1: Find potential suppliers: ............................................................................... 38 3.2.2 Step 2: Creating the SS decision matrix: .................................................................. 38 3.2.3 Step 3: Choose SS MCDM method: ......................................................................... 38 3.2.4 Step 4: Order samples from e.g. the top ranked suppliers: ....................................... 38 3.2.5 Step 5: Test the material samples.............................................................................. 39 3.2.6 Step 6: Creating the MS decision matrix: ................................................................. 39 3.2.7 Step 7: Choose MS MCDM method(s):.................................................................... 39 3.2.8 Step 8: Select the final material ................................................................................ 39 Case Study .................................................................................................................40 ix 4.1 Background ................................................................................................................... 40 4.2 The Decision Making Process ...................................................................................... 44 4.2.1 Step 1: Find Potential Suppliers ................................................................................ 44 4.2.2 Step 2: Creating the SS Decision Matrix .................................................................. 44 4.2.3 Step 3: Choose SS MCDM Method .......................................................................... 48 4.2.4 Step 4: Order material samples from the top 3 suppliers .......................................... 56 4.2.5 Step 5: Test samples.................................................................................................. 56 4.2.6 Step 6: Create the MS decision matrix ..................................................................... 63 4.2.7 Step 7: Choose the MS MCDM method ................................................................... 65 4.2.8 Step 8: Select the final material supplier .................................................................. 69 Conclusions and Recommendations .......................................................................70 5.1 Summary and Conclusions ........................................................................................... 70 5.2 Limitations of the Work ................................................................................................ 71 5.3 Recommendations for Future Work.............................................................................. 72 Bibliography .................................................................................................................................73 Appendices ....................................................................................................................................95 : Experimental Tests Used in this Study ............................................................. 95 A.1 Tensile Test ............................................................................................................... 95 A.2 Scratch Resistance Test............................................................................................. 96 A.3 Impact Test................................................................................................................ 98 A.4 Weathering Resistance .............................................................................................. 99 A.5 Aesthetics ................................................................................................................ 100 x List of Tables Table 2-1 Recent examples of MCDM used in supplier selection problems ........................... 23 Table 2-2 Recent examples of MCDM used in material selection problems .......................... 30 Table 4-1 The Supplier Selection decision matrix ................................................................... 46 Table 4-2 Results of the screening of the suppliers ................................................................. 47 Table 4-3 Decision matrix to be used for SS MCDM .............................................................. 48 Table 4-4 Results from the lexicographic method with YIB as the most important criterion . 49 Table 4-5 The SS decision matrix after data is converted to ranks .......................................... 50 Table 4-6 The MDL implementation for the SS MCDM problem .......................................... 50 Table 4-7 Numerical results of the scratch resistance test using MDL method ...................... 59 Table 4-8 Test results of density change % of different material samples under weathering test ....................................................................................................................................................... 62 Table 4-9 The MDL results of the aesthetic testing of samples ............................................... 63 Table 4-10 The material selection (MS) decision matrix; +/- signs indicate the higher the better, or the low the better type of criteria, respectively ........................................................................ 64 Table 4-11 The correlation matrix of the MS criteria ................................................................ 64 Table 4-12 The P-values (statistical significance) of the calculated correlations of the MS criteria ........................................................................................................................................... 65 Table 4-13 The best and worst material criteria selected for the BW method ........................... 67 Table 4-14 The Best-to-Others comparisons in the BWM ........................................................ 67 Table 4-15 The Others-to-Worst comparisons in the BWM ...................................................... 67 Table 4-16 Weights generated from the BWM .......................................................................... 68 xi Table 4-17 Results of the linear normalization of MS data ....................................................... 68 Table 4-18 The result of SAW material selection ...................................................................... 68 Table 4-19 Ranking of the SAW results for the candidate materials ......................................... 69 xii List of Figures Figure 1-1 Organization of the thesis .......................................................................................... 4 Figure 2-1 Taxonomy of MADM methods [8] ........................................................................... 7 Figure 3-1 Proposed workflow for a decision-making process involving both supplier selection (SS) and material selection (MS) .................................................................................................. 37 Figure 4-1 Insulated skirting product ........................................................................................ 40 Figure 4-2 Historical exchange rates for CAD-USD (Source: Bank of Canada) ...................... 41 Figure 4-3 How the installed product looks as it is bent around a corner ................................. 43 Figure 4-4 Stress versus strain response of the material samples from top ranked suppliers. The circle represents where the weakest repeat breaks ........................................................................ 57 Figure 4-5 Stress and strain response of the material samples before the failure points of the weakest repeat ............................................................................................................................... 57 Figure 4-6 Test results for the impact test of the Control material ........................................... 60 Figure 4-7 Test results for the impact test of the Company A material .................................... 61 Figure 4-8 Test results for the impact test of the Company D material .................................... 61 Figure 4-9 Test results for the impact test of the Company M material ................................... 62 Figure A-1 Dimensions used for the tensile test specimens……………………………………95 Figure A-2 Specimen used for the tensile test ............................................................................ 96 Figure A-3 Tensile test specimen set up on the Instron 5969 .................................................... 96 Figure A-4 Example of specimens used for the scratch resistance test. Left piece is used to scratch the right piece ................................................................................................................... 97 Figure A-5 Gardner impact test set-up with specimen loaded ................................................... 99 xiii Figure A-6 A test specimen before and after exposed to weathering ...................................... 100 Figure A-7 The environmental chamber used in the study ...................................................... 100 xiv List of Abbreviations MCDM Multiple Criteria Decision Making PVC Polyvinyl Chloride DM Decision Maker(s) MADM Multiple Attribute Decision Making MODM Multiple Objective Decision Making EBA Elimination by Aspects SAW Simple Additive Weighting AHP Analytic Hierarchy Process TOPSIS Technique for Order Preference by Similarity to Ideal Solution BWM Best-Worst Method DL Digital Logic MDL Modified Digital Logic SS Supplier Selection MS Material Selection MA Material Availability TC Technological Capability YIB Years in Business MFE Mean Failure Energy xv Acknowledgements I would like to firstly express my sincere gratitude to my co-supervisors, Dr. Abbas S. Milani for all of his great guidance and support, and Dr. Rehan Sadiq for countless talks and discussions that have inspired me greatly. I would also like to express my gratitude to all of the encouragement they gave me throughout this thesis project and helped me make it a success. The great comments and recommendations by my thesis committee members Dr. Kasun Hewage and Dr. Ray Taheri are highly appreciated. I would like to acknowledge Mathematics of Information Technology and Complex Systems (MITACS) agency for the financial assistance that they provided for this industrial project. Special thanks are due to my friends and colleagues at the Composites Research Network (CRN) Okanagan and throughout the School of Engineering for making this journey a very enjoyable one. Finally, I would like to thank my family for their support and love, without which none of my academic successes would be possible. xvi Dedication To my Family & Best friends Without whom none of this would have been possible. 1 Introduction 1.1 Background Before a new product is manufactured, it needs to undergo some form of design process. Product design is often defined by means of four steps [1]:  Idea development: The need is recognized and preliminary design concepts are established.  Concepts screening: Different design concepts are evaluated against the product objectives, followed by screening the concepts.  Preliminary design and testing: The selected preliminary design is created and it undergoes prototyping and market testing.  Final design: The design of product is fine-tuned and finalized for formal launch. The relevance of this study is to the final design stage, where one of the main tasks of manufacturers/designers is “identifying specific materials needed for the product and the suppliers that can be used” during business [1]. Supplier selection is one of the most important issues for manufacturing industries [2]. Criteria that are considered in such selection problems may be qualitative or quantitative [3]. The selection also often requires different combinations of mathematical decision models (e.g. compensatory and noncompensatory [2]), in order to meet diverse sub-criteria of a supplier selection problem. For instance, when considering different suppliers for a given company’s product, ultimately the materials used for the product also change. Each material has its own set of mechanical and physical properties that will determine how it performs in service; 2 additionally, it may have different aesthetics that will determine how the users would perceive the new product [4]. Accordingly, for the success of a new production plan, it is vital that companies select their suppliers based on general business capabilities of the supplier candidates, combined with their engineering technical capabilities (such as quality and properties of the materials and manufacturing processes applied) [5]. Systematic multiple criteria decision making (MCDM) methods can be developed and employed for such multi-faceted supplier selection problems, as exemplified in the current thesis. This thesis was inspired by an industrial project (case study) performed at a local small to medium enterprise (SME). The company is located in Kelowna, BC, and currently distributes insulated house skirting products to the Canadian market, using US-based manufacturing suppliers. However, they have been facing increasing exchange costs recently and have opted to shift to a local supplier. Nationally, there are a large number of options (alternatives) that can be considered as new potential suppliers. It is critical to develop a systematic way to differentiate between the numerous alternatives in order to select the overall, most optimum supplier, while ensuring the material properties and performance of the end product are maintained, or even improved. 1.2 Objectives and Scope The general scope of this research, through a SME-based case study, is to use multiple criteria decision making (MCDM) techniques to aid in selecting the best suppliers for manufacturing a house skirting product in Canada. The targeted methodology is “customizable” for different 3 scenarios surrounding similar decision making problems. For example, in our case study, the company has been looking to change its material supplier from the U.S. to Canada and has a certain number of criteria determined by the client with regards to both supplier and material selections. However, another client may use other criteria depending on their business scenarios or preferences. The decision making method will have two steps. First, we will conduct the “Company Selection” process to find the best potential supplier(s) based on a number of business performance criteria. The candidate suppliers will be ranked and the top ranked companies will be requested to send material samples. Then, using the received samples, the second step, i.e. “Material Selection”, will be conducted, consisting of evaluating the quality of the samples by conducting various mechanical and physical tests. The specific objectives of the thesis are:  Develop a multi-stage decision making framework using a hybrid of different multiple criteria optimization techniques to aid decision makers in supplier selection problems;  Demonstrate the application of the method in the development of house skirting products, through an industrial case study. The constraints associated with the case study are the following:  Basic design (geometry) of the product is given.  The material for the product is PVC, but different grades can be considered.  Suppliers based in Canada is considered only.  The manufacturing of the product is conducted by the candidate suppliers using the extrusion process. 4  Specific decision making criteria are to be selected based on the direct requirements from industrial partner, complemented with the current literature. 1.3 Thesis Organization This thesis has been arranged into five chapters, per Figure 1.1. Chapter 2 briefly reviews the theory of MCDM, and its applications in Supplier Selection as well as Material Selection problems. Chapter 3 discusses the methodology that has been developed in this thesis, and the justification behind it. The methodology will include a step-by-step procedure to perform first the supplier selection MCDM problem and then implement the material selection MCDM problem, using a hybrid of compensatory and non-compensatory techniques for comparison purposes. Chapter 4 consists of the case study (on production of insulated house skirting products) to showcase the use of the methodology with an industrial example, along with the experimental results. Chapter 5 summarizes the research findings and proposes recommendations for future work. Figure 1-1 Organization of the thesis Chapter 1: IntroductionChapter 2: Literature ReviewChapter 3: MethodologyChapter 4: Case StudyChapter 5: Conclusion5 Literature Review 2.1 Multiple Criteria Decision Making Throughout life, every individual is involved in ‘multicriteria’ decision making in one form or another. Sometimes these decisions are small and at times very important. From the beginning of conscious thought up to old age, humans are making decisions. Decision making involves choosing a potential option from a set of existing or potential new alternatives [6]–[8]. Decision making problems can range e.g. from choosing which job to take, to selecting the best vehicle that fits one’s needs; the problems that decision makers (DM) have to consider usually involve multiple conflicting criteria in nature [9], [10]. The decision making process is formally known as ‘multiple criteria decision making’ or MCDM [11]. The highly diverse MCDM problems in real-world can be divided into two branches; Multiple Attribute Decision Making (MADM) and Multiple Objective Decision Making (MODM) [9]. MODM does not involve problems that have ‘predetermined’ alternatives [6], [12]. It involves problems with a continuous decision space [13], [14]. It is more appropriate for design problems rather than selection [6]. MADM involves problems with decision spaces that are discrete and the related techniques revolve around selecting a number of options from alternatives that are usually finite and predetermined [13]–[15]. All categories of MADM problems have some common features/definitions as follows [9]:  Alternatives: a limited set of potential solutions are screened, ranked and selected. 6  Multiple attributes/criteria: The problem at hand consists of a number of attributes. Appropriate attributes must be selected by the DM and the number of selected attributes depends on requirements and constraints associated with the problem.  Incommensurable units: Every attribute consists of a distinct measurement unit. These can be expressed numerically or even in nonnumeric terms.  Attribute weights: Information about the importance of attributes relative to one another is required in most MADM methods.  Decision Matrix: MADM problems can be presented in a matrix form, where normally rows represent alternatives and columns represent the attributes. A taxonomy of MADM methods was developed by Yoon and Hwang [9] as seen in Figure 2.1. They are classified depending on the type of information available to the decision maker. For instance, if there is no available information on relative priority of criteria, then the Dominance method would be suitable to use. If information regarding the decision environment is optimistic or pessimistic in nature, then Maximax or Maximin method would be suitable, respectively. If there is some availability in the information of the relative priority of attributes, other methods can be employed. For example, if such information is provided as standard levels in a given decision making problem (e.g. maximum available production budget, or minimum level of required mechanical properties from design perspective, etc) then Conjunctive and Disjunctive methods would be suitable. Elimination by Aspect (EBA) or Lexicographic method may be employed if the information provided assesses the attributes weights by an ordinal scale. Otherwise, when the DM assesses the weights by cardinal scales, methods such as Simple 7 Additive Weighting (SAW), Weight Product and TOPSIS, Median Ranking Method and Analytic Hierarchy Process (AHP) etc. may be used. Figure 2-1 Taxonomy of MADM methods [9]. From K. P. Yoon and C. L. Hwang, Multiple Attribute Decision Making: An Introduction. Thousand Oaks, California: Sage Publications, 1995, which was adapted from Springer-Verlag, Multiple Attribute Decision Making: Methods and Applications by Hwang, C. L., and Yoon, K. (1981). Used with permission from © Sage and © Springer. According to Hwang [16] , MADM methods can also be classified by given data type. He identified data as rank, Yes-No, and numeric types. In problems which involve rank data, Dominance and Lexicographic methods would be applied. In problems with Yes-No data type, MADMNo Information DominanceInformation on EnvironmentPessimistic MaximinOptimistic MaximaxInformation on AttribureStandard LevelConjunction MethodDisjunction MethodOrdinalLexicographic MethodElimination by AspectCardinalSimple Additive WeightingWeighted ProductTOPSISElectreMedian Ranking MethodAHPType of Information from DM Salient Feature of Information Major Class of Method 8 Dominance, Lexicographic and EBA would be suitable. Problems involving numeric data types would benefit from SAW, TOPSIS, etc. From another practical viewpoint, MADM methods can be divided into two main groups of ‘compensatory’ and ‘non-compensatory’ [15]. Non-compensatory techniques allow for no trade-offs between the attributes in a given problem. Low scores in one attribute cannot be offset by better scores in others. [15]. Each criteria will have equal importance in the decision making. Non-compensatory methods have the advantage of being fairly simplistic and are ideal for a DM having insufficient ability and knowledge. [15]. Examples include the dominance, elimination by aspects, lexicographic, maximax, maximin, conjuctive and disjunctive methods.[9], [15] . In contrast, compensatory methods do allow for trade-offs between attributes [15]. An alternative with slightly low scores in some criteria may turn out to be the best solution if it performs well in the other criteria. Examples of such methods are SAW, weighted product and TOPSIS. Overall, compensatory methods tend to be more cognitively demanding [9]. More details of select MADM methods as pertinent to this research are discussed in the following section. 2.2 Considerations of Select MCDM Techniques 2.2.1 Dominance An alternative A1 is more preferable than an alternative A2 and would be selected if it performs better than A2 on one or more criteria, while simultaneously not being worse on any other criteria [17]. A nondominated alternative is one that is not exceeded in every criteria that is being considered by another alternative [9]. 9 2.2.2 Maximin In an occasion where there is no information regarding which criteria dominates the outcome, a pessimistic view should be taken [9]. The alternative of which the worst criteria score is better than the worst score of the other alternatives should be selected [9]. The logic is that the DM should not select an alternative that has the least attractive criteria [17]. A DM will assess the values of criteria for the alternatives and identify the one with the lowest value, then will choose the alternative with the highest among them [15]. Here, the alternative is represented by its weakest criteria and all other attributes are disregarded [15]. Since in many cases the smallest value is from different criteria, this method requires the criteria to be measured (quantified) on the same scale, so that their values can be comparable [15]. If A+ is the preferred alternative, it should satisfy equation 2.1 [15]. 𝐴+ = {𝐴𝑖| 𝑚𝑎𝑥𝑖 𝑚𝑖𝑛𝑗 𝑟𝑖𝑗} , i= 1, 2, . . ., m ; j= 1, 2, . . ., n (2.1) Where 𝑟𝑖𝑗 is a comparable (normalized) ) scale of 𝑥𝑖𝑗 (original value of alterative i under criteria j). 2.2.3 Maximax Maximax makes selection based on the highest criteria value [15]. The highest criteria values of each alternative are identified [15] and the alternative with the largest of these values would be selected. The logic is that the “best of the best” should be chosen. An alternative is represented by its strongest criteria and all other attributes are disregarded [15]. Different type of attributes may be compared in this selection method, and hence they should use the same scale for comparison [15]. If A+ is the preferred alternative under this method, it should satisfy equation 2.2 [15]. 10 𝐴+ = {𝐴𝑖| 𝑚𝑎𝑥𝑖 𝑚𝑎𝑥𝑗 𝑟𝑖𝑗}, i = 1, 2, . . . , m ; j = 1, 2, . . . , n (2.2) Where 𝑟𝑖𝑗 is a comparable (normalized) scale of 𝑥𝑖𝑗. 2.2.4 Elimination By Aspects Elimination by Aspects (EBA) was developed by Tversky [18]. He described EBA as being similar to the Lexicographic method where one criterion is considered at a time. However, there are some differences between the two. Firstly, the criteria are not ordered on their importance before the rejection process, but on their probabilistic discrimination power [9], [18]. Also, alternatives are rejected when they do not satisfy a threshold or standard. This process goes on until only one alternative is left [18]. For instance, if the most and second most effective aspect (criteria) to use to reject alternatives are denoted as X1 and X2 respectively, then the preferred alternative set A1 is represented by equation 2.3 [9]. 𝐴1 = {𝐴𝑖 |𝑥𝑖1 𝑠𝑎𝑡𝑖𝑠𝑓𝑖𝑒𝑠 𝑋1}, 𝑖 = 1, 2, … , 𝑚 (2.3) If the {𝐴1} set only contains one element, then this alternative will be selected. Otherwise, one can consider next best set (equation 2.4). 𝐴2 = {𝐴1 |𝑥𝑖2 𝑠𝑎𝑡𝑖𝑠𝑓𝑖𝑒𝑠 𝑋2}, 𝑖 ∈ {𝐴1} (2.4) If only one element is in the {𝐴2} set, then that would be the alternative that is preferred. If not, then this is continued with X3 and so on until a single alternative is found. 11 2.2.5 Conjunctive Method In this method, a minimum threshold is set for each of the criteria and an alternative must possess value above these thresholds in order to be selected [9], [19]. Rejection can be caused by failure of even one attribute under the minimum value set [9]. An alternative would be suitable under this method if it satisfies equation 2.5 [9]: 𝑥𝑖𝑗 ≥ 𝑥𝑗0, 𝑗 = 1, 2, … , 𝑛 (2.5) Where 𝑥0𝑗 is the smallest value that is acceptable for the jth criterion. The values selected for the thresholds are an important component in rejecting unsuitable alternatives. If these values are set too high (too conservative), then all the alternatives may be rejected. However, setting them too low would have an opposite effect and all or too many alternatives may be left. One possible way to cope with this problem would be to raise the thresholds in an iterative manner, in order to narrow down the alternatives until one is remaining. [9] 2.2.6 Disjunctive Method The disjunctive method also sets a minimum threshold for each criterion, and alternatives are essentially evaluated on their best criteria values [9], [19]. Selection of an alternative will occur if it satisfies the minimum threshold of at least one (most important) criterion. An alternative would be suitable under this method if it satisfies equation 2.6 [9]. 𝑥𝑖𝑗 ≥ 𝑥𝑗0, 𝑗 = 1 𝑜𝑟 2 … 𝑜𝑟 𝑛 (2.6) Where 𝑥0𝑗 is the smallest value that is acceptable for the jth criteria. 12 This method would make sense to use if an alternative is being sought for acceptable performance at least under one criterion [19]. When the threshold of only a single criterion is required to be exceeded, a majority of alternatives will not be rejected. Hence, the values may need to be set near or at the highest level. In the scenario that all the alternatives are rejected, the threshold can be lowered for one or more criteria and the process is restarted until the ideal alternative is found [9]. 2.2.7 Lexicographic Method Fishburn [21] described sequential screening procedures as an example of where the lexicographic concept can be used. Alternatives are initially screened with regards to a criterion and then the alternatives that are not rejected are screened again under another (next important) criterion. This process may continue until the remaining alternatives in the last step are ranked. Yoon and Hwang [9] described the lexicographic method as appropriate for decision making scenarios where the consideration of one attribute outweighs all others. This includes scenarios where “buy cheapest” is the rule. In such situations, alternatives are screened under the most important criterion first. The best one is selected and the process ends. If there is a tie between two or more alternatives, then these alternatives are compared under the next important criterion over and over again until the best one is selected or comparisons have been made under all of the criteria. If more than one alternative is left in the end, then they are regarded as equal. If the most and second-most important criteria are denoted as x1 and x2, respectively, then the preferred alternative set A1 is represented by equation 2.7. 𝐴1 = {𝐴𝑖 | max𝑖 𝑥𝑖1}, 𝑖 = 1, 2, … , 𝑚 (2.7) 13 If 𝐴1 has only one element then this alternative will be selected. Otherwise, we will consider 𝐴2, represented by equation 2.8: 𝐴2 = {𝐴1 | max𝑖 𝑥𝑖2}, 𝑖 ∈ {𝐴1} (2.8) Again, if only one element is in 𝐴2, then that would be the alternative that is preferred. If not, then this is continued until a single alternative is found or all criteria have been used for comparison. 2.2.8 Simple Additive Weighting This is one of the most popular MCDM methods to date. In this method, contributions of every criteria are added in order to get a score for each alternative [9]. In order to use this technique, the various criteria, usually having different units need to be comparable along a scale; and hence some form of data normalization is required (usually linear normalization). Each alternative is scored by multiplying and adding the normalized values of the criteria by criteria weights; the latter may be assigned directly by the DM or determined using some other weighting methods, which will be discussed in other sections of the thesis. This scoring method is represented by equation 2.9 [9]: 𝑉𝑖 = ∑ 𝑤𝑗𝑟𝑖𝑗 , 𝑖 = 1, . . . , 𝑚𝑛𝑗=1 (2.9) Where 𝑉𝑖 and 𝑟𝑖𝑗 are the value (score) of alternative 𝐴𝑖 and the normalized value of 𝑥𝑖𝑗, respectively. And, 𝑤𝑗 is the weight of criteria 𝑥𝑗. 14 2.2.9 Weighted Product Method This method is quite similar to SAW but different in that when calculating the value of alternative 𝐴𝑖 , instead of summation, multiplication is used [13]. Also, it does not require normalization of dimensions to a comparable scale and is sometimes referred to as “dimensionless analysis” [13]. Furthermore, the weights are used as exponents of the criteria values [9]. This scoring method is represented by equation 2.10 [9], [13]: 𝑉𝑖 = ∏ 𝑥𝑖𝑗𝑤𝑗 ,𝑛𝑗=1 𝑖 = 1, . . . , 𝑚 (2.10) Where 𝑉𝑖 is the value of alternative 𝐴𝑖 and, 𝑤𝑗 is the weight of criteria 𝑥𝑗. 2.2.10 TOPSIS A Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) was developed by Hwang and Yoon [15]. The idea is that the best alternative should have the shortest and longest distances from the positive-ideal (best imaginary) and negative-ideal (worst imaginary) solutions, respectively. The steps required to find the preferred alternative are as follows [15]: Step 1: The normalized values are calculated by using vector normalization for 𝑟𝑖𝑗 (equation 2.11): 𝑟𝑖𝑗 =𝑥𝑖𝑗√∑ 𝑥𝑖𝑗2𝑚𝑖=1 , 𝑖 = 1, . . . , 𝑚; 𝑗 = 1, . . . , 𝑛. (2.11) Step 2: The weighted normalized values are calculated for 𝑣𝑖𝑗 (equation 2.12): 𝑣𝑖𝑗 = 𝑤𝑗𝑟𝑖𝑗 , 𝑖 = 1, . . . , 𝑚; 𝑗 = 1, . . . , 𝑛. (2.12) Step 3: Determine the positive-ideal (A*) and negative-ideal (A-) solutions. 𝐴∗ = {𝑣1∗, 𝑣2∗, . . . , 𝑣𝑗∗, . . . , 𝑣𝑛∗} = {(𝑚𝑎𝑥𝑖𝑣𝑖𝑗| 𝑗 ∈ 𝐽), (𝑚𝑖𝑛𝑖𝑣𝑖𝑗| 𝑗 ∈ 𝐽′) | 𝑖 = 1, . . . , 𝑚} (2.13) 15 𝐴− = {𝑣1−, 𝑣2−, . . . , 𝑣𝑗−, . . . , 𝑣𝑛−} = {(𝑚𝑖𝑛𝑖𝑣𝑖𝑗| 𝑗 ∈ 𝐽), (𝑚𝑎𝑥𝑖𝑣𝑖𝑗| 𝑗 ∈ 𝐽′) | 𝑖 = 1, . . . , 𝑚} (2.14) where J and J’ and sets of benefit- and cost-type criteria, respectively. Step 4: Determine the separation (distance) measures from the positive-ideal and negative-ideal solutions. 𝑆𝑖∗ = √∑ (𝑣𝑖𝑗 − 𝑣𝑗∗)2𝑛𝑗=1 , 𝑖 = 1, . . . , 𝑚. (2.15) 𝑆𝑖− = √∑ (𝑣𝑖𝑗 − 𝑣𝑗−)2𝑛𝑗=1 , 𝑖 = 1, . . . , 𝑚. (2.16) Step 5: Determine relative closeness to the positive-ideal solution (equation 2.17): 𝐶𝑖∗ =𝑆𝑖−𝑆𝑖∗+𝑆𝑖− , 𝑖 = 1, . . . , 𝑚, 0 ≤ 𝐶𝑖∗ ≤ 1 (2.17) Alternatives with higher 𝐶𝑖∗ are preferred. 2.2.11 Median Ranking Method When qualitative data is available, we can obtain rank data and employ them for MADM using the median ranking method. The ranks of criteria often conflict with one another, but it is important for the DM to get a consensus from the ranks [9]. A distance function was developed by Cook and Seiford [22] in order to determine consensus ranking. It acts as a measure of agreement or disagreement between ranks [22]. When assuming equal importance between attributes, then for 𝐴𝑖 to be the kth rank overall, the rank distance is defined as equation 2.18. 𝑑𝑖𝑘 = ∑ |𝑠𝑖𝑗 − 𝑘|𝑛𝑗=1 (2.18) Where 𝑠𝑖𝑗 is the attributewise rank of 𝐴𝑖. If the different criteria have different relative importance, the distance equation becomes [9]: 𝑑𝑖𝑘 = ∑ 𝑤𝑗|𝑠𝑖𝑗 − 𝑘|𝑛𝑗=1 (2.19) 16 Where 𝑤𝑗 is the weight of the criteria. Then, for the alternatives to have final ranks assigned to them, the Hungarian Method [23] can be used. 2.2.12 Best-Worst Method The Best-Worst Method (BWM) was recently developed by Rezaei [24], [25] and is a vector based MCDM technique as opposed to matrix based methods. From the attributes, the DM selects the most important one, or the “best”, and the least important one, or the “worst”. The attribute that is the “best” is then compared with each of the other attributes. Similarly, then the “worst” attribute is compared with each of the other attributes, and finally the criterial weighting are found. The method consists of the following detailed steps: Step 1: The set of decision criteria {c1, c2, …, cn} needed for the decision making should be determined by the DM. Step 2: Determine the best and worst criteria based on the DM experience. Step 3: Determine the preference of the best criterion over all the other criteria by using a number between 1 and 9; where 1 indicates equal preference and 9 indicates extreme preference. The best-to-others resulting from this will be AB = (aB1, aB2, …aBn), where aBj shows the preference of the best criterion B over criterion j, with aBB= 1 Step 4: Determine the preference of all the other criteria over the worst criterion by using a number between 1 and 9. The others- to-worst resulting from this will be AW = (a1W, a2W, …anW)T, where e.g. a1W shows the preference of the criterion 1 over worst criterion W; note that aWW=1. Step 5: Determine the optimal weights of criteria (𝑤1∗, 𝑤2∗, . . . , 𝑤𝑛∗). The optimal weighting for the attributes is one where wB/wj=aBj and wj/wW=ajW . To meet these conditions the maximum 17 absolute difference of the set {|𝑤𝐵 − 𝑎𝐵𝑗𝑤𝑗|, |𝑤𝑗 − 𝑎𝑗𝑤𝑤𝑤|} should be minimized and the problem can be formulated as follows [24]: min 𝑚𝑎𝑥𝑗 {|𝑤𝐵 − 𝑎𝐵𝑗𝑤𝑗|, |𝑤𝑗 − 𝑎𝑗𝑤𝑤𝑤|} (2.20) Such that: ∑ 𝑤𝑗 = 1𝑗 , 𝑤𝑗 ≥ 0, 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑗 This optimization problem can be transferred to a linear programming as follows: |𝑤𝐵 − 𝑎𝐵𝑗𝑤𝑗| ≤ 𝜉𝐿 , 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑗 |𝑤𝑗 − 𝑎𝑗𝑤𝑤𝑤| ≤ 𝜉𝐿 , 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑗 ∑ 𝑤𝑗 = 1𝑗 𝑤𝑗 ≥ 0, 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑗 This linear problem gives a unique solution, where the optimal weights (𝑤1∗, 𝑤2∗, . . . , 𝑤𝑛∗) and 𝜉𝐿 . 𝜉𝐿 can be considered an indicator of consistency; the closer its value is to zero, the higher will be the consistency. 2.2.13 AHP Saaty [26] developed the Analytical Hierarchical Process (AHP). The method decomposes decision making problems into a hierarchical form [13]. This hierarchy consists of at least three levels: the goal at the first, the criteria at the second, and the competing alternatives on the third level. 18 Pair-wise comparisons are utilized to assess the inputs from the decision makers or experts. Then, these are used in order to determine the relative importance (weights) of the criteria [27]. Similarly, pair-wise evaluation of alternatives is performed with regards to how well they satisfy each criterion [27]. Then the performance score of each criterion is multiplied by its weight and summed over all criteria to obtain the overall performance score for all alternatives [27]. 2.2.14 Modified Digital Logic The Digital Logic (DL) method is a simple yet very effective technique to generate weights, especially for DMs with less experience. Pairwise comparisons of attributes is conducted and a score of 1 is assigned to the attribute that is more attractive, and 0 to the attribute that is less attractive. A modified version of this called the Modified Digital Logic (MDL) was developed by Dehghan-Menshadi et al. [28]. It is based on the same idea of the DL method but instead of just binary scores of 1 and 0, it uses other scores (1, 2 or 3). Attributes that are less attractive are assigned a score of 1 and 3 is assigned to attributes that are more attractive. Attributes that are equally attractive can both receive a score of 2. Eventually, these ranking scores are summed and normalized to final the weighting factors [27]. 2.3 Supplier Selection as an MCDM Problem Choosing the right suppliers is a critical element for businesses looking to bring down costs, increase competitiveness and improve customer satisfaction [29]–[40]. Quality of products and services is also associated with proper supplier selections [36], [41]. 19 Additionally, materials and services that are purchased through the suppliers account for a significant amount of the overall product costs, up to 80% in some industries [39], [42]. With so much dependent on effective suppliers, the selection of poorly performing suppliers can have serious consequences that can risk the success of a business [38], [41], [43]. Supplier selection (SS) requires assessing candidate suppliers on their capabilities with the goal of providing a continuous flow of service and material to support the business activities [31], [41]. This includes collecting data and then analyzing the selection aspects that may influence the final success of the business [33]. Generally speaking, the best suppliers are the ones which supply products or services that are able to match or go beyond the requirements of the business [37]. The selection of the best suppliers is dependent on a number of alternatives and usually conflicting criteria, making supplier selection an MCDM problem [44], [45]. These criteria may be qualitative and quantitative in nature, such as quality and price [36], [37], [39], [45]–[49]. A preferred supplier may be associated with the lowest cost, but also supplier’s products with lower quality, or e.g. poor timely delivery performance may be of concern [31]. Traditionally, suppliers were selected based on cost alone, but now consideration of other criteria is taking place and the decision process is moving towards a trend of searching for fewer, more trustworthy, and more collaborative partners that can form longer-term relationships [32], [39], [43], [46], [50], [51]. Focusing on cost criteria alone can lead to a business purchasing the cheapest alternative and leave them with a product that is not necessarily capable of functioning as originally designed, hence causing great potential hits to business competitiveness [51] 20 The current trend in research in this field is to create mathematical models using decision making techniques [52]. They usually involve some form of pre-qualification that takes place from the pool of potential suppliers, before the selection of the best supplier from the ones that pass the minimum business performance requirements [43], [53].When businesses want to select a supplier selection method, their specific needs must be accounted for, therefore there is need for a certain level of flexibility with testing a sufficient number of different selection methods (here MADM methods) depending on various applications or scenarios [35]. There are numerous case studies that have used MCDM for the supplier selection problem. Hruška et al. [54] proposed a model using AHP and applied it to an example that selects the best supplier among three potential candidates. Wang [55] developed a model using AHP for the supplier selection of maintenance and repair parts. Kamath [56] proposed a methodology using AHP to assess raw material suppliers for a steel pipe manufacturing plant. Tahriri et al. [57] used AHP and developed a supplier selection model for a steel manufacturing company. Hemaida and Schmits [58] developed a model using AHP for the selection of the optimal supplier to subcontract for a paint-dipping tank. Haridasan and Sudharsan [59] used AHP to develop a rating system for supplier selection of pipes for the engineering construction industy. John et al. [60] worked on a study using AHP to assess suppliers for valves. Tam and Tummala [61] created a model using AHP for selection of a telecommications system supplier. Hudymáčová et al. [62] developed a methodology using AHP for supplier selection of grub screw parts. A fuzzy version of AHP has also been used in the literature. Kahraman et al. [63] used a fuzzy AHP model for supplier selection of aspirators for a white goods manufacturer. Chan et al. [64] created a method 21 for the selection of a global supplier by implementing fuzzy AHP. Kilincci and Onal [65] used fuzzy AHP to develop a process of supplier selection for a washing machine production company. Other techniques used in the litrature to evaluate suppliers include e.g. the fuzzy TOPSIS method. Sevkli et al. [66] proposed a fuzzy TOPSIS model to select forging parts for propellor shafts. Kumar et al. [67] illustrated a model using fuzzy TOPSIS for a steel manufacturing plant that is seeking raw materials. Gupta and Barua [68] created a study using fuzzy TOPSIS to select suppliers for an automobile company. Nag and Helal [69] used fuzzy TOPSIS to select a supplier for a pharmaceutical distributor. Hsu and Hu [70] used ANP (analtyic network prcess) to incorporate hazardous substance management to the supplier selection problem. Tan et al. [71] developed a model using ANP and applied it for the supplier selection of a diesel engine manufacturing firm. Alidrisi [72] showed a model for the supplier selection problem for electric companies using ANP. Gencer and Gurpinar [73] used ANP to select a supplier for an electronic company. Xiang, Feng and Yong [74] proposed a method based on ANP for the supplier selection of building engineering materials. Vinodh et al. [75] developed a model using fuzzy ANP for the selection of a supplier for an electronic switch manufacturing company. Dargi et al. [76] developed a framework to support the selection of a supplier in the automotive industry. Pang [77] proposed a methodology using fuzzy ANP to select the best supplier for a technology manufacturing firm purchasing key components for a new product. Kang, Lee and Yang [78] proposed a model using fuzzy ANP to for the selection of packaging company for the semiconductor industry. Wei et al. [79] proposed 22 a model using fuzzy ANP to help the managers generate weights for the suppleir selection problem. Abdel-Baset et al. [80] developed a model using VIKOR for the supplier selection for an importing company. Cheraghalipour et al. [81] considered a framework using VIKOR to select a supplier for an agricultural industry corporation. Sanayei, Mousavi and Yazdankhah [82] proposed a fuzzy VIKOR method to select a supplier for new components of a new product in the automobile part manufacturing industry. Dai, Liu and Zhang [83] proposed a methodology using fuzzy VIKOR for supplier selection of the optimal logistic service provider. Birgun and Cihan [84] developed a model using ELECTRE and illustrated for a computer hardware manufacturing firm searching for a supplier of their new part. Kumar et al. [85] developed a method using ELECTRE and demonstrated the supplier selection for spherical roller bearing. Cristea and Cristea [86] proposed a methodology using ELECTRE to select the optimal supplier for the flexible packaging industry. Sevkli [87] proposed using fuzzy ELECTRE to select supplier of forging parts for propeller shafts. Hanane, Brahim and Bouchra [88] proposed a methodology using PROMETHEE to select suppliers of process chemicals used for refining processes. Chang et al. [89] proposed a method that uses fuzzy DEMATEL to develop supplier selection criteria. Nouranifar and Montazer [90] suggested using fuzzy COPRAS for the selection of optimal raw materials supplier. The summary of the above case study applications can be found in Table 2.1. 23 Table 2-1 Recent examples of MCDM used in supplier selection problems MCDM Study Refer-ence AHP A model is proposed with an application of a manufacturing company selecting optimal selection from three potential suppliers. [54] AHP A model is developed to select a supplier for maintenance and repair parts. [55] AHP A methodology is proposed to evaluate suppliers of raw materials for a steel pipe manufacturing firm. [56] AHP A model was developed for a steel manufacturing company to select suppliers. [57] AHP A model was developed to find the best supplier to select to subcontract for a paint-dipping tank. [58] AHP A rating system was developed for supplier selection of the purchase of pipes for the engineering construction industry. [59] AHP A study was done to evaluate the suppliers of valves for a company. [60] AHP A model is created for the selection of a vendor for telecommunications system. [61] AHP A methodology was developed to select a supplier for grub screw component parts. [62] Fuzzy AHP A model is used to select a supplier for aspirators for a white goods manufacturer. [63] Fuzzy AHP A method is created for the global supplier selection process. [64] Fuzzy AHP A process is developed for the supplier selection for a washing machine production company. [65] Fuzzy TOPSIS A model for supplier selection is proposed for selection of forging parts for propeller shafts. [66] Fuzzy TOPSIS A model for supplier is illustrated for a steel manufacturing plant looking for raw materials. [67] Fuzzy TOPSIS A study on selection suppliers on the basis of green innovation ability for an automobile company. [68] Fuzzy TOPSIS A method of supplier selection for a pharmaceutical distributor. [69] ANP An approach is presented that incorporates hazardous substance management into supplier selection. [70] 24 Table 2-1 Continued MCDM Study Refer-ence ANP A model is developed for a diesel engine manufacturing firm to assess its suppliers. [71] ANP A model is presented for the supplier selection problem for electric companies. [72] ANP A model is developed for the selection of suppliers for an electronic company. [73] ANP A method is proposed for the selection of supplier of building engineering materials [74] Fuzzy ANP A model has been developed for the supplier selection for an electronic switch manufacturing company. [75] Fuzzy ANP A framework is developed to give support to the supplier selection in the automotive industry. [76] Fuzzy ANP A methodology is proposed for selection of an optimal supplier for a technology manufacturing firm looking to purchase the key components of new products. [77] Fuzzy ANP A model is proposed to select a packaging company for the semiconductor industry. [78] Fuzzy ANP A model was proposed to help in selecting of weights for the supplier selection problem [79] VIKOR A framework was developed and applied for optimal supplier selection for an importing corporation. [80] VIKOR A framework is considered for supplier selection for an agricultural industry corporation. [81] Fuzzy VIKOR A method is proposed for the supplier selection of components for a new product for the automobile part [82] Fuzzy VIKOR A methodology is proposed in order to select the best logistic service provider. [83] ELECTRE A model was developed and illustrated for a computer hardware manufacturing firm seeking supplier for the sub-part of a new model. [84] ELECTRE A method is used to show the selection of a supplier for spherical roller bearing out of available alternatives. [85] ELECTRE A methodology is proposed to select the best supplier in the flexible packaging industry. [86] Fuzzy ELECTRE A method was proposed for the supplier selection for forging parts for propeller shafts. [87] 25 Table 2-1 Continued MCDM Study Refer-ence PROMETHEE A methodology is proposed for the supplier selection of process chemicals used for refining processes. [88] Fuzzy DEMATEL A method is proposed for the development of supplier selection criteria [89] Fuzzy COPRAS A model is proposed for the selection of the optimal supplier of raw materials for a firm. [90] Overall, from the conducted review it appears that one of the most widely used MCDM techniques for supplier selection problems is AHP. However, it has the disadvantage of potentially suffering from rank reversals and inconsistencies due to the use of pairwise comparisons [91], [92]. Additionally, as the number of criteria and alternatives increase, it required high computational time [93]. Fuzzy AHP involves making pairwise comparisons one at a time between ‘qualitative’ factors with fuzzy data, which has been occasionally regarded as “tedious an cumbersome” [94], [95]. Similarly to AHP, rank reversals can occur in fuzzy AHP, especially when a new alternative is included [91]. Also, a disadvantage of Fuzzy AHP is that it consists of complicated fuzzy operation and lacks ways to address consistency [96]. In contrast, one of the limitations that Madi et al. [97] stated for most fuzzy TOPSIS methodologies is that they have reliability issues. A number of fuzzy MCDM hybrids have been also proposed in the literature, involving complex computation process and outcomes that may be counterintuitive [98], [99]. According to Mahmoud and Garcia [100], for a method to be most effective, understanding the method should require minimal time and effort because this will lead to better use and effective implementation. 26 In general, non-expert decision makers (DMs) often prefer “simple, more transparent methods”[101]. Other methods exist that can be potentially used for the supplier selection problems, such as the Median Ranking method (which is one of the main methods to be considered in this thesis). In particular, the median ranking method has been shown to be effective for qualitative decision making cases [9]. The method is inspired from an established group decision making technique [102], in the realm of consensus rankings [103]. It generates an optimum solution to the distance-minimizing type of consensus problem. Instead of combining preferences of a number of DMs form a consensus, Yoon and Hwang [9] proposed combining attribute ranks instead to form a consensus ranking, hence, giving the ability to rank the alternatives. 2.4 Material Selection as an MCDM Problem Material selection (MS) is an important part of engineering design and its objective is to choose the most effective materials for a specific application so that the product can perform as intended by designers, according to some predetermined technical requirements [104]–[111]. The MS is critical for competitiveness and profitability of all manufacturing sectors [112], [113]. It is also a crucial aspect to ensure high performance and reliability of the products with lower costs [105], [108]. It can also drastically cause changes to the final design and impact customer satisfaction [114]. Poor selection of a product material can impact the reputation and profitability of the business [106]. 27 Material selection typically occurs during the initial design stages, or when changing the product to fit market demands, or due to past product failure [107]. The easiest way of choosing or replacing a material is to use designers (here DMs) experience or trial and error methods; however, these can be quite time- and resource-consuming and may not lead to an optimal solution [108], [115]. Effective MS consists of determining the product’s property requirements, creating a list of alternatives and finally selecting the optimal material [104], [116]. A material selection problem may take many types of properties into account including electrical, mechanical, physical, chemical properties [111], [117]. Example of these properties would include tensile strength, density, the Young’s modulus, etc. [112], [118]. There already exist a large number of materials available on market for selection in different engineering applications and the number is increasing rapidly by innovations on new material systems (e.g. new composites), each having their own advantages and drawbacks [105], [106], [112], [119]. Hence, it is crucial that the designers have complete understanding of the properties of the materials options in a given application [105], [113]. Many products have failed in the past due to poor material selection and that did not fully map the considered properties to final requirements of the product [113]. These properties can be often determined by conducting engineering tests [120]. Material selection consists of numerous criteria and alternatives that are often conflicting in nature, where trade-offs between the properties may need to be considered; hence raising the application of MCDM methods [105], [106], [109], [121], [122]. MS also usually involves non-commensurable units which may be quantitative and qualitative [105], [112] ,[121], [122]. Since 28 selection of the right material can be a challenging and time-consuming task [105], [106], [115], [119], [121], [122], DMs would benefit from employing some decision-aids to assist the decision making process [107], [115]. There has been extensive use of MCDM in the literature for materials selection in a variety of product designs. Chauhan et al. [123] used SAW for the selection of piezoelectric material for ultrasonic transducers and actuators. Taherian and Nasr [124] used SAW for the material selection of nanocomposite bipolar plate in fuel cells. Senyigit and Demirel [125] used SAW for the selection of packaging material for carbonated drinks. Taherian [126] used SAW for the material selection of composite and metallic bipolar plates in proton exchange membrane fuel cells. Torrez et al. [127] used SAW to obtain the material selection for light-weight naval crafts. Anupam et al. [128] uses SAW for the selection of raw materials for paper and pulp industry. Taka et al. [129] developed an optimal procedure for the material selection of the best tool insert. Mansor et al. [130] used SAW to select the most appropriate thermoplastic matrix based on design specifications. Xie [131] proposed a procedure using TOPSIS for the material selection of electrical insulation. Shanian and Savadogo [132] developed a method using TOPSIS to select material for metallic bipolar plates for polymer electrolyte fuel cell. Milani et al. [120] used TOPSIS to select material for gear systems. Govindan et al. [133] used TOPSIS for the selection of material of bricks for the construction industry. Anupam et al. [134] used TOPSIS for the raw material selection for pulp and papermaking. Jee and Kang [135] developed a procedure using TOPSIS for the selection of optimal material for a flywheel. 29 Li et al. [136] used AHP to determine the optimal material selection for cutting tools. Cao et al. [137] used AHP to determine the selection of material for hosing of an electronic device. Baykan [138] determined the selection of material using AHP for building of a wall. Shimin, Shah and Lokhande [139] used AHP to conduct the material selection for semiconductor switching devices in electric vehicles. Sia et al. [140] developed a model using AHP for screw manufacturing while minimizing environmental impacts. Maskepatil, Gandigude and Kale [141] used AHP for the material selection of wind turbine blades. Shanian and Savadogo [142] used ELECTRE to select the material for mass-produced non-heat-treatable cylindrical cover material. Hassan, Rosli and Redzuan [143] used ELECTRE to select material for a badminton racket. Shanian and Savadogo [144] used ELECTRE for the material selection of bipolar plates for polymer electrolyte membrane fuel cell. Mangera et al. [145] used ELECTRE for material selection for a paediatric prosthetic knee. Kiani, Liang and Gross [146] proposed a procedure using VIKOR to aid in selecting repair material for concrete structures. Ishak, Malingam and Mansor [147] used VIKOR to select the material of natural fibers used in the composites for a car’s front hood. Chatterjee and Chakraborty [148] developed a model for material selection using COPRAS. Mahmoudkelaye et al. [149] used ANP for the material selection of an exterior building enclosure. Jiao et al. [150] developed an approach using PROMETTHEE for the material selection problem and illustrated it for the selection of material for a wing-spar of a human-powered aircraft. . The summary for the literature mentioned above can be seen in Table 2.2. 30 As was the case for the supplier selection MCDM, each MCDM method used for material selection problems has had benefits and drawbacks and it cannot be concluded that a single techniques is generally the best [151], [152]. The mechanics of most MCDM methods are not easy to interpret and at times not understood easily, and by untrained users can often be seen as “scientific witchcraft”[152]. It is crucial for the user to have easy interpretation in order for the selected methods to be practical tools and aid decision makers in day-to-day problems [152]. Table 2-2 Recent examples of MCDM used in material selection problems Method Description Reference SAW Material Selection for piezoelectric material for ultrasonic transducers and actuators. [123] SAW Material Selection for nanocomposite bipolar plate in proton exchange membrane fuel cells. [124] SAW Material selection for carbonated soft drink packaging. [125] SAW Material Selection of composite and metallic bipolar plates in proton exchange membrane fuel cells. [126] SAW Material Selection for light-weight naval crafts. [127] SAW Material Selection for raw material for pulp and paper. [128] SAW Material selection of tool and work piece combination. [129] SAW Material Selection of thermoplastic matrix. [130] TOPSIS Material Selection for electrical insulation. [131] TOPSIS Material Selection of metallic bipolar plates for polymer electrolyte fuel cell. [132] TOPSIS Material Selection of gear material. [120] TOPSIS Sustainable material selection of bricks for construction industry. [133] TOPSIS Raw material selection for papermaking. [134] TOPSIS Material Selection of a flywheel. [135] AHP Optimal material Selection for cutting tools. [136] AHP Material Selection for housing for electronic device. [137] AHP Material Selection of material for building of a wall. [138] AHP Material Selection for semiconductor switching devices in electric vehicles. [139] AHP Material Selection in screw manufacturing for minimizing environmental impacts. [140] 31 Table 2-2 Continued Method Description Reference AHP Material Selection for wind turbine blade. [141] ELECTRE Material Selection for mass-produced non-heat-treatable cylindrical cover material. [142] ELECTRE Material selection for frame of badminton racket. [143] ELECTRE Material selection of bipolar plates for polymer electrolyte membrane fuel cell. [144] ELECTRE Material selection for paediatric prosthetic knee [145] VIKOR Material selection of repair material for concrete structures. [146] VIKOR Material selection for natural fiber for fiber reinforced composites for car front hood. [147] COPRAS Material selection model based on COPRAS developed. [148] ANP Material selection for building enclosure. [149] PROMETHEE Material selection for wing-spar of a human-powered aircraft. [150] Dyer et al.[153] mentions that understandable and simple methodologies are needed in dealing with MCDM problems. SAW is perhaps the most commonly used MCDM technique [154] in material selection problems. With its clear logic, simple computation and straightforward implementation, it is highly user friendly [155]–[157] and easy to interpret [158]. Among the other MCDM methods, Mousavi-nasab and Sotoudeh-anvari [151] concluded that, aside from a few exceptions, AHP and ELECTRE are generally not appropriate for the material selection problems, mostly due to their computational expenses. Furthermore, The role of weights in TOPSIS is not always intuitive [152]. In comparison of rank reversal problem of several MCDM techniques, as reviewed by Mousavi-nasab and Sotoudeh-anvari [151], SAW has had few rank reversals and the TOPSIS has performed the worst in this regard. Kaliszewski and Podkopae [152] describes SAW as 32 belonging “nowadays to the folklore of the domains of decision making and expert systems” and “hardly needs much explanation” of the decision mechanisms. In fact, they describe SAW as a “natural language” and propose using it as a metamodel to explain the mechanics of the more complex (and less intuitive) MCDM techniques. Additionally, Mousavi-nasab and Sotoudeh-anvari [151] name SAW as one of the most important MCDM techniques for the material selection problem. 33 Methodology 3.1 Background Selecting a new material or replacing an older one is often a difficult task for designers due to the sheer number of materials available. Different factors have to be considered such as the suitability and quality of the material and finding an effective supplier to supply it consistently and promptly. Proper supplier selection can be a crucial task for businesses. Good suppliers allow the lowering of costs and their proper selection can affect the success of the business. They also allow for flexibility and aid in new design and development efforts. All materials have different properties and they all have different benefits and drawbacks for any given application. Properties of materials can be obtained using mechanical tests. Conducting own tests by businesses is often preferred because it ensures reliability of the results and also sometimes the grade and properties of the material is not known. It is typical that the number of materials being considered to be fairly large at an early stage of selection. To simplify the material selection process, it is important to have the potential alternatives to undergo some form of screening using MCDM. The next step would be choosing the smaller number of the screened options for testing [159], and eventually comparing them again using MCDM. As discussed in Chapter 2, the decision making techniques can be loosely divided into two categories: ones that are compensatory and ones that are noncompensatory. The key difference 34 between these two is that compensatory methods can allow trade-offs between attribute values. That is, that good values on some criteria can make up for bad values on other criteria. However, in noncompensatory techniques that is not the case. Compensatory techniques are generally more cognitively demanding. The selection of appropriate MCDM methods for a given application can vary in how accurate they may be, as well as how much effort is required to perform them [160], [161]. These factors can affect what type of strategy a DM will use [161]. Decision makers tend to gravitate towards minimizing cognitive effort [162], [163]. Some DMs may steer away from using certain selection processes because of the large amount of effort required and instead opt for a simpler technique [162]. Cognitive effort is the total amount of cognitive resources that are needed overall for a decision-making task [164], [165]. A technique considering just one attribute at a time may require less effort and have lower accuracy for some decision problems, than one that takes into account more attributes at a time for calculations [160]. A typical DM would be unwilling to use more cognitive effort than is necessary for the level of confidence that he/she hopes to get for a particular scenario [17]. If the level of confidence required for a decision situation is high or if the importance of the situation is high, then the DM is more likely to use a higher amount of cognitive effort. 35 Another factor the DM may consider in selecting the MCDM technique is how much time is available for implementation of the project. In scenarios where time is critical, techniques that require less cognitive effort may be preferable, such as EBA or lexicographic methods, to quicken the decision-making process [166]. In less time sensitive situations, the DM would be more willing to make additional effort to get more accurate results using more sophisticated methods [166]. 3.2 Step-by-Step Procedure This section explains the multistage MCDM strategy, used to solve the problem of selecting the best product supplier. The method is flexible in that it can be used for various applications with different accuracy and effort levels depending on the requirements of the given business case. The idea is to select the best material by screening the suppliers from business performance perspective first, followed by a technical material selection problem solving. The first stage, i.e. supplier selection (SS) MCDM, would normally encompass qualitative (and perhaps a few quantitative) criteria; whereas the second stage (material selection MCDM from the screened suppliers) would normally entail quantitative criteria where the alternatives can undergo different mechanical tests. The steps of the proposed process can be seen in Figure 3.1. The process has also been exemplified through a case study in the current research for a business involving insulated skirting products (to be presented in the next Chapter). Remark: The logic behind the order of decision making in this methodology is as follows. It is common that the number of material options and their suppliers for a target product is fairly large in practice. It would not be feasible to request samples from all the existing suppliers for testing 36 their materials one by one, especially if the pool of suppliers is large. Hence, some form of ore-screening must take place to reduce the number of selections, e.g. using a set of business criteria under a supplier selection MCDM. Once top suppliers are screened, material samples can be inquired from them and tested. Also, conducting the material and supplier selection problems at the same time would not be recommended analytically, as it would force the DM to compare the business requirement attributes with those of material properties, e.g. during criteria weighting; an example would be when trying to compare a material delivery time from suppliers with the material toughness and figuring out which attribute would be more important. The proposed methodology is customizable in the sense that the criteria selection can be redefined based on the requirements of a given client. This would be particularly suitable for small companies which do not have high experience to deal with complex decision problems. An example of such customizable criteria is the supplier location. Because Canada is such a large country, location was included in this case study as some local manufacturers are significantly far away and would bring high transportation costs. However, for another imaginary scenario where one may consider international suppliers within a given country, location may not be of primary concern, due to shipment costs being similar. For example, assuming Chinese suppliers only, the costs of freight to Canada will not be very different if the choice of manufacturer was between Tianjin and Beijing. In contrast, if the choice is between suppliers in British Columbia and Ontario, that would meaningfully bring different transportation costs into the decision matrix. 37 Figure 3-1 Proposed workflow for a decision-making process involving both supplier selection (SS) and material selection (MS) 38 3.2.1 Step 1: Find potential suppliers: This can be accomplished by conducting a survey and contacting numerous potential suppliers of the material that has been chosen in the design stage and taking notes about each individual alternative. 3.2.2 Step 2: Creating the SS decision matrix: The decision matrix represents the alternatives, and attributes and weights with respect to the objective of the problem. This matrix will have two parts; the first part will have the alternatives undergoing a screening with “deal breakers”; for simplicity, the latter can merely have yes-no type of data, where if any of the criteria is not satisfied, then that alternative (supplier) can be discarded. In the second part of the matrix, more qualitative data of verbal form (e.g. Poor, Fair, Good, Very Good, and Excellent) can be used. 3.2.3 Step 3: Choose SS MCDM method: Depending on the business situation regarding required accuracy and time, different MCDM methods can be used on the alternatives (suppliers) that have passed the screening in step 2. If the overall good performance is required for decision making with high accuracy, then a model that is compensatory, such as the Median Ranking Method, would be appropriate for the application. Otherwise, if it is a time-critical situation and the decision accuracy level is not deemed to be crucial, then a simple noncompensatory model, such as the Lexicographic Method, would be sufficient for the application. 3.2.4 Step 4: Order samples from e.g. the top ranked suppliers: Select e.g. the top 3 alternatives from the appropriate MCDM technique found in step 3 and then request from them samples of their materials that are available for your product. 39 3.2.5 Step 5: Test the material samples According to the criteria selected by a technical DM or designer, conduct the appropriate mechanical, electrical, etc. tests to ensure the properties of the candidate materials map correctly to the final requirements of the product. 3.2.6 Step 6: Creating the MS decision matrix: This matrix will consist of all the experimental results found in the previous step. Most of the data will be quantitative (e.g. elastic moduli) and a few qualitative (e.g. aesthetics). The decision matrix should represent the material alternatives, design and selection attributes as well as their weights with respect to the final objective and application of the product. 3.2.7 Step 7: Choose MS MCDM method(s): Depending on the situation regarding required accuracy and time availability, different MCDM may be applied on the alternatives that have been listed in Step 6. If the results accuracy for decision making is critical and ample time is available, then a model that is compensatory, such as the SAW or BWM, will be appropriate for the application. Otherwise, if it is a time-critical situation then a simple noncompensatory model, such as the Lexicographic Method, would be sufficient. 3.2.8 Step 8: Select the final material Select the top alternative material from the MCDM analysis in the previous step and use it for the product, potentially through partnership with the supplier of that material selected in Step 3. If no satisfactory material is found, the entire process may be re-iterated by considering other options from the pool of potential suppliers found in step 1. 40 Case Study 4.1 Background A distributing company based in Canada supplies the Canadian market with insulated skirting products (Figure 4.1) using material suppliers based in the US. However, recently they have faced higher costs associated with importing products to Canada due to unfavorable exchange rates, lowering competitiveness and the profitability of their business. Figure 4-1 Insulated skirting product Over the past years, Canada has frequently experienced favorable exchange rates (Figure 4.2) with the US which has made importing products relatively cheaper and attractive over local means of production. However, in more recent times, the increases exchange rates have left businesses that exploited the above option with difficulties due to more expensive import costs. 41 Figure 4-2 Historical exchange rates for CAD-USD (Data source: Bank of Canada, used according to terms of use) Also, the recent rhetoric over trade wars and new tariffs have made these businesses more anxious with regards to the stability of their international supply streams. Naturally, some of these businesses seek more risk-free options and have opted to shifting their focus on obtaining supplies locally. However, many smaller businesses cannot afford large consulting firms to assist in this transitional endeavor and neither have experience for this form of complex multiple criteria decision-making problems. Here we intend to use the methodology of Chapter 3 to assist a Canadian company in this decision process as follows. 0.911.11.21.31.41.52007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017CAD - USD Exchange Rates42 From preliminary meetings with the company, we defined the MCDM problem constraints as such:  The product will be made of vinyl (due to its already proven performance);  The product will be made using extrusion processes (given its simple cross-section profile);  The product will be preferably supplied by a local manufacturer (to save shipment costs). In meetings with the company we also determined the in-service performance criteria required for the new product, and mapped them to required material tests as follows. Ease of installation: One of the main concerns for the insulation skirting installers was at least making the new product as easy to deal with as their current product. Their current product could be bent around corners without cracking and the need of cutting new pieces (Figure 4.3). Contractors have enjoyed the current product due to the ability to install it easily with minimum waste. Also, this means that they would be more likely recommend it to their other clients. This service property was determined to be toughness (from material properties point of view) and would be determined by conducting a tensile test on the material samples. Impact resistance: This was important so that if a family is playing e.g. sports around the house or if a pebble is kicked up by the lawnmower and it hits the side of the house, it does not puncture and break the product. This will be determined, from materials property perspective, by using a Gardner impact tester on material samples. 43 Aesthetics: The product should look attractive to customers since it is essentially an aesthetic part of the house. The new product should look at least as good as the current product. This will be tested by conducting a survey and generating a ‘group decision making’ score using the MDL method. Figure 4-3 How the installed product looks as it is bent around a corner Scratch resistant: If some sharp object is being moved close to the wall during service and is dragged along the side of the wall, it should not leave a scratch on the product. This will be tested, from material performance perspective, by running a scratch test method and finding scores using the MDL method. Resistant to weathering: It is important for the business provider whether or not there will be any degradation of the product once in is installed and exposed to the outdoor environment. To test this property, the samples will be exposed to simulated extreme environmental conditions by 44 submerging them in water for 24 hours in an environmental testing chamber, and then be tested physically to see if they display differences in density compared with unexposed samples. Methodological details of the identified material tests can be founds in the Appendix A. Remark: Manufacturing cost was not included as part of the decision criteria in this case study as the company was already gaining considerable savings through the replacement of international supplier with local suppliers (i.e. avoiding high exchange rates). The quality and properties of the material itself were of primary concern. 4.2 The Decision Making Process 4.2.1 Step 1: Find Potential Suppliers Following the workflow proposed in Chapter 3, the first step of decision making was formed by searching for plastic manufacturers that operated locally. After the search, a database was created with all the suppliers that could potentially produce the skirting product locally. The contact information of each company was included in the database as well. All the companies were contacted via email initially and then over the phone for further discussions. Overall, dozens of local plastic manufacturers were contacted. Notes were carefully taken according to the criteria required for supplier selection (to be discussed in next step). The companies that did not respond to our inquiries via email were discarded from the analysis. 4.2.2 Step 2: Creating the SS Decision Matrix The notes taken in step 1 were used to construct the SS decision matrix. The matrix was divided into two parts; the first contained yes-no type of data to help screening the potential suppliers in a simple manner. The criteria for this part were chosen as: 45  Material Availability (MA): Whether the suppliers are able to supply the material that was requested; i.e. PVC.  Technological capability (TC): Whether they have the technical ability to perform extrusion processes.  Ability to supply amount: Whether they can supply the minimum amount of the material that has been ordered (20,000 feet for each profile). If any of the criteria for a given supplier receives a “no”, then that company will not be considered in the subsequent decision making. In the second part of the matrix, the verbal criteria (i.e. Poor, Fair, Good, Very Good, and Excellent) were used. The criteria for this part were:  Geographical Location: Where, nationally, the supplier is located. The closer is it to the distributer location, the better; as the delivery costs will be lower.  Communication: How quick were the suppliers in responding to inquiries and how thorough were their responses.  Years in business (YIB): How much experience they have in their area of expertise.  Willingness: How much interest they showed in the project and partnership. This was assessed e.g. in the form of asking for additional meetings and showing willingness to take part in the design process. The ensuing decision matrix can be seen in Table 4.1. For the first part, with yes-no data, the screening of the suppliers was performed per Table 4.2. Then, the DM was left with the decision matrix in Table 4.3, which can be used for the final SS decision making using an MCDM technique. 46 Table 4-1 The Supplier Selection decision matrix Company MA TC Ability to supply amount Location Communication YIB Willingness A Yes Yes Yes E E E G B Yes No Yes P E G F C Yes Yes Yes P E VG VG D Yes Yes Yes E VG E VG E Yes Yes Yes P E VG E F Yes No Yes P E E VG G Yes No Yes E E E F H Yes No Yes E E VG F I Yes No Yes E E P F J Yes No Yes E VG E F K Yes Yes No P E E F L Yes No Yes P VG E G M Yes Yes Yes P VG E E N Yes Yes Yes F P VG VG O Yes No Yes P P E VG P No No Yes VG E P E Q No No Yes VG G P G R Yes Yes No P VG E P P: Poor; F: Fair; G: Good; VG: Very Good; E: Excellent 47 Table 4-2 Results of the screening of the suppliers Company MA TC Ability to supply amount Screening outcome A Yes Yes Yes Pass B Yes No Yes Fail C Yes Yes Yes Pass D Yes Yes Yes Pass E Yes Yes Yes Pass F Yes No Yes Fail G Yes No Yes Fail H Yes No Yes Fail I Yes No Yes Fail J Yes No Yes Fail K Yes Yes No Fail L Yes No Yes Fail M Yes Yes Yes Pass N Yes Yes Yes Pass O Yes No Yes Fail P No No Yes Fail Q No No Yes Fail R Yes Yes No Fail 48 Table 4-3 Decision matrix to be used for SS MCDM Screened Companies Location Communication YIB Willingness A E E E G C P E VG E D E VG E VG E P E VG E M VG VG E E N F E VG VG P: Poor; F: Fair; G: Good; VG: Very Good; E: Excellent 4.2.3 Step 3: Choose SS MCDM Method If the results required for SS decision making should be highly accurate and time is available, then a model that is compensatory, such as the Median Ranking Method, would be suitable. Otherwise, if it is a time-critical situation, then a simple noncompensatory model such as the Lexicographic Method may be sufficient for the application. For this case study, both methods were used to demonstrate whether they would differ in their decisions. Scenario 1: In this scenario, the noncompensatory lexicographic method was tested. The attributes were determined to be in the order of importance of:  Years in Business  Location  Willingness  Communication 49 Using the lexicographic method [8], the alternatives can be screened using the most important criterion first, and the most effective alternative(s) are accordingly selected. If there is a tie between two or more alternatives, then these alternatives are compared under the next important criterion; and this process continues until the best one is selected or comparisons have been made under all of the criteria. For the current application, the Lexicographic process for the decision matrix can be seen in Table 4.4. For the suggested most important criterion by the distributer, years in business, the best alternatives are found to be companies A, D and M that are tied. Table 4-4 Results from the lexicographic method with YIB as the most important criterion Company Location Communication Years in Business Willingness A E E E G D E VG E VG M VG VG E E P: Poor; F: Fair; G: Good; VG: Very Good; E: Excellent At this stage, we already found the top 3 companies that we were searching for and the SS decision process can end. It can be seen that the Lexicographic method is quick and easy to implement for decision making; however it does not give detailed ranking of the alternatives. Scenario 2: In this scenario, given the time for project implementation it would be best to apply a compensatory technique, i.e. here the median ranking method. As explained in Chapter 2 50 (section 2.2.11), in this method the first step is to obtain ranks from the given data. When there is a tie between two options, then the alternatives that are tied should receive an average rank. The decision matrix of Table 4.3 will translate to the ranks shown in Table 4.5. Table 4-5 The SS decision matrix after data is converted to ranks Company Location Communication YIB Willingness A 1.5 2.5 2 6 C 5.5 2.5 5 2 D 1.5 5.5 2 4.5 E 5.5 2.5 5 2 M 3 5.5 2 2 N 4 2.5 5 4.5 Next, the importance of the attributes were determined using the Modified Digital Logic approach with direct input from the client; results can be found in Table 4.6. The MDL considers predominance of one criterion to another at a time and hence it is simple to implement for non-expert DMs. The comparison was made sequentially in a pairwise manner in order to learn the preference of one criterion over another until all the criteria comparisons were fulfilled. Table 4-6 The MDL implementation for the SS MCDM problem Goals Number of Possible Decisions Positive Decisions Weighting Factors 1 2 3 4 5 6 Location 3 1 3 7 0.292 Communication 1 1 1 3 0.125 YIB 3 3 3 9 0.375 Willingness 1 3 1 5 0.208 51 Now that the DM attains the criteria ranks and the weights, we can use the following equation 2.19 to determine the total distance of each alternative: 𝑑𝑖𝑘 = ∑ 𝑤𝑗|𝑠𝑖𝑗 − 𝑘|𝑛𝑗=1 . For the first alternative A, e.g. one can calculate the rank distances as: 𝑑𝐴1 = 0.292|1.5 − 1| + 0.125|2.5 − 1| + 0.375|2 − 1| + 0.208|6 − 1| = 1.75 𝑑𝐴2 = 0.292|1.5 − 2| + 0.125|2.5 − 2| + 0.375|2 − 2| + 0.208|6 − 2| = 1.04 𝑑𝐴3 = 0.292|1.5 − 3| + 0.125|2.5 − 3| + 0.375|2 − 3| + 0.208|6 − 3| = 1.50 𝑑𝐴4 = 0.292|1.5 − 4| + 0.125|2.5 − 4| + 0.375|2 − 4| + 0.208|6 − 4| = 2.08 𝑑𝐴5 = 0.292|1.5 − 5| + 0.125|2.5 − 5| + 0.375|2 − 5| + 0.208|6 − 5| = 2.67 𝑑𝐴6 = 0.292|1.5 − 6| + 0.125|2.5 − 6| + 0.375|2 − 6| + 0.208|6 − 6| = 3.25 For alternative C: 𝑑𝐶1 = 0.292|5.5 − 1| + 0.125|2.5 − 1| + 0.375|5 − 1| + 0.208|2 − 1| = 3.21 𝑑𝐶2 = 0.292|5.5 − 2| + 0.125|2.5 − 2| + 0.375|5 − 2| + 0.208|2 − 2| = 2.21 𝑑𝐶3 = 0.292|5.5 − 3| + 0.125|2.5 − 3| + 0.375|5 − 3| + 0.208|2 − 3| = 1.75 𝑑𝐶4 = 0.292|5.5 − 4| + 0.125|2.5 − 4| + 0.375|5 − 4| + 0.208|2 − 4| = 1.42 𝑑𝐶5 = 0.292|5.5 − 5| + 0.125|2.5 − 5| + 0.375|5 − 5| + 0.208|2 − 5| = 1.08 𝑑𝐶6 = 0.292|5.5 − 6| + 0.125|2.5 − 6| + 0.375|5 − 6| + 0.208|2 − 6| = 1.79 For alternative D: 𝑑𝐷1 = 0.292|1.5 − 1| + 0.125|5.5 − 1| + 0.375|2 − 1| + 0.208|4.5 − 1| = 1.81 52 𝑑𝐷2 = 0.292|1.5 − 2| + 0.125|5.5 − 2| + 0.375|2 − 2| + 0.208|4.5 − 2| = 1.10 𝑑𝐷3 = 0.292|1.5 − 3| + 0.125|5.5 − 3| + 0.375|2 − 3| + 0.208|4.5 − 3| = 1.44 𝑑𝐷4 = 0.292|1.5 − 4| + 0.125|5.5 − 4| + 0.375|2 − 4| + 0.208|4.5 − 4| = 1.77 𝑑𝐷5 = 0.292|1.5 − 5| + 0.125|5.5 − 5| + 0.375|2 − 5| + 0.208|4.5 − 5| = 2.31 𝑑𝐷6 = 0.292|1.5 − 6| + 0.125|5.5 − 6| + 0.375|2 − 6| + 0.208|4.5 − 6| = 3.19 For alternative E: 𝑑𝐸1 = 0.292|5.5 − 1| + 0.125|2.5 − 1| + 0.375|5 − 1| + 0.208|2 − 1| = 3.21 𝑑𝐸2 = 0.292|5.5 − 2| + 0.125|2.5 − 2| + 0.375|5 − 2| + 0.208|2 − 2| = 2.21 𝑑𝐸3 = 0.292|5.5 − 3| + 0.125|2.5 − 3| + 0.375|5 − 3| + 0.208|2 − 3| = 1.75 𝑑𝐸4 = 0.292|5.5 − 4| + 0.125|2.5 − 4| + 0.375|5 − 4| + 0.208|2 − 4| = 1.42 𝑑𝐸5 = 0.292|5.5 − 5| + 0.125|2.5 − 5| + 0.375|5 − 5| + 0.208|2 − 5| = 1.08 𝑑𝐸6 = 0.292|5.5 − 6| + 0.125|2.5 − 6| + 0.375|5 − 6| + 0.208|2 − 6| = 1.79 For alternative M: 𝑑𝑀1 = 0.292|3 − 1| + 0.125|5.5 − 1| + 0.375|2 − 1| + 0.208|2 − 1| = 1.73 𝑑𝑀2 = 0.292|3 − 2| + 0.125|5.5 − 2| + 0.375|2 − 2| + 0.208|2 − 2| = 0.73 𝑑𝑀3 = 0.292|3 − 3| + 0.125|5.5 − 3| + 0.375|2 − 3| + 0.208|2 − 3| = 0.90 𝑑𝑀4 = 0.292|3 − 4| + 0.125|5.5 − 4| + 0.375|2 − 4| + 0.208|2 − 4| = 1.65 𝑑𝑀5 = 0.292|3 − 5| + 0.125|5.5 − 5| + 0.375|2 − 5| + 0.208|2 − 5| = 2.40 𝑑𝑀6 = 0.292|3 − 6| + 0.125|5.5 − 6| + 0.375|2 − 6| + 0.208|2 − 6| = 3.27 53 For alternative N: 𝑑𝑁1 = 0.292|4 − 1| + 0.125|2.5 − 1| + 0.375|5 − 1| + 0.208|4.5 − 1| = 3.29 𝑑𝑁2 = 0.292|4 − 2| + 0.125|2.5 − 2| + 0.375|5 − 2| + 0.208|4.5 − 2| = 2.29 𝑑𝑁3 = 0.292|4 − 3| + 0.125|2.5 − 3| + 0.375|5 − 3| + 0.208|4.5 − 3| = 1.42 𝑑𝑁4 = 0.292|4 − 4| + 0.125|2.5 − 4| + 0.375|5 − 4| + 0.208|4.5 − 4| = 0.67 𝑑𝑁5 = 0.292|4 − 5| + 0.125|2.5 − 5| + 0.375|5 − 5| + 0.208|4.5 − 5| = 0.71 𝑑𝑁6 = 0.292|4 − 6| + 0.125|2.5 − 6| + 0.375|5 − 6| + 0.208|4.5 − 6| = 1.71 The summary of these distances can be expressed in the matrix form as: 1st 2nd 3rd 4th 5th 6th A 1.75 1.04 1.50 2.08 2.67 3.25 C 3.21 2.21 1.75 1.42 1.08 1.79 D 1.81 1.10 1.44 1.77 2.31 3.19 E 3.21 2.21 1.75 1.42 1.08 1.79 M 1.73 0.73 0.90 1.65 2.40 3.27 N 3.29 2.29 1.42 0.67 0.71 1.71 Next, the Hungarian Method was used to assign the ranks to each alternative, based on the following steps [8]: Step 1: Row Reduction. Subtract the minimum value of each row from all the values in that row. 54 1st 2nd 3rd 4th 5th 6th A 0.71 0 0.46 1.04 1.63 2.21 C 2.13 1.13 0.67 0.34 0 0.71 D 0.71 0 0.34 0.67 1.21 2.09 E 2.13 1.13 0.67 0.34 0 0.71 M 1 0 0.17 0.92 1.67 2.54 N 2.62 1.62 0.75 0 0.04 1.04 Step 2: Column Reduction. Subtract the minimum value of each column from all values in the column. 1st 2nd 3rd 4th 5th 6th A 0 0 0.29 1.04 1.63 1.50 C 1.42 1.13 0.50 0.34 0 0 D 0 0 0.17 0.67 1.21 1.38 E 1.42 1.13 0.50 0.34 0 0 M 0.29 0 0 0.92 1.67 1.83 N 1.91 1.62 0.58 0 0.04 0.33 Step 3: Cover the Zeros. Draw the smallest number of lines that will cover all zeros. 55 1st 2nd 3rd 4th 5th 6th A 0 0 0.29 1.04 1.63 1.50 C 1.42 1.13 0.50 0.34 0 0 D 0 0 0.17 0.67 1.21 1.38 E 1.42 1.13 0.50 0.34 0 0 M 0.29 0 0 0.92 1.67 1.83 N 1.91 1.62 0.58 0 0.04 0.33 Since it takes 6 lines to cover all of the zeros, an optimal solution can be found and there is no need to create new zeros. Step 4: Make assignments; the assignments can be seen as highlights below. 1st 2nd 3rd 4th 5th 6th A 0 0 0.29 1.04 1.63 1.50 C 1.42 1.13 0.50 0.34 0 0 D 0 0 0.17 0.67 1.21 1.38 E 1.42 1.13 0.50 0.34 0 0 M 0.29 0 0 0.92 1.67 1.83 N 1.91 1.62 0.58 0 0.04 0.33 Finally, this method could rank the alternatives from first to last. From the Median Ranking results from step 4, we find that the top 3 suppliers are the companies A, then D and then M. 56 4.2.4 Step 4: Order material samples from the top 3 suppliers Since the solutions from the above analyses both suggested A, D, and M companies, we contacted these companies to request material samples, to be used for testing. 4.2.5 Step 5: Test samples In this step we should look for results for the material tests that were determined by the DM in Step 2. The tests were conducted on samples sent from companies A, D and M and were compared with the current supplier’s product, which is referred to as ‘control’ hereafter. Tensile testing: Results from the tensile tests were used to determine the toughness of the material samples. Toughness is the ability of a material to absorb energy, plastically deform and resist fracturing when force is applied. This can be determined by calculating the total area up to fracture under a stress-strain curve. The average toughness of the three repeats will be fed into the subsequent MS MCDM for the decision making. At the peak stress point the material begins to undergo damage but the final failure occurs later. The failure point was determined visually at the point where the test specimen begins to split apart. Due to various reasons such as micro-cracks in the material, the repeats of each material do not fail (break) at the same exact strain point. This is the reason for the large error bars seen in Figure 4.4; i.e. close to the end of each curve (after failure), the standard deviation becomes very large. A comparison of materials before the final breakage can be seen in Figure 4.5. This graph contains the curves of the samples until the first point of failure (shown as circles in Figure 4.4). As such, here we get a more clear comparison of the materials, and under reasonable error levels. 57 Figure 4-4 Stress versus strain response of the material samples from top ranked suppliers. The circles represent the earliest (weakest) breakage points among the test repeats of a given company material Figure 4-5 Stress and strain response of the material samples before the failure points of the weakest repeat 01020304050600 0.2 0.4 0.6 0.8 1 1.2Stress (MPa)StrainControlCompany ACompany DCompany M58 Here we can see that the error bars for each of the materials except for Company D are fairly small. It is clear from the above results that on average all the top three suppliers can provide a material with superior toughness compared to the current product. Namely, the toughness values of Control, A, D, M options were measured (using the under curve areas upon to the final points of the curves then averaged) to be 3.15, 39.35, 15.69, and 9.82 J/m3, respectively. Scratch resistance testing: The results from the scratching tests were as follows. For samples of company A:  A scratches M  A does not scratch D  A does not scratch Control For samples of company D:  D scratches M;  D scratches A;  D does not scratch the Control. For samples of company M:  M does not scratch D;  M does not scratch A;  M does not scratch the Control For the control samples:  Control scratches M  Control scratches A 59  Control does not scratch D From the results above, the DM can conclude that the D and the Control samples are the most scratch resistant and have similar surface hardness. Next preference under this criterion would be company M and in the last place is company A. The DM can use the MDL with the above results in order to generate ‘numerical scores’ of these alternatives, as seen in Table 4.7 below. Table 4-7 Numerical results of the scratch resistance test using MDL method Options 1 2 3 4 5 6 Positive decisions Weights (scores) Control 3 2 3 8 0.33 A 1 1 3 5 0.21 D 2 3 3 8 0.33 M 1 1 1 3 0.13 Impact testing: The results from the impact tests for the Control, Company A, Company D and Company M samples can be seen in Figures 4.6, 4.7, 4.8 and 4.9, respectively. Mean failure height (h) parameter in each test (also see the Appendix A) was calculated using equation 4.1: ℎ = ℎ0 + 𝑑ℎ(𝐴𝑁± 0.5) (4.1) Where, 𝑑ℎ is increment of weight heights (here 25 mm); N is the total number of failure or non-failure “events” (whichever smaller), ℎ0 (in mm) is the lowest height at which an event occurred. The value of A can be calculated via: A = ∑ 𝑛𝑖𝑘𝑖=0 (4.2) 60 Where, i= 0, 1, 2 . . . k (counting index, starts at ℎ0); 𝑛𝑖 is the number of events that occurred at ℎ𝑖. The negative sign is used when the events are failures and the positive sign when the events are non-failures. Mean failure energy (MFE) can be calculated using: 𝑀𝐹𝐸 =ℎ ×𝑚×𝑔1000 (4.3) Where, h is the mean failure height in mm, m is the mass used for the test (here 2 kg), and g is the gravity (9.81 N/kg). For each case, to determine the starting point, a test is conducted on the material by dropping the weight at the lowest height then incrementally increasing the height until the first failure occurs. This point is then selected as the starting point for the actual test. Height (mm) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 125 100 f f f 75 p f p p f f f f p f 50 p p p p p p p 25 A = (0 × 6) + (1 × 3) = 3; h = 75 + 25 (39− 0.5) = 70.83 mm MFE =70.83 ×2×9.811000= 1.39 J Figure 4-6 Test results for the impact test of the Control material 61 Height (mm) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 150 125 f f f f f 100 f f f p p p p p p 75 p p p f p 50 p 25 A = (0 × 1) + (1 × 3) + (2 × 5) = 13; h = 75 + 25 (139− 0.5) = 98.61 mm MFE =98.61 × 2 × 9.811000= 1.93 J Figure 4-7 Test results for the impact test of the Company A material Height (mm) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 225 200 175 f 150 f f f f f f p f f p 125 p p p p p p p p p 100 𝐴 = (0 × 8) + (1 × 1) = 1; ℎ = 150 + 25 (19− 0.5) = 140.27 𝑚𝑚 𝑀𝐹𝐸 =140.27 × 2 × 9.811000= 2.75 𝐽 Figure 4-8 Test results for the impact test of the Company D material 62 Height (mm) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 575 550 525 f f p 500 p p p 475 f f f p 450 p f p p f f p 425 p p p 100 𝐴 = (0 × 3) + (1 × 3) + (2 × 0) + (3 × 2) = 9; ℎ = 450 + 25 (98− 0.5) = 465.63 𝑀𝐹𝐸 =465.63 × 2 × 9.811000= 9.14 𝐽 Figure 4-9 Test results for the impact test of the Company M material Weathering resistance testing: The test values as a percentage of density change in the sample due to environmental exposure can be seen in Table 4.8 . Table 4-8 Test results of density change % of different material samples under weathering test Company Density Change (%) Control 0.01 A 3.45 D 8.46 M 2.52 63 From the table above, the DM can see that the control product wold be the most suited for resisting weathering as it had minimal change in material density; whereas the sample from Company D performed the worst with a density change as high as 8.46%. Aesthetics testing: Aesthetics of the sample materials were rated by conducting a survey where a group of engineers at CRN Okanagan Laboratory compared the candidates in a pairwise manner and selected which one in each pair would be more appealing aesthetically if installed on the side of a residential building. Then, the Modified Digital Logic (MDL) method was used to generate the final scores of alternatives. The results of the aesthetics test (Table 4.9) suggested that the Control would be the best option with a score of 0.306. Company A was a close second option with a score of 0.296; and companies D and M were ranked third and fourth with scores of 0.231 and 0.167, respectively. Table 4-9 The MDL results of the aesthetic testing of samples Company Average Score Standard Deviation Control 0.306 0.088 A 0.296 0.073 D 0.231 0.089 M 0.167 0.047 4.2.6 Step 6: Create the MS decision matrix All the test results from step 5 were compiled together to construct the MS decision matrix as seen in Table 4.10. 64 Table 4-10 The material selection (MS) decision matrix; +/- signs indicate the higher the better, or the low the better type of criteria, respectively Material Options Toughness (J/m3) (+) Impact MFE (J) (+) Density Change (%) (-) Scratch Resistance (+) Aesthetics (+) Control 3.15 1.39 0.00 0.33 0.31 A 39.35 1.93 3.45 0.21 0.30 D 15.69 2.75 8.46 0.33 0.23 M 9.82 9.14 2.52 0.13 0.17 One of the main assumptions of a MCDM problems is that the criteria are independent [166], meaning that one criterion’s variation due to different alternatives is independent from the other criteria. We can check this assumption by statistically testing the correlation values between the criteria pairs, which can be calculated by using equation 4.4. The correlation matrix and corresponding P-values are reported in Table 4.11 and Table 4.12, respectively 𝑟 = ∑ (𝑥𝑖𝑖 −?̅?)(𝑦𝑖−?̅?) √∑ (𝑥𝑖𝑖 −?̅?)2√∑ (𝑦𝑖𝑖 −?̅?)2 (4.4) Table 4-11 The correlation matrix of the MS criteria Toughness Impact Density Change Scratch Resistance Aesthetics Toughness 1 Impact -0.2668 1 Density Change 0.285945 0.04989 1 Scratch Resistance -0.26865 0.79602 0.226468 1 Aesthetics 0.291011 0.92553 -0.30096 0.585206 1 65 Table 4-12 The P-values (statistical significance) of the calculated correlations of the MS criteria Toughness Impact Density Change Scratch Resistance Aesthetics Toughness - Impact (J) 0.7332 - Density Change 0.7141 0.9501 - Scratch Resistance 0.7314 0.2040 0.7735 - Aesthetics 0.7090 0.0745 0.6990 0.4148 - The P-Values of all the correlations are greater than 0.05, indicating no statistical significance. Hence, we can assume that all of the criteria in the given case are independent from one another. 4.2.7 Step 7: Choose the MS MCDM method Similar to the case during the choosing of the SS MCDM method (section 4.2.3), if high accuracy of decision results are required for DM along with available time, then a model that is compensatory, such as the Best-Worst Method with SAW, can be used in the present case. Otherwise, if it is a time-critical situation then a simple noncompensatory model, such as the Lexicographic Method, would be suitable. For this part of the case study, both methods will be used to demonstrate their differences. Scenario 1: In this scenario, the DM chooses to apply the noncompensatory lexicographic method. The MS attributes were determined to be in the order of importance of:  Toughness  Aesthetics  Impact Resistance 66  Scratch Resistance  Weathering (density change) Using the lexicographic method, the alternatives were screened using the most important criterion first, and if there is a tie between two or more alternatives, then they are compared under the next important criterion; and this process continues until the best one is selected or comparisons have been made under all the criteria. Starting from the decision matrix in Table 4.10, the lexicographic approach using the most important criterion, toughness, made Company A as the sole best option, having the highest toughness value. Scenario 2: In this scenario, the DM opts to apply a compensatory technique, in this case, the Best-Worst Method (BWM) in order to determine the weights accurately and combined them with the SAW MCDM for the final decision making. Under a linear programming as described in section 2.2.12., in the BWM, the best and worst criteria are selected first. Pairwise comparisons are made where the best criterion is compared with the other criteria and then other criteria are compared to the worst criterion. The weights of the criteria are determined using an optimization model. Similar to scenario 1, toughness and density change have been selected as the best and worst criteria, respectively (Table 4.13). The Best-to-Others comparisons can be seen in Table 4.14 and the Others-to-Worst comparisons can be seen in Table 4.15. 67 Table 4-13 The best and worst material criteria selected for the BW method Criteria Name Reasoning Best (most important) Toughness Allows for increased ease of installation making it preferable to contractors. Worst (least important) Density Change The climate in Kelowna is very mild and does not go through extreme weather changes. Table 4-14 The Best-to-Others comparisons in the BWM Best to Others Toughness Impact Density Change Scratch Resistance Aesthetics Best: Toughness 1 4 6 5 2 Table 4-15 The Others-to-Worst comparisons in the BWM Others to Worst Worst: Density Change Toughness 6 Impact 4 Density Change 1 Scratch Resistance 3 Aesthetics 5 The weights that were determined by solving the BWM equations (using Microsoft Excel’s solver function) can be found in Figure 4.16, with a inconsistency factor of 𝜉 L* = 0.095. As stated previously, 𝜉𝐿 can be considered as an indicator of inconsistency in the BWM; the closer its value is to zero, the higher is the consistency of obtained weights (in the current case: 1-0.095. i.e. over 90% consistency). 68 Table 4-16 Weights generated from the BWM Criteria Toughness Impact Density Change Scratch Resistance Aesthetics Weights 0.43 0.13 0.06 0.11 0.26 Finally, for using the SAW method to obtain the final rank of the materials, since the data in table 4.10 are of different units and they cannot be summed, a data normalization is required to obtain a common scale. Linear normalization is the most commonly used method in conjunction with SAW [8]. It is implemented simply by dividing the value of each criterion to its maximum value. The result of this normalization and SAW can be seen in Table 4.17 and 4.18, respectively. Table 4-17 Results of the linear normalization of MS data Toughness Impact Density Change Scratch Resistance Aesthetics Control 0.08 0.15 0.00 1 1 A 1 0.21 0.41 0.64 0.97 D 0.40 0.30 1 1 0.74 M 0.25 1 0.30 0.40 0.55 Table 4-18 The result of SAW material selection Toughness Impact Density Change Scratch Resistance Aesthetics Score Control 0.04 0.02 0 0.11 0.27 0.43 A 0.44 0.03 0.02 0.07 0.26 0.77 D 0.17 0.04 0.06 0.11 0.20 0.46 M 0.11 0.13 0.02 0.04 0.15 0.41 69 4.2.8 Step 8: Select the final material supplier From Table 4.19, the DM can find that the best material is from Company A. It would be by far an optimum decision to select A as the new material and supplier. The materials from suppliers D and M have performed overall very closely to the Control, and may be considered as secondary options. Table 4-19 Ranking of the SAW results for the candidate materials Materials Score Rank Control 0.43 3 A 0.77 1 D 0.4 2 M 0.41 4 70 Conclusions and Recommendations 5.1 Summary and Conclusions A distribution company based in Canada supplies the local market with insulated skirting product. The company had faced problems with their current material supplier overseas and wanted to shift to a local supplier. Locally, there were a large number of options that could be a candidate supplier. The key was to find a systematic way to screen the alternatives and select the optimum one according to the company’s both business and technical requirements. As a consequence of changing the supplier, the material of the skirting product may also face some changes, in terms of mechanical properties. Hence, material selection was deemed to be crucial for the success of this strategic decision making by the company. A customizable, multi-stage MCDM methodology was developed in this research to compare numerous suppliers and their materials using a hybrid of compensatory and non-compensatory, as well as qualitative and quantitative decision models. The methodology is customizable in the sense that the criteria in the decision matrix highly depend on the scenarios surrounding the SME client; where different users can adapt different set of criteria depending on the product and business case. All the decision criteria were first identified during meetings with the company staff. Constraints (or must-fully-satisfy criteria) were also identified and included in the case study. Alternatives were initially screened on these constraints, and only feasible alternatives were kept in the subsequent MCDM implementation. During MCDM, suppliers were first scored in the Supplier Selection stage using a number of business-oriented criteria (Years in Business, Location, Willingness, and Communication). Subsequently the top 3 companies were requested 71 to send material samples. Then, in the Material Selection phase, these samples were tested according to the predetermined set of mechanical and aesthetics performance attributes, and finally the supplier with the highest overall score was selected. The latter criteria in the order of DM preference included: toughness, aesthetics, impact resistance, scratch resistance and weathering. Also, the independence of these criteria was tested using a correlation analysis. For a compensatory MCDM solution, which next to ranking clearly showed the relative scores of the alternatives, the criteria weights were determined using the MDL and BWM methods, for Supplier Selection and Material Selection phases, respectively. For a non-compensatory MCDM solution, however, no criteria weights were required, hence simpler and faster to implement but at the cost of losing decision accuracy. 5.2 Limitations of the Work One of the motivations behind the selection of the MCDM techniques for this research was the ease of implementation for the general (non-expert) end users, especially for SMEs. Simplistic and intuitive techniques would result in more likely application of the methodology. However, the presented methodology was designed for a single DM only, and not under a group MCDM. Another limitation was that all the candidate suppliers did not have the same manufacturing abilities. Namely, the control product (with a given shape and dimensions) was textured and that contributed to its unusually high score under the aesthetics criteria. Although, the other companies could conduct extrusion and make the correct shape and profile of the skirting product as the control, they were not equipped to form any surface texturing. Another limitation was not including UV testing in the weathering resistance assessment. 72 5.3 Recommendations for Future Work The following recommendations may be proposed as future directions of the research:  The methodology can be adapted to account for group decision making environments.  The methodology can be expanded to include different shapes and sizes of the product, which may have different set of functionalities/criteria.  Different manufacturing methods and their factors including cost could be added in the decision making.  In weathering tests, one can conduct some form of accelerated UV testing to test the materials on their ability to resist UV degradation, as applicable for outdoor applications.  Applications other than insulated skirting may be tested against the proposed methodology.  The future work could also involve more complex decision approaches that employ e.g. fuzzy numbers in the decision making process.73 Bibliography [1] R. D. Reid and N. R. Sanders, Operations management. Hoboken, NJ: John Wiley & Sons, 2013. [2] C. T. Chen, C. T. Lin, and S. F. Huang, “A fuzzy approach for supplier evaluation and selection in supply chain management,” International Journal of Production Economics, vol. 102, no. 2, pp. 289–301, Aug. 2006. [3] T. Y. Choi and J. L. Hartley, “An exploration of supplier selection practices across the supply chain,” Journal of Operations Management, vol. 14, no. 4, pp. 333–343, Nov. 1996. [4] M. T. MacLean-Blevins, Designing Successful Products with Plastics: Fundamentals of Plastic Part Design. Kidlington, Oxford, United Kingdom: William Andrew, 2018. [5] J. Kaspar, D. Baehre, and M. Vielhaber, “Material selection based on a product and production engineering integration framework,” Procedia CIRP, vol. 50, pp. 2–7, 2016. [6] C. L. Hwang, A. S. M. Masud, Multiple Objective Decision Making: Methods and Applications: A State-of-the-Art Survey. Berlin: Springer, 1979. [7] W. Pedrycz, P. Ekel, and R. Parreiras, Fuzzy Multicriteria Decision-Making Models, Methods and Applications. Chichester, West Sussex, U.K.: Wiley, 2011. [8] A. Yildiz and A. Y. Yayla, “Multi-criteria decision-making methods for supplier selection: A literature review,” The South African Journal of Industrial Engineering, vol. 26, no. 2, pp. 158–177, Mar. 2015. [9] K. P. Yoon and C. L. Hwang, Multiple Attribute Decision Making: An Introduction. Thousand Oaks, California: Sage Publications, 1995. 74 [10] P. Wang, Z. Zhu, and Y. Wang, “A novel hybrid MCDM model combining the SAW, TOPSIS and GRA methods based on experimental design,” Information Sciences, vol. 345, pp. 27–45, Jun. 2016. [11] V. Shukla, G. Auriol, and K. W. Hipel, “Multicriteria decision-making methodology for systems engineering,” IEEE Systems Journal, vol. 10, no. 1, pp. 4–14, Mar. 2016. [12] S. J. Chen and C. L. Hwang, Fuzzy Multiple Attribute Decision Making: Methods and Applications. Berlin: Springer, 1992. [13] E. Triantaphyllou, Multi-criteria Decision Making Methods: A Comparative Study. Dordrecht; Boston: Kluwer Academic Publishers, 2000. [14] C. Kahraman, S. C. Onar, and B. Oztaysi, “Fuzzy multicriteria decision-making: A literature review,” International Journal of Computational Intelligence Systems, vol. 8, no. 4, pp. 637–666, May 2015. [15] C.-L. Hwang and K. Yoon, Multiple Attribute Decision Making Methods and Applications A State-of-the-Art Survey. Berlin, Heidelberg: Springer Berlin Heidelberg, 1981. [16] F. Hwang, ‘An Expert Decision-making Support System for Multiple Attribute Decision-making’, Kansas State University, 1987. [17] H. Montgomery and O. Svenson, “On decision rules and information processing strategies for choices among multiattribute alternatives,” Scandinavian Journal of Psychology, vol. 17, no. 1, pp. 283–291, Sep. 1976. [18] A. Tversky, “Elimination by aspects: A theory of choice.,” Psychological Review, vol. 79, no. 4, pp. 281–299, Jul. 1972. 75 [19] R. M. Dawes, “Social selection based on multidimensional criteria.,” The Journal of Abnormal and Social Psychology, vol. 68, no. 1, pp. 104–109, Jan. 1964 [20] P. C. Fishburn, “Lexicographic Orders, Utilities and Decision Rules: A Survey,” Management Science, vol. 20, no. 11, pp. 1442–1471, Jul. 1974. [21] P. C. Fishburn, “Lexicographic Orders, Utilities and Decision Rules: A Survey,” Management Science, vol. 20, no. 11, pp. 1442–1471, Jul. 1974. [22] W. D. Cook and L. M. Seiford, “Priority ranking and consensus formation,” Management Science, vol. 24, no. 16, pp. 1721–1732, Dec. 1978. [23] H. W. Kuhn, “The hungarian method for the assignment problem,” Naval Research Logistics, vol. 52, no. 1, pp. 7–21, Feb. 2005. [24] J. Rezaei, “Best-worst multi-criteria decision-making method: Some properties and a linear model,” Omega, vol. 64, pp. 126–130, Oct. 2016. [25] J. Rezaei, “Best-worst multi-criteria decision-making method,” Omega, vol. 53, pp. 49–57, Jun. 2015. [26] T. L. Saaty, The Analytic Hierarchy Process: Planning, Priority setting, Resource Allocation. New York, NY: McGraw-Hill, 1980. [27] W. G. Stillwell, D. A. Seaver, and W. Edwards, “A comparison of weight approximation techniques in multiattribute utility decision making,” Organizational Behavior and Human Performance, vol. 28, no. 1, pp. 62–77, Aug. 1981. [28] B. Dehghan-Manshadi, H. Mahmudi, A. Abedian, and R. Mahmudi, “A novel method for materials selection in mechanical design: Combination of non-linear normalization and a modified digital logic method,” Materials & Design, vol. 28, no. 1, pp. 8–15, Jan. 2007. 76 [29] C. N. Liao and H. P. Kao, “Supplier selection model using Taguchi loss function, analytical hierarchy process and multi-choice goal programming,” Computers & Industrial Engineering, vol. 58, no. 4, pp. 571–577, May 2010. [30] J. H. Dyer, D. S. Cho, and W. Chu, “Strategic Supplier Segmentation: The Next ‘Best Practice’ in Supply Chain Management,” California Management Review, vol. 40, no. 2, pp. 57–77, Jan. 1998. [31] V. M. Athawale, P. Mukherjee, and S. Chakraborty, “Supplier selection using multi-criteria decision-making methods,” IUP Journal of Operations Management, vol. 8, no. 3/4, pp. 41–60, Aug. 2009. [32] P. Agarwal, M. Sahai, V. Mishra, M. Bag, and V. Singh, “A review of multi-criteria decision making techniques for supplier evaluation and selection,” International Journal of Industrial Engineering Computations, vol. 2, no. 4, pp. 801–810, Oct. 2011. [33] P. Ávila, A. Pires, J. Bastos, G. Putnik, and J. Teixeira, “Supplier's selection model based on an empirical Study,” Procedia Technology, vol. 5, pp. 625–634, 2012. [34] D. W. Zhang, A. B. A. Hamid, and A. C. Thoo, “Sustainable supplier selection: An international comparative literature review for future investigation,” Applied Mechanics and Materials, vol. 525, pp. 787–790, Feb. 2014. [35] K. Govindan, S. Rajendran, J. Sarkis, and P. Murugesan, “Multi criteria decision making approaches for green supplier evaluation and selection: a literature review,” Journal of Cleaner Production, vol. 98, pp. 66–83, Jul. 2015. [36] P. Palanisamy and H. A. Zubar, “Hybrid MCDM approach for vendor ranking,” Journal of Manufacturing Technology Management, vol. 24, no. 6, pp. 905–928, Jul. 2013. 77 [37] J. Wei and A. Sun, “The selection of supplier based on fuzzy-ANP,” 2009 International Conference on Future BioMedical Information Engineering, pp.160-163, Dec. 2009. [38] D. Simić, I. Kovačević, V. Svirčević, and S. Simić, “50 years of fuzzy set theory and models for supplier assessment and selection: A literature review,” Journal of Applied Logic, vol. 24, pp. 85–96, Nov. 2017. [39] M. Zeydan, C. Çolpan, and C. Çobanoğlu, “A combined methodology for supplier selection and performance evaluation,” Expert Systems with Applications, vol. 38, no. 3, pp. 2741–2751, Mar. 2011. [40] S. Hamdan and A. Cheaitou, “Supplier selection and order allocation with green criteria: An MCDM and multi-objective optimization approach,” Computers & Operations Research, vol. 81, pp. 282–304, May 2017. [41] M. Y. Bayrak, N. Çelebi, and H. Taşkin, “A fuzzy approach method for supplier selection,” Production Planning & Control, vol. 18, no. 1, pp. 54–63, Jan. 2007. [42] K. G. Gulen, “Supplier selection and outsourcing strategies in supply chain management,” Journal of Aeronautics and Space Technologies, vol. 3, no. 2, pp. 1–6, Jun. 2007. [43] W. L. Ng, “An efficient and simple model for multiple criteria supplier selection problem,” European Journal of Operational Research, vol. 186, no. 3, pp. 1059–1067, May 2008. [44] N. Aissaoui, M. Haouari, and E. Hassini, “Supplier selection and order lot sizing modeling: A review,” Computers & Operations Research, vol. 34, no. 12, pp. 3516–3540, Dec. 2007. 78 [45] K. Renganath and M. Suresh, “Supplier selection using fuzzy MCDM techniques: A literature review,” 2016 IEEE International Conference on Computational Intelligence and Computing Research (ICCIC), Dec. 2016. [46] W. Ho, X. Xu, and P. K. Dey, “Multi-criteria decision making approaches for supplier evaluation and selection: A literature review,” European Journal of Operational Research, vol. 202, no. 1, pp. 16–24, Apr. 2010. [47] G. Büyüközkan and F. Göçer, “Application of a new combined intuitionistic fuzzy MCDM approach based on axiomatic design methodology for the supplier selection problem,” Applied Soft Computing, vol. 52, pp. 1222–1238, Mar. 2017. [48] L. D. Boer, E. Labro, and P. Morlacchi, “A review of methods supporting supplier selection,” European Journal of Purchasing & Supply Management, vol. 7, no. 2, pp. 75–89, Jun. 2001. [49] V. Jain, A. K. Sangaiah, S. Sakhuja, N. Thoduka, and R. Aggarwal, “Supplier selection using fuzzy AHP and TOPSIS: a case study in the Indian automotive industry,” Neural Computing and Applications, vol. 29, no. 7, pp. 555–564, Aug. 2016. [50] Y. J. Chen, “Structured methodology for supplier selection and evaluation in a supply chain,” Information Sciences, vol. 181, no. 9, pp. 1651–1670, May 2011. [51] P. Parthiban, H. A. Zubar, and C. P. Garge, “A multi criteria decision making approach for suppliers selection,” Procedia Engineering, vol. 38, pp. 2312–2328, 2012. [52] J. Chai, J. N. Liu, and E. W. Ngai, “Application of decision-making techniques in supplier selection: A systematic review of literature,” Expert Systems with Applications, vol. 40, no. 10, pp. 3872–3885, Aug. 2013. 79 [53] K. Zimmer, M. Fröhling, and F. Schultmann, “Sustainable supplier management – a review of models supporting sustainable supplier selection, monitoring and development,” International Journal of Production Research, vol. 54, no. 5, pp. 1412–1442, Sep. 2015. [53] R. Hruška, P. Průša, and D. Babić, “The Use Of Ahp Method For Selection Of Supplier,” Transport, vol. 29, no. 2, pp. 195–203, Apr. 2014. [54] Y. Wang, “An Application of the AHP in Supplier Selection of Maintenance and Repair Parts,” 2009 First International Conference on Information Science and Engineering, Dec. 2009. [55] G. B. Kamath, R. Naik, and S. Prasad, “A Vendors Evaluation–Using Ahp For An Indian Steel Pipe Manufacturing Company,” International Journal of the Analytic Hierarchy Process, vol. 8, no. 3, Feb. 2016. [56] F. Tahriri, M. R. Osman, A. Ali, R. M. Yusuff, and A. Esfandiary, “AHP approach for supplier evaluation and selection in a steel manufacturing company,” Journal of Industrial Engineering and Management, vol. 1, no. 2, Dec. 2008. [57] R. Hemaida and J. Schmits, “An analytical approach to vendor selection,” Industrial Management, vol. 48, no. 3, Jan. 2006. [58] V. Haridasan and S. M, “Vendor Rating Using Analytical Hierarchical Process - Insights from Indian Engineering Construction Industry,” International Journal of Scientific Research and Management, vol. 6, no. 02, Feb. 2018. [59] K. John, Vinod Yeldho, and G. S. Mangalathu, “Vendor evaluation and rating using analytical hierarchy process,” International Journal of Engineering Science and Innovative Technology, vol. 2, no. 3, May 2013. 80 [60] M. C. Tam and V. Tummala, “An application of the AHP in vendor selection of a telecommunications system,” Omega, vol. 29, no. 2, pp. 171–182, Apr. 2001. [61] M. Hudymáčová, M. Benková, J. Pócsová, and S. Tomas, “Supplier selection based on multi-criterial AHP method,” Acta Montanistica Slovaca, vol. 15, no. 3, pp. 249–255, Mar. 2010. [62] C. Kahraman, U. Cebeci, and Z. Ulukan, “Multi‐criteria supplier selection using fuzzy AHP,” Logistics Information Management, vol. 16, no. 6, pp. 382–394, Dec. 2003. [63] F. T. S. Chan, N. Kumar, M. K. Tiwari, H. C. W. Lau, and K. L. Choy, “Global supplier selection: a fuzzy-AHP approach,” International Journal of Production Research, vol. 46, no. 14, pp. 3825–3857, Jul. 2008. [64] O. Kilincci and S. A. Onal, “Fuzzy AHP approach for supplier selection in a washing machine company,” Expert Systems with Applications, vol. 38, no. 8, pp. 9656–9664, Aug. 2011. [65] M. Sevkli, S. Zaim, A. Turkyilmaz, and M. Satir, “An application of fuzzy Topsis method for supplier selection,” International Conference on Fuzzy Systems, Jul. 2010. [66] S. Kumar, S. Kumar, and A. G. Barman, “Supplier selection using fuzzy TOPSIS multi criteria model for a small scale steel manufacturing unit,” Procedia Computer Science, vol. 133, pp. 905–912, 2018. [67] H. Gupta and M. K. Barua, “Supplier selection among SMEs on the basis of their green innovation ability using BWM and fuzzy TOPSIS,” Journal of Cleaner Production, vol. 152, pp. 242–258, May 2017. 81 [68] K. Nag and M. Helal, “A Fuzzy TOPSIS approach in multi-criteria decision making for supplier selection in a pharmaceutical distributor,” 2016 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM), Dec. 2016. [69] C.-W. Hsu and A. H. Hu, “Applying hazardous substance management to supplier selection using analytic network process,” Journal of Cleaner Production, vol. 17, no. 2, pp. 255–264, Jan. 2009. [70] X. Tan, K. Ma, W. Guo, and T. Huang, “An Application of ANP with Benefits, Opportunities, Costs and Risks in Supplier Selection: A Case Study in a Diesel Engine Manufacturing Firm,” 2007 IEEE International Conference on Automation and Logistics, pp. 1446–1451, Aug. 2007. [71] H. Alidrisi, “An ANP-based multi criteria decision making model for supplier selection,” 2014 IEEE International Conference on Industrial Engineering and Engineering Management, Dec. 2014. [72] C. Gencer and D. Gürpinar, “Analytic network process in supplier selection: A case study in an electronic firm,” Applied Mathematical Modelling, vol. 31, no. 11, pp. 2475–2486, Nov. 2007. [73] X. Chen, X. F. Zhou, and Y. Zhang, “Research on Building Engineering Materials Supplier Selection Based on ANP Method,” Key Engineering Materials, vol. 474-476, pp. 2089–2094, Apr. 2011. [74] S. Vinodh, R. A. Ramiya, and S. Gautham, “Application of fuzzy analytic network process for supplier selection in a manufacturing organisation,” Expert Systems with Applications, vol. 38, no. 1, pp. 272–280, Jan. 2011. 82 [75] A. Dargi, A. Anjomshoae, M. R. Galankashi, A. Memari, and M. B. M. Tap, “Supplier Selection: A Fuzzy-ANP Approach,” Procedia Computer Science, vol. 31, pp. 691–700, 2014. [76] B. Pang, “A Fuzzy ANP Approach to Supplier Selection Based on Fuzzy Preference Programming,” 2009 International Conference on Management and Service Science, pp. 1–4, Sep. 2009. [77] H.-Y. Kang, A. H. I. Lee, and C.-Y. Yang, “A fuzzy ANP model for supplier selection as applied to IC packaging,” Journal of Intelligent Manufacturing, vol. 23, no. 5, pp. 1477–1488, Aug. 2010. [78] J.-Y. Wei, A.-F. Sun, and C.-H. Wang, “The application of fuzzy-ANP in the selection of supplier in supply chain management,” 2010 International Conference on Logistics Systems and Intelligent Management (ICLSIM), Jan. 2010. [79] M. Abdel-Baset, V. Chang, A. Gamal, and F. Smarandache, “An integrated neutrosophic ANP and VIKOR method for achieving sustainable supplier selection: A case study in importing field,” Computers in Industry, vol. 106, pp. 94–110, Apr. 2019. [80] A. Cheraghalipour, M. M. Paydar, and M. Hajiaghaei-Keshteli, “Applying a hybrid BWM-VIKOR approach to supplier selection: a case study in the Iranian agricultural implements industry,” International Journal of Applied Decision Sciences, vol. 11, no. 1, p. 1, 2018. [81] A. Sanayei, S. F. Mousavi, and A. Yazdankhah, “Group decision making process for supplier selection with VIKOR under fuzzy environment,” Expert Systems with Applications, vol. 37, no. 1, pp. 24–30, Jan. 2010. 83 [82] L. Dai, Y. Liu, and Z. Zhang, “Supplier Selection with Multiple Criteria under Fuzzy Environment,” 2008 4th International Conference on Wireless Communications, Networking and Mobile Computing, Oct. 2008. [83] S. Birgun and E. Cihan, “Supplier selection process using ELECTRE method,” 2010 IEEE International Conference on Intelligent Systems and Knowledge Engineering, Nov. 2010. [84] N. Kumar, T. Soota, N. Gupta, and S. K. Rajput, “Multi attribute outranking approach for supplier selection,” IOP Conference Series: Materials Science and Engineering, vol. 404, Sep. 2018. [85] C. Cristea and M. Cristea, “A multi-criteria decision making approach for supplier selection in the flexible packaging industry,” MATEC Web of Conferences, vol. 94, 2017. [86] M. Sevkli, “An application of the fuzzy ELECTRE method for supplier selection,” International Journal of Production Research, vol. 48, no. 12, pp. 3393–3405, May 2009. [87] A. Hanane, O. Brahim, and F. Bouchra, “An ANP-PROMETHEE model for supplier selection and a case study,” 2015 International Conference on Industrial Engineering and Systems Management (IESM), Oct. 2015. [88] B. Chang, C.-W. Chang, and C.-H. Wu, “Fuzzy DEMATEL method for developing supplier selection criteria,” Expert Systems with Applications, vol. 38, no. 3, pp. 1850–1858, Mar. 2011. [89] K. Nourianfar and G. A. Montazer, “A fuzzy MCDM approach based on COPRAS method to solve supplier selection problems,” The 5th Conference on Information and Knowledge Technology, May 2013. 84 [90] F. R. L. Junior, L. Osiro, and L. C. R. Carpinetti, “A comparison between Fuzzy AHP and Fuzzy TOPSIS methods to supplier selection,” Applied Soft Computing, vol. 21, pp. 194–209, Aug. 2014. [91] G. Yadav, S. K. Mangla, S. Luthra, and S. Jakhar, “Hybrid BWM-ELECTRE-based decision framework for effective offshore outsourcing adoption: a case study,” International Journal of Production Research, vol. 56, no. 18, pp. 6259–6278, May 2018. [92] P. Chatterjee, V. M. Athawale, and S. Chakraborty, “Materials selection using complex proportional assessment and evaluation of mixed data methods,” Materials & Design, vol. 32, no. 2, pp. 851–860, Feb. 2011. [93] N. R. Ware, S. P. Singh, and D. K. Banwet, “Multi-criteria analysis of supplier selection using AHP, fuzzy AHP, fuzzy TOPSIS, IRP and weighted-IRP: A comparative study,” 45 International Conference on Computers & Industrial Engineering, Oct. 2015. [94] P. Melin, Analysis and design of intelligent systems using soft computing techniques. Berlin: Springer, 2007. [95] P. Rezakhani, “Fuzzy MCDM Model for Risk Factor Selection in Construction Projects,” Engineering Journal, vol. 16, no. 5, pp. 79–94, Oct. 2012. [96] E. N. Madi, J. M. Garibaldi, and C. Wagner, “An exploration of issues and limitations in current methods of TOPSIS and fuzzy TOPSIS,” 2016 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), Jul. 2016. [97] R. M. Alguliyev, R. M. Aliguliyev, and R. S. Mahmudova, “Multicriteria Personnel Selection by the Modified Fuzzy VIKOR Method,” The Scientific World Journal, vol. 2015, pp. 1–16, 2015. 85 [98] M. Velasquez and P. T. Hester, “An Analysis of Multi-Criteria Decision Making Methods,” International Journal of Operations Research, vol. 10, no. 2, pp. 56–66, May 2013. [99] M. R. Mahmoud and L. A. Garcia, “Comparison of different multicriteria evaluation methods for the Red Bluff diversion dam,” Environmental Modelling & Software, vol. 15, no. 5, pp. 471–478, Jul. 2000. [100] B. F. Hobbs, V. Chankong, W. Hamadeh, and E. Z. Stakhiv, “Does choice of multicriteria method matter? An experiment in water resources planning,” Water Resources Research, vol. 28, no. 7, pp. 1767–1779, Jul. 1992. [101] C.-L. Hwang and M.-J. Lin, Group decision making under multiple criteria: methods and applications. Berlin: Springer, 1987 [102] V. Boltenkov, V. Kuvaieva, O. Galchonkov, and A. Ishchenko, “The research of possibilities for fast calculation of median consensus rankings,” Eastern-European Journal of Enterprise Technologies, vol. 4, no. 4 (94), pp. 27-35, Aug. 2018 [103] D. Das, S. Bhattacharya, and B. Sarkar, “Decision-based design-driven material selection: A normative-prescriptive approach for simultaneous selection of material and geometric variables in gear design,” Materials & Design, vol. 92, pp. 787–793, Feb. 2016. [104] V. M. Athawale, R. Kumar, and S. Chakraborty, “Decision making for material selection using the UTA method,” The International Journal of Advanced Manufacturing Technology, vol. 57, no. 1-4, pp. 11–22, Apr. 2011. [105] P. Chatterjee and S. Chakraborty, “Material selection using preferential ranking methods,” Materials & Design, vol. 35, pp. 384–393, Mar. 2012. 86 [106] A. Jahan, M. Y. Ismail, S. Shuib, D. Norfazidah, and K. Edwards, “An aggregation technique for optimal decision-making in materials selection,” Materials & Design, vol. 32, no. 10, pp. 4918–4924, Dec. 2011. [107] A. Shanian and O. Savadogo, “A methodological concept for material selection of highly sensitive components based on multiple criteria decision analysis,” Expert Systems with Applications, vol. 36, no. 2, pp. 1362–1370, Mar. 2009. [108] A. Jahan, M. Y. Ismail, F. Mustapha, and S. M. Sapuan, “Material selection based on ordinal data,” Materials & Design, vol. 31, no. 7, pp. 3180–3187, Aug. 2010. [109] A. Mayyas, M. A. Omar, and M. T. Hayajneh, “Eco-material selection using fuzzy TOPSIS method,” International Journal of Sustainable Engineering, vol. 9, no. 5, pp. 292–305, Mar. 2016. [110] X. J. Xie, “Research on Material Selection with Multi-Attribute Decision Method and G1 Method,” Advanced Materials Research, vol. 952, pp. 20–24, May 2014. [111] S. Manghani and G. Kumar, “Automotive Composites and Polymer Material Selection for Fairing of a Human Powered Vehicle Using Multi-Attribute Decision Making Methodology,” SAE Technical Paper Series, Apr. 2016. [112] M. Farag, “Quantitative methods of materials substitution: Application to automotive components,” Materials & Design, vol. 29, no. 2, pp. 374–380, Jan. 2008. [113] A. Jahan, M. Bahraminasab, and K. Edwards, “A target-based normalization technique for materials selection,” Materials & Design, vol. 35, pp. 647–654, Mar. 2012. [114] M. Yazdani and A. F. Payam, “A comparative study on material selection of microelectromechanical systems electrostatic actuators using Ashby, VIKOR and TOPSIS,” Materials & Design (1980-2015), vol. 65, pp. 328–334, Jan. 2015. 87 [115] S. H. Mousavi-Nasab and A. Sotoudeh-Anvari, “A comprehensive MCDM-based approach using TOPSIS, COPRAS and DEA as an auxiliary tool for material selection problems,” Materials & Design, vol. 121, pp. 237–253, May 2017. [116] R. V. Rao and J. P. Davim, “A decision-making framework model for material selection using a combined multiple attribute decision-making method,” The International Journal of Advanced Manufacturing Technology, vol. 35, no. 7-8, pp. 751–760, Nov. 2006. [117] V. Chandrasekar, K. Raja, and P. Marimuthu, “Composite material selection using multi criteria decision making for automobile torsion bar,” Applied Mechanics and Materials, vol. 573, pp. 649–654, Jun. 2014. [118] A. Jahan and K. L. Edwards, “A state-of-the-art survey on the influence of normalization techniques in ranking: Improving the materials selection process in engineering design,” Materials & Design, vol. 65, pp. 335–342, Jan. 2015. [119] A. Milani, A. Shanian, R. Madoliat, and J. Nemes, “The effect of normalization norms in multiple attribute decision making models: a case study in gear material selection,” Structural and Multidisciplinary Optimization, vol. 29, no. 4, pp. 312–318, Sep. 2004. [120] H.-C. Liu, J.-X. You, L. Zhen, and X.-J. Fan, “A novel hybrid multiple criteria decision making model for material selection with target-based criteria,” Materials & Design, vol. 60, pp. 380–390, Aug. 2014. [121] L. Anojkumar, M. Ilangkumaran, and V. Sasirekha, “Comparative analysis of MCDM methods for pipe material selection in sugar industry,” Expert Systems with Applications, vol. 41, no. 6, pp. 2964–2980, May 2014. [122] A. Chauhan, R. Vaish, and C. Bowen, “Piezoelectric material selection for ultrasonic transducer and actuator applications,” Proceedings of the Institution of Mechanical 88 Engineers, Part L: Journal of Materials: Design and Applications, vol. 229, no. 1, pp. 3–12, Jun. 2013. [123] R. Taherian and M. Nasr, “Performance and material selection of nanocomposite bipolar plate in proton exchange membrane fuel cells,” International Journal of Energy Research, vol. 38, no. 1, pp. 94–105, Sep. 2013. [124] E. Senyigit and B. Demirel, “Determination of the material for the carbonated soft drink packaging with multi-criteria decision making methods,” Sigma Journal of Engineer ing and Natural Sciences , vol. 35, no. 3, pp. 471–480, Apr. 2017. [125] R. Taherian, “A review of composite and metallic bipolar plates in proton exchange membrane fuel cell: Materials, fabrication, and material selection,” Journal of Power Sources, vol. 265, pp. 370–390, Nov. 2014. [126] J. Torrez, A. Milani, and D. Schuetze, “Material selection for light-weight naval crafts using the modified digital logic method: dealing with ranking abnormalities,” International Journal of Materials and Structural Integrity, vol. 6, no. 2/3/4, p. 241, 2012. [127] K. A. Anupam, V. Swarop, A. K. Sharma, P. S. Lal, and V. Bist, “Sustainable raw material selection for pulp and paper using SAW multiple criteria decision making design,” IPPTA: Quarterly Journal of Indian Pulp and Paper Technical Association, vol. 27, no. 1, pp. 67–76, Jan. 2015. [128] M. Taka, S. P. Raygor, R. Purohit, and V. Parashar, “Selection of tool and work piece combination using Multiple Attribute Decision Making Methods for Computer Numerical Control turning operation,” Materials Today: Proceedings, vol. 4, no. 2, pp. 1199–1208, 2017. 89 [129] M. R. Mansor, S. Sapuan, E. S. Zainudin, A. Nuraini, and A. A. Hambali, “Thermoplastic Matrix Material Selection Using Multi Criteria Decision Making Method for Hybrid Polymer Composites,” Applied Mechanics and Materials, vol. 564, pp. 439–443, Jun. 2014. [130] X. J. Xie, “Material Selection Using TOPSIS Combined with Grey Relation Analysis,” Applied Mechanics and Materials, vol. 540, pp. 476–479, Apr. 2014. [131] A. Shanian and O. Savadogo, “TOPSIS multiple-criteria decision support analysis for material selection of metallic bipolar plates for polymer electrolyte fuel cell,” Journal of Power Sources, vol. 159, no. 2, pp. 1095–1104, Sep. 2006. [132] K. Govindan, K. M. Shankar, and D. Kannan, “Sustainable material selection for construction industry – A hybrid multi criteria decision making approach,” Renewable and Sustainable Energy Reviews, vol. 55, pp. 1274–1288, Mar. 2016. [133] K. Anupam, P. S. Lal, V. Bist, A. K. Sharma, and V. Swaroop, “Raw material selection for pulping and papermaking using TOPSIS multiple criteria decision making design,” Environmental Progress & Sustainable Energy, vol. 33, no. 3, pp. 1034–1041, Sep. 2013. [134] D.-H. Jee and K.-J. Kang, “A method for optimal material selection aided with decision making theory,” Materials & Design, vol. 21, no. 3, pp. 199–206, Jun. 2000. [135] A. Li, J. Zhao, Z. Gong, and F. Lin, “Optimal selection of cutting tool materials based on multi-criteria decision-making methods in machining Al-Si piston alloy,” The International Journal of Advanced Manufacturing Technology, vol. 86, no. 1-4, pp. 1055–1062, Jan. 2016. 90 [136] H. J. Cao, F. Liu, C. B. Li, and C. Liu, “An Integrated Method for Product Material Selection Considering Environmental Factors and a Case Study,” Materials Science Forum, vol. 532-533, pp. 1032–1035, Dec. 2006. [137] L. Uğur and U. Baykan, “A Model Proposal for Wall Material Selection Decisions by Using Analytic Hierarchy Process (AHP),” Acta Physica Polonica A, vol. 132, no. 3, pp. 577–579, Sep. 2017. [138] S. V. V, V. A. Shah, and M. M. Lokhande, “Material selection for semiconductor switching devices in electric vehicles using Analytic Hierarchy Process (AHP) method,” 2016 IEEE 1st International Conference on Power Electronics, Intelligent Control and Energy Systems (ICPEICES), Jul. 2016. [139] S. C. Kiong, L. Y. Lee, S. H. Chong, M. A. Azlan, and N. H. M. Nor, “Decision Making with the Analytical Hierarchy Process (AHP) for Material Selection in Screw Manufacturing for Minimizing Environmental Impacts,” Applied Mechanics and Materials, vol. 315, pp. 57–62, Apr. 2013. [140] L. P. Maskepatil, A. U. Gandigude, and S. A. Kale, “Selection of Material for Wind Turbine Blade by Analytic Hierarchy Process (AHP) Method,” Applied Mechanics and Materials, vol. 612, pp. 145–150, Aug. 2014. [141] A. Shanian and O. Savadogo, “A material selection model based on the concept of multiple attribute decision making,” Materials & Design, vol. 27, no. 4, pp. 329–337, Jan. 2006. [142] M. F. C. Hassan, M. U. M. Rosli, and M. A. M. Redzuan, “Material selection in a sustainable manufacturing practice of a badminton racket frame using Elimination and 91 Choice Expressing Reality (ELECTRE) Method,” Journal of Physics: Conference Series, vol. 1020, p. 012012, May 2018. [143] A. Shanian and O. Savadogo, “A non-compensatory compromised solution for material selection of bipolar plates for polymer electrolyte membrane fuel cell (PEMFC) using ELECTRE IV,” Electrochimica Acta, vol. 51, no. 25, pp. 5307–5315, Jul. 2006. [144] T. Mangera, F. Kienhöfer, K. J. Carlson, M. Conning, A. Brown, and G. Govender, “Optimal material selection for the construction of a paediatric prosthetic knee,” Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, vol. 232, no. 2, pp. 137–147, Dec. 2015. [145] B. Kiani, R. Y. Liang, and J. Gross, “Material selection for repair of structural concrete using VIKOR method,” Case Studies in Construction Materials, vol. 8, pp. 489–497, Jun. 2018. [146] N. M. Ishak, M. R. Mansor, and S. D. Malingam, “Selection of natural fibre reinforced composites using fuzzy VIKOR for car front hood,” International Journal of Materials and Product Technology, vol. 53, no. 3/4, p. 267, 2016. [147] P. Chatterjee and S. Chakraborty, “Materials selection using COPRAS and COPRAS-G methods,” International Journal of Materials and Structural Integrity, vol. 6, no. 2/3/4, pp. 111–133, Oct. 2012. [148] S. Mahmoudkelaye, K. T. Azari, M. Pourvaziri, and E. Asadian, “Sustainable material selection for building enclosure through ANP method,” Case Studies in Construction Materials, vol. 9, Dec. 2018. 92 [149] Q. Jiao, Y. Lan, Z. Guan, and Z. Li, “A new material selection approach using PROMETHEE method,” Proceedings of 2011 International Conference on Electronic & Mechanical Engineering and Information Technology, pp. 2950–2954, Aug. 2011. [150] S. H. Mousavi-Nasab and A. Sotoudeh-Anvari, “A new multi-criteria decision making approach for sustainable material selection problem: A critical study on rank reversal problem,” Journal of Cleaner Production, vol. 182, pp. 466–484, May 2018. [151] I. Kaliszewski and D. Podkopaev, “Simple additive weighting—A metamodel for multiple criteria decision analysis methods,” Expert Systems with Applications, vol. 54, pp. 155–161, Jul. 2016. [152] J. S. Dyer, P. C. Fishburn, R. E. Steuer, J. Wallenius, and S. Zionts, “Multiple Criteria Decision Making, Multiattribute Utility Theory: The Next Ten Years,” Management Science, vol. 38, no. 5, pp. 645–654, May 1992. [153] A. Salehi and M. Izadikhah, “A novel method to extend SAW for decision-making problems with interval data,” Decision Science Letters, vol. 3, no. 2, pp. 225–236, Jan. 2014. [154] A. Kolios, V. Mytilinou, E. Lozano-Minguez, and K. Salonitis, “A Comparative Study of Multiple-Criteria Decision-Making Methods under Stochastic Inputs,” Energies, vol. 9, no. 7, p. 566, Jul. 2016. [155] A. Kumar, B. Sah, A. R. Singh, Y. Deng, X. He, P. Kumar, and R. Bansal, “A review of multi criteria decision making (MCDM) towards sustainable renewable energy development,” Renewable and Sustainable Energy Reviews, vol. 69, pp. 596–609, Mar. 2017. 93 [156] A. Sotoudeh-Anvari, S. J. Sadjadi, S. M. H. Molana, and S. Sadi-Nezhad, “A new MCDM-based approach using BWM and SAW for optimal search model,” Decision Science Letters, pp. 395–404, 2018. [157] W. Serrai, A. Abdelli, L. Mokdad, and Y. Hammal, “Towards an efficient and a more accurate web service selection using MCDM methods,” Journal of Computational Science, vol. 22, pp. 253–267, Sep. 2017. [158] A. Jahan, K. L. Edwards, and M. Bahraminasab, Multi-criteria Decision Analysis: For Supporting the Selection of Engineering Materials in Product Design. Amsterdam: Elsevier, 2016. [159] J. W. Payne, E. J. Johnson, and J. R. Bettman, The Adaptive Decision Maker. New York, NY: Cambridge Univ. Press, 2009. [160] J. R. Bettman, E. J. Johnson, and J. W. Payne, “A componential analysis of cognitive effort in choice,” Organizational Behavior and Human Decision Processes, vol. 45, no. 1, pp. 111–139, Feb. 1990. [161] E. Cooper-Martin, “Measures of cognitive effort,” Marketing Letters, vol. 5, no. 1, pp. 43–56, Jan. 1994. [162] E. J. Johnson and J. W. Payne, “Effort and accuracy in choice,” Management Science, vol. 31, no. 4, pp. 395–414, Apr. 1985. [163] J. E. Russo and B. A. Dosher, “Strategies for multiattribute binary choice.,” Journal of Experimental Psychology: Learning, Memory, and Cognition, vol. 9, no. 4, pp. 676–696, Nov. 1983. 94 [164] J. Payne, E. Johnson, J. Bettman, and E. Coupey, “Understanding contingent choice: a computer simulation approach,” IEEE Transactions on Systems, Man, and Cybernetics, vol. 20, no. 2, pp. 296–309, Mar. 1990. [165] J. Zhang and P. Pu, “Effort and accuracy analysis of choice strategies for electronic product catalogs,” Proceedings of the 2005 ACM symposium on Applied computing - SAC 05, Mar. 2005. [166] J. L. Yang, H. N. Chiu, G. H. Tzeng, and R. H. Yeh, “Vendor selection by integrated fuzzy MCDM techniques with independent and interdependent relationships,” Information Sciences, vol. 178, no. 21, pp. 4166–4183, Nov. 2008. 95 Appendices : Experimental Tests Used in this Study A.1 Tensile Test The tensile test was used in order to generate the load-extension curves of the candidate materials. The specimens were prepared according to ASTM D638 and the dimensions can be seen in Figure A-1. Figure A-1 Dimensions used for the tensile test specimens The DXF files of the specimens were created using SolidWorks and was cut into shape using water jet cutting; a sample specimen can be seen in Figure A-2. For the experiment, the width and thickness were measured using a Vernier caliper. Then, the specimen were placed in the grips of the INSTRON 5969, as seen in Figure A-3. The speed of testing was set at 5 mm/min and 3 repeats of the test were conducted for each material. 96 Figure A-2 Specimen used for the tensile test Figure A-3 Tensile test specimen set up on the Instron 5969 A.2 Scratch Resistance Test Scratch resistance of materials surface was determined by comparing their relative hardness against each other. Namely, the specimens used in this test are simple square pieces that have 97 sharp corners and are cut to shape using water jet cutting; Figure A-4. This test is conducted by placing the sharp corner of one specimen on the flat surface of another and attempting to scratch it. Figure A-4 Example of specimens used for the scratch resistance test. Left piece is used to scratch the right piece The scenarios that encountered may be one of the following:  If Specimen 1 scratches Specimen 2, then Specimen 1 is harder than Specimen 2.  If Specimen 1 cannot scratch Specimen 2, then Specimen 2 is harder than Specimen 1  If the two specimen cannot scratch each other, then Specimen 1 and Specimen 2 have equal hardness.  If Specimen 1 can be scratched by Specimen 2 but not by Specimen 3, then Specimen 1 has a hardness between that of Specimen 2 and Specimen 3. Corner used to scratch Scratch that was generated 98 This method is ideal for a study that involves a limited set of alternatives as the pairwise comparisons will be significantly large as the number of alternatives increases. A.3 Impact Test This test was conducted according to ASTM D4226 in order to determine the impact energy required for the samples to fail due to impact. Using the Gardner Impact tester, PF-5545 model, the mass of 2 kg was used. The setup is shown in Figure A-5. A total of 20 impacts were made and the Up-and Down Method was used with the recorded data. This will allow for the Mean Failure Height to be determined, as follows:  Raise the weight and the impactor and place the specimen flat on the anvil so that it covers the hole.  If the estimated failure energy is not known, then run a series of impact tests at different heights in order to capture the failure onset.  Place the impactor on the specimen and raise the weight to the estimated failure energy and release it so that it strikes the impactor.  Remove the specimen and check to see if it has failed. If it did not fail, then increase the height of the weight by one increment or if it did fail then decrease the height by one increment and test again at another point on the specimen.  Mark failures with an “f” and non-failures with a “p”. 99 Figure A-5 Gardner impact test set-up with specimen loaded A.4 Weathering Resistance In order to understand the effect of the environmental condition on the specimens, their densities were tested before and after exposure to moisture and temperature variation. The square specimen with 25 mm lengths (Figure A-6) were placed in a Thermotron Environmental Chamber, seen in Figure A-7, and were conditioned according to ASTM D618 with the samples being submerged in water at 23 °C for 24 hours. 100 Figure A-6 A test specimen before and after exposed to weathering Figure A-7 The environmental chamber used in the study A.5 Aesthetics Aesthetics of the samples was determined via pair-wise comparisons in a survey among expert engineers at UBC CRN Okanagan laboratory. Here, participants compared materials two at a time and determined if they would prefer one over another or would find them equally appealing aesthetically. The preferences were recorded and scores for each material were then generated using the Modified Digital Logic method [27].
Thesis/Dissertation
eng
Mechanical Engineering
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
A customizable, multi-stage multi-criteria decision analysis approach for material-supplier selection problem in SMEs : a case study of insulated housing products
Text