Supplier Selection Using AHP and F-AHP Approach: A Case Study

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1 ISSN (Online): Ipact Factor (202): Supplier Selection Using AHP and F-AHP Approach: A Case Study Sachin B. Chhabile, R. S. Dalu 2 M.Tech scholar (Production Engineering), Governent College of Engineering, Aravati, India 2 Professor and Head, Mechanical Engineering, Governent College of Engineering, Aravati, India Abstract: Supplier selection is a process by which an organization identifies, evaluate and contract with suppliers. To get the quality aterial at a reasonable cost and at right tie, proper supplier selection is ust. Looking to its iportance, various ethods have been developed for this purpose. Supplier selection process becoes coplicated in case of ultiple supplier and nuber of criteria s. Therefore, widely used ulti criteria decision aking tool Analytical Hierarchy Process (AHP) and Fuzzy AHP can be utilized as an approach for supplier selection proble. This paper focuses on application of AHP and Fuzzy AHP for deterining the best supplier in ediu scale industry. Keywords: Analytical Hierarchy Process (AHP), Fuzzy AHP.. Introduction Supplier selection is defined as the process of finding the suppliers being able to provide the buyer with the right quality products and/or services at the right price, at the right quantities and at the right tie. Basically there are two types of supplier selection probles. In single sourcing type, one supplier can satisfy all the buyer s needs. In the ultiple sourcing type, no supplier can satisfy all the buyer s requireents. Hence the anageent wants to split order quantities aong different suppliers [3]. Supplier Selection is iportant task of any purchasing departent. The ain obective of supplier selection process is to reduce purchase risk, axiize overall value to the purchaser, and develop closeness and long-ter relationships between buyers and suppliers, which is effective in helping the copany to achieve Just-In-Tie (JIT) production [6]. Supplier evaluation and selection are very iportant to the success for any industry because the cost and quality of goods and services sold are directly related to the cost and quality of goods and services purchased. Therefore, purchasing and supplier selection have an iportant role in the supply chain process. Traditionally, vendors are selected on their ability to eet the quality requireents, delivery schedule, and the price offered. The proble of finding and evaluating the ost suitable vendors usually eerges when the purchase is coplex, high-dollar value, and perhaps critical. The supplier selection process is a ulti-obective decision, encopassing any tangible and intangible factors in a hierarchical anner [5]. Supplier selection proble is affected by different tangible and intangible criteria such as quality, price, delivery, technical capability and any ore. So selecting the right supplier by a decision aker with reduce purchasing cost iproves copetitive ability and increase custoer satisfaction[2]. 2. Case Study trolly, precleaner, lint cleaner, stea huidificator, etc. To optiize the average annual inventory cost, industry is planning to adopt scientific approach in selection the best supplier. On this basis the obectives of this paper are; To select best supplier using AHP To select best supplier using Fuzzy AHP Coparasion of result and recoendation of best supplier. 3. Analytic Hierarchy Process (AHP) AHP, developed by Saaty, addresses how to deterine the relative iportance of a set of activities in a ulti-criteria decision proble [8]. The process akes it possible to incorporate udgents on intangible qualitative criteria alongside tangible quantitative criteria. The AHP ethod is based on three principles: first, structure of the odel; second, coparative udgent of the alternatives and the criteria; third, synthesis of the priorities. In the first step, a coplex decision proble is structured as a hierarchy. AHP initially breaks down a coplex ulticriteria decisionaking proble into a hierarchy of interrelated decision criteria, decision alternatives. With the AHP, the obectives, criteria and alternatives are arranged in a hierarchical structure siilar to a faily tree. A hierarchy has at least three levels: overall goal of the proble at the top, ultiple criteria that define alternatives in the iddle, and decision alternatives at the botto [2]. The second step is the coparison of the alternatives and the criteria. Once the proble has been decoposed and the hierarchy is constructed, prioritization procedure starts in order to deterine the relative iportance of the criteria within each level. The pair-wise udgent starts fro the second level and finishes in the lowest level, Fig. shown AHP Hierarchical odel. The ediu scale industry considered here is established in986.it has 750 eployees with turnover nearly equal to 25 crore. The industry has ISO certification. The ain products are Ginning and Pressing achine, center Volue 3 Issue 5, May Paper ID: Licensed Under Creative Coons Attribution CC BY

2 ISSN (Online): Ipact Factor (202): Table 6: Priorities of Supplier w. r. t. Cost Alternatives Local Priorities Global Priorities(L.P.*0.3898) A B C λ ax =3.0648,C.R.=C.I./R.I.=0.0324/0.52=0.0623<0.0 Figure : Hierarchical structure of the proble 3. Application of AHP Steps for AHP are follows ) Rating of criteria using questionnairee filled by experts fro industry. scale of preference is entioned in Table (Appendix) 2) Developent of Hierarchy and Coparasion atrix of criteria and alternatives w. r. t. each criteria. 3) Synthesis of priorities, in which calculate the eigenvector or relative weights and λ ax for each atrix of order n, copute the consistency index for each atrix of order n by the forulae: CI =( λ ax -n)/(n-) The consistency ratio is then calculated using the forulae: CR=CI/RI, It ust be less than 0.0 where Rando Consistency Index (RI) varies depending upon the order of atrix. Tables 2 shows(appendix) the value of the Rando Consistency Index (RI) for atrices of order to 0 obtained by approxiating rando indices using a saple size of 500 [8]. 4) Selection of supplier according to highest ranking. For the purpose of priority calculation, assistance of Online CGI Software was taken into consideration for AHP and for FAHP, calculation is done anually Table 3: Coparison Matrix for Criteria Criteria Cost Quality Delivery Capacity Cost 3 5 Quality 3 5 Delivery /3 /3 3 Capacity /5 /5 /3 Table 4: Priorities of criteria Criteria Local Priorities Global Priorities Cost Quality Delivery Capacity λ ax=4.0434, C.R.=C.I./R.I.=0.04/0.89=0.062<0.0 Table 5: Coparison Matrix for Alternatives w. r. t. Cost A /3 5 B 3 7 C /5 /7 Table 7: Coparison Matrix for Alternatives w. r. t. Quality A 5 /3 B /5 /7 C 3 7 Table 8: Priorities of Supplier w. r. t. Quality Alternatives Local Priorities Global Priorities(L.P.*0.3898) A B C λ ax =3.0648,C.R.=C.I./R.I.=0.0324/0.52=0.0623<0.0 Table 9: Coparison Matrix for Alternatives w. r. t. Delivery Alternatives A B C A 5 7 B / /5 3 C / /7 /3 Table 0: Priorities of Supplier w. r. t. Delivery Alternatives Local Priorities Global Priorities(L.P.*0.523) A B C λ ax =3.0648,C.R.=C.I./R..I.=0.0324/0.52=0.0623<0.0 Table : Coparison Matrix for Alternatives w. r. t. Capacity A 5 5 B / /5 C / /5 Table 2: Priorities Of Supplier w. r. t. Capacity Alternatives Local Priorities Global Priorities(L.P.*0.0679) A B C λ ax =3,C.R.=C.I./R.I.= =0/0.52=0<0.0 Table 3: Final Priorities of Alternatives and Criteria Supplier Cost Quality Delivery Capacity Total A B C Total The su of priorities for the supplier A=0.3770, B=0.393, C= It eans that supplier A satisfying all the criteria i.e. we suggest supplier A is the best supplier. Volue 3 Issue 5, May Paper ID: Licensed Under Creative Coons Attribution CC BY

3 4. Fuzzy AHP International Journal of Science and Research (IJSR) ISSN (Online): Ipact Factor (202): The Analytic Hierarchy Process (AHP) is a powerful and flexible decision-aking process to help anagers set priorities and ake the best decision when both qualitative and quantitative aspects of a decision need to be considered. By reducing coplex decisions to a series of one-on-one coparisons, then synthesizing the results, any researchers have concluded that AHP is a useful, practical and systeatic ethod for vendor rating. it has certainly, been applied successfully. However, in any practical cases the huan preference odel is uncertain and decision-akers ight be reluctant or unable to assign exact nuerical values to the coparison udgents. For instance, when evaluating different suppliers, the decision-akers are usually unsure about their level of preference due to incoplete and uncertain inforation about possible suppliers and their perforances [7]. Since soe of the supplier evaluation criteria are subective and qualitative, it is very difficult for the decision-aker to express the strength of his preferences and to provide exact pair-wise coparison udgents. For this reason, a ethodology based on fuzzy AHP can help us to reach an effective decision. By this way we can deal with the uncertainty and vagueness in the decision process. Since basic AHP does not include vagueness for personal udgents, it has been iproved by benefiting fro fuzzy logic approach. In F-AHP, the pair wise coparisons of both criteria and the alternatives are perfored through the linguistic variables, which are represented by triangular nubers [4]. If the uncertainty (fuzziness) of huan decision-aking is not taken into account, the results fro the odels can be isleading. Fuzzy theory has been applied in a variety of fields since its introduction. fuzzy AHP ethods is proposed to solve various types of probles. The ain thee of these ethods is using the concepts of fuzzy set theory and hierarchical structure analysis to present systeatic approaches in selecting or ustifying alternatives []. In this study, the extent analysis ethod by Chang (992, 996) is adopted because the steps of this approach are relatively easier, less tie taking and less coputational expense than any other fuzzy AHP approaches, and at the sae tie, it can overcoe the deficiencies of conventional AHP. The approach not only can adequately handle the inherent uncertainty and iprecision of the huan decision aking process but also can provide the robustness and flexibility needed for the decision aker to understand the decision proble. To decide the final priority of different decision criteria, triangular fuzzy nubers is used in pair-wise coparison, and the extent analysis ethod for the synthetic value of the pair-wise coparison is applied definition and ebership function of fuzzy nubers shown in table 4 (Appendix) Table 5: Coparison atrix for criteria by using fuzzy scale Cost Quality Delivery Capacity Cost,,3,,3,3,5 3,5,7 Quality,,3,,3,3,5 3,5,7 sdelivery /5,/3, /5,/3,,,3,3,5 Capacity /7,/5,/3 /7,/5,/3 /5,/3,,,3 n M g i= = Volue 3 Issue 5, May =(,,3)+(,,3)+(,3,5)+(3,5,7)+..+(,,3) =(5.8857, , ) n M =(/ ,/ ,/5.8857) g i= = Paper ID: Licensed Under Creative Coons Attribution CC BY = M g = = = =(,,3)+(,,3)+(,3,5)+(3,5,7)=(6,0,8) 2 =(6,0,8) 3 =(2.4,4.667,0) 4 =(.4857,.7333,4.6667) The fuzzy synthetic degree values of control criterion, for cost can be calculated as follows: F = = M gi n M gi i= = =(6,0,8) (/ ,/ ,/5.8857) =(0.84,0.3788,.337) Then fuzzy synthetic degree values of control criterion for quality, delivery and capacity can be calculated as follows: F 2 =(0.84,0.3788,.337) F 3 =(0.0473,0.768,0.6295) F 4 =(0.0293,0.0656,0.2937), (F,F 2,F 3,F 4 are fuzzy synthetic degree value for cost, quality, delivery and capacity respectively.) A convex fuzzy nuber can be calculated as follows: V(F F, F 2,..F k )=in V(F F i ), i=,2,.k d(f i )=in V(F i F k )=w, i, k=,2,,n and k i V(F F 2 )=, V(F F 3 )=, V(F F 4 )=, V(F 2 F )=, V(F 2 F 3 )=, V(F 2 F 4 )=, V(F 3 F )= ( ( )) = 0.78, V(F 3 F 2 )=0.78, V(F 3 F 4 )=, V(F 4 F )= V(F 4 F 2 )= V(F 4 F 3 )=0.689 The weight vectors are calculated as follows: d(f )=in V(F F 2,F 3,F 4 )=in (,,)= d(f 2 )=in V(F 2 F,F 3,F 4 )=in (,,)= d(f 3 )=in V(F 3 F,F 2,F 4 )=in (0.78,0.78,)=0.78 d(f 4 )=in V(F 4 F,F 2,F 3 )=in (0.3636,0.3636,0.689)= W =(d(f ), d(f 2 ), d(f 3 ), d(f 4 ))

4 =(,,0.78,0.3636) International Journal of Science and Research (IJSR) ISSN (Online): Ipact Factor (202): After noralization, the noralized weight vector of control criteria is: W=(0.3245,0.3245,0,2330,0.8). Siilar procedures are carried out to calculate relative iportance weight of each alternative with respect to each criterion is follows: Table 6: Coparison atrix for alternatives w. r. t. Cost Supplier A,,3 /5,/3, 3,5,7 Supplier B,3,5,,3 5,7,9 Supplier C /7,/5,/3 /9,/7,/5,,3 The noralized weight vector of alternatives w. r. t. Cost is: W cost =(0.396,0.5456,0.0582). Table 7: Coparison atrix for alternatives w. r. t. Quality Supplier A,,3 3,5,7 /5,/3, Supplier B /7,/5,/3,,3 /9,/7,/5 Supplier C,3,5 5,7,9,,3 The noralized weight vector of alternatives w. r. t. Quality is: W quality =(0.4092,0.0569,0.5338). Table 8: Coparison atrix for alternatives w. r. t. Delivery Supplier A,,3 3,5,7 5,7,9 Supplier B /7,/5,/3,,3,3,5 Supplier C /9,/7,/5 /5,/3,,,3 The noralized weight vector of alternatives w. r. t. Delivery is: W Delivery =(0.68,0.3203,0.066). Table 9: Coparison atrix for alternatives w. r. t. Capacity Supplier A,,3 3,5,7 3,5,7 Supplier B /7,/5,/3,,3,,3 Supplier C /7,/5,/3,,3,,3 The noralized weight vector of alternatives w. r. t. Capacity is: W Capacity =(0.5796,0.202,0.202). The priority weights of the three suppliers obtained by ultiplying the priority weights of criteria to the suppliers weights with respect to all criteria. Table 20: Priority weight of each criteria are as follows W Cost W Quality W Delivery W Capacity Volue 3 Issue 5, May Table 2: Priority weights of each supplier are as follows : Supplier Cost Quality Delivery Capacity Total Weight of supplier A B C Total The su of priorities for the supplier A=0.4734, B=0.2948, C=0.23. It eans that supplier A satisfying all the criteria i.e. We suggest supplier A is the best supplier. 5. Conclusion In both AHP and FAHP, Supplier A has highest ranking, so supplier A is best supplier aong three. By applying the odel, decision akers can evaluate the perforance of each supplier on various factors and deterine the overall ranking of the supplier. In ediu scale industry it was found that cost and quality has equal iportance and followed by delivery and capacity. In AHP, single nubers were introduced for coparison and in F-AHP triangular fuzzy ebers were introduced into the conventional AHP in order to iprove the udgents of decision akers and experts. The ranking of criteria have been ade according to their final scores on the basis of weight. In AHP cost and quality percentage is % and in FAHP it is 32.43% and 5.23% for delivery (AHP) and %( FAHP) (Q-D) AHP= 23.75%, (Q-D) FAHP=9.5%. it show that the difference between cost or quality and delivery is4.60 it is very large as copare to rating in AHP than FAHP, so we can conclude that FAHP gives accuracy and includes uncertainty and vagueness. References [] Ay H.I. Lee (2009) A fuzzy supplier selection odel with the consideration of benefits, opportunities, costs and risks 36, [2] Betül Özkan, Hüseyin Basligil, Nergis Sahin(20) Supplier Selection Using Analytic Hierarchy Process : An Application Fro Turkey,Vol.2. [3] Heung-Suk Hwang, Chiung Moon,Chun-Ling Chuang,Meng-Jong Goan, (2005) Supplier Selection and Planning Model Using AHP, international Journal of the Inforation Systes for Logistics and Manageent (IJISLM), Vol., No., [4] Mustafa Batuhan Ayhan(203) a fuzzy ahp approach for supplier selection proble: a case study in a gearotor copany International Journal of Managing Value and Supply Chains (IJMVSC) Vol.4, No. 3. [5] Petroni and Braglia, (2000) Vendor Selection Using Principal Coponent Analysis, The Journal of Supply Chain Manageent: A Global Review of Purchasing and Supply, [6] Raeev Jain, A.R. Sing P.K. Mishra,( 203) Prioritization of Supplier Selection Criteria: A Fuzzy- AHP Approach MIT International Journal of Mechanical Engineering, Vol. 3, No., [7] Saro Koul, Rakesh Vera, dynaic vendor selection: a fuzzy ahp approach [8] Sanay Kuar, Neera Parashar, Dr. Abid Halee,( 2009) analytical hierarchy process applied to vendor Paper ID: Licensed Under Creative Coons Attribution CC BY

5 ISSN (Online): Ipact Factor (202): selection proble: sall scale, ediu scale and large scale industries business intelligence ournal Appendix Tables Table : Scale of Preference between Two Eleent (Sanay Kuar et.al) S. No. Preference weights/level of iportance Definition Explanation Equally Two activities contribute equally to the obective 2 3 Moderately Experience and udgent slightly favour one activity over another 3 5 Strongly pre- Experience and udgent ferred 4 7 Very strongly 5 9 Extreely 6 2,4,6,8 Interediates values 7 Reciprocals Reciprocals for inverse coparison strongly or essentially An activity is strongly favoured over another and its doinance deonstrated in practice The evidence favouring one activity over another is of the highest degree possible of affiration Used to represent coproise between the preferences listed above Table 2: Average rando index (RI) based on Matrix Size (Sanay Kuar et.al) S.No. Size of Matrix (n) Rando Consistency Index (RI) Table 4: Definition and ebership function of fuzzy nubers (Raeev Jain et.al) Intensity of Fuzzy Definition Mebership Iportance nuber function ~ Equally iportant/ (,, 3) 3 ~ Moderately ore 3 iportant/ 5 ~ Strongly ore 5 iportant/ 7 ~ Very strongly ore 7 iportant/ 9 ~ Extreely ore 9 iportant/ (, 3, 5) (3, 5, 7) (5, 7,9) (7, 9, ) Volue 3 Issue 5, May Paper ID: Licensed Under Creative Coons Attribution CC BY