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International Journal of Modern Engineering Research (IJMER)
                  www.ijmer.com         Vol.2, Issue.6, Nov-Dec. 2012 pp-4189-4194       ISSN: 2249-6645

    A Fuzzy Logic Multi-Criteria Decision Approach for Vendor Selection
                          Manufacturing System
                                                    Harish Kumar Sharma1
                              National Institute of Technology, Durgapur (WEST BENGAL) - 1713209

Abstract: The success of an industry depends on                         decision making ( MCDM) are coherently derived to
optimization of product cost and for achieving above goal               manage the problem ( Shyur &Shih, 2006).Evaluating
Internal selection should be efficient. In the present study            vendors many criteria including quantitative, such as cost,
an efficient Multi-Criteria Decision Making (MCDM)                      price as well as qualitative, a considerable number of
approach has been proposed for quality evaluation and                   decision models have been developed based on the MCDM
performance appraisal in vendor selection. Vendor                       theory.
selection is a Multi-Criteria Decision Making (MCDM)                             To resolve the problem, this paper suggests
problem influenced by several parameters which are in                   evaluating vendor using a multiple levels multiple criteria
linguistic. Multiple.Performance criteria/attributes. These             decision making method under fuzzy logic method
criteria attributes may be both qualitative as well as                  maintenance alternative for industries planning of the basis
quantitative. Qualitative criteria estimates are generally              of quantitative and qualitative factors formula are clearly
based on previous experience and perfomanance maker’s                   displayed. Classified to benefit and cost criteria has the
opinion on suitability. Therefore to quantity the linguistic            larger the better, ratings of vendor and importance weights
variables fuzzy logic and set theory is used. The fuzzy set             of all the criteria are assessed in linguistic values
theory helps in vagueness of the system. a fuzzy decision               represented by fuzzy numbers.
approach is developed where are resourcing of vendors to                 Selection of fuzzy number & their membership
select suitable vendor for materials is made MCDM method                     functions.
has been illustrated in this reporting through a case study.             Fuzzy logic of the scale function
                                                                         Averaging the fuzzy numbers as given by the
Keywords: Vendor’s selection Fuzzy sets, Decision matrix,                    performance makers in terms linguistics variables.
Rank, Multiple criteria decision making, weight                          Determinations of fuzzy normalize weight.
                                                                         Overall ranking of alternatives.
                       I. Introduction                                   Finally result of multi criteria decision making
          Iron and steel industry is an important basic                          In this paper the vendor selection by a MCDM for
industry for any industrial economy providing the primary               these logic method identified a criteria based on product,
material for construction, automobile machinery and other               cost ,quality ,service etc. these criteria short out the vendor
industries. the importance of maintenance function has                  by using the performance makers P1,P2,P3,P4,P5, and PN
increased due to its role in keeping and improving the                  these performance makers gives the data in a logistics
availability, product       quality cost-effectiveness levels.          variable weight of the criteria then we find the suitable
Maintenance costs constitute an important part of the                   vendor material
operating budget of manufacturing firms. Maintenance
selection is one of the most critical activities for many                       II. REVIEW OF PREVIOUS WORK
industries. The selection of an appropriate maintenance may                      [1]The vendor selection a focus area of research
reduce the purchasing cost and also improve                             since the 1966s.literature (Dickson,1966; Weber
competitiveness.                                                        ,1991)several dimensions are mentioned that are important
          It is impossible for a company to successfully                for              the            multiple             vendor
produce, low-cost, high-quality products without                        selectiondecision.nmaking,price,quality,delivery,performan
satisfactory maintenance. The selection of appropriate                  ce,history,capacity,service Production facilities and
maintenance has been one of the most important function                 technical capabilities etc. the problem is how to select
for a industries. If the relationship between a supplier and            vendor that perform optimally on the desired dimensions.[2]
manufacturing industries. Many studies have pointed out                 Weber et al.(1991) reviewed 74 vendor(supplier)
that key is to set effective evaluation criteria for the supplier       selection articles from 1966 to 1991 and showed that more
selection                                                               than 63% of them were in a multi criteria decision making.
       Vendor selection is a common problem for acquiring               other researchers also endorsed using a weighted linear
the necessary materials to support the output of                        method of multiple for the VSP. Gaballa (1974) is the
organizations. The problem is to find and evaluate                      first author who applied mathematical programming to a
periodically the best or most suitable vendor for the                   vendor selection problem in a real case. He used a mixed
organization based on various vendor. Due to the fact that              integer programming .model to minimize the total
the evaluation always involves conflicting performance                  discounted price of it misallocated to the VSP. Weber
criteria of vendors. The techniques of multiple criteria
                                                        www.ijmer.com                                                      4189 | Page
International Journal of Modern Engineering Research (IJMER)
                                                    www.ijmer.com         Vol.2, Issue.6, Nov-Dec. 2012 pp-4189-4194       ISSN: 2249-6645
and Current (1993) developed a multi objective MIP for                                                                                                                     normality with at least one element with degree of
vendor selection and order allocation among the selected
vendors .they applied the proposed model in a proposed                                                                                                                               x  a                         x  a            
model in a practical case.[3] Buffa and Jackson (1983) and                                                                                                                                    a  x  b                       a  xb
Sharma et al. (1989), respectively, used linear and non-                                                                                                                             b  a                         b  a            
linear mixed-integer goal programming (GP) for price,                                                                                                                               c  x
                                                                                                                                                                                                        
                                                                                                                                                                                                                     1b  x  c
                                                                                                                                                                                                                                          
                                                                                                                                                                                                                                           
                                                                                                                                                                           x             b  x  c    x                       
                                                                                                                                                                                    c  a                           x  d  c  x  d 
service level, delivery and quality goals. Failure base
                                                                                                                                                                                                         
maintenance (FBM) is         performed when a failure or                                                                                                                            0                                c  d            
breakdown occurs, no action is taken to detect the onset of                                                                                                                                                                             
or to present failure. The maintenance related costs are                                                                                                                            
                                                                                                                                                                                                        
                                                                                                                                                                                                                     
                                                                                                                                                                                                                      0                   
                                                                                                                                                                                                                                           
usually high, but it may be considered cost effective in
certain cases.[4] fuzzy multi agent system is proposed for                                                                                                                (a) fA is a continuous mapping from R to [0, 1];
ta-chung chu,Rangnath varma (2011),developed to depict                                                                                                                    (b) fA(x) = 0,∀ x ∈ (-∞,a ]
the relationship among parent criteria and their sub-criteria                                                                                                             (c) fA is strictly increase on [a, b];
and criteria and the weight of all criteria,[5] amit karami                                                                                                               (d) fA (x) = 1, x e [b, c];
and zhiling Gua We demonstrate that the fuzzy logic                                                                                                                      (e) fA is strictly decreasing on [c, d];(f) fA(x) = 0,∀ x ∈[d,∞);
approach provides a robust analysis for vendor selection,                                                                                                                Where a, b, c and d are real numbers. We may let a -1, or a=b,
[6]eleonona botani ,Antonio Rizzi (2007) An adapted multi                                                                                                                or b=c or c=d or d= +1
–criteria approach to suppliers and products selection An
application oriented to lead-time reduction. An extensive                                                                                                                    IV. OPERATIONS ON FUZZY NUMBERS
case study is presented to show the practical application of                                                                                                             Let A=(a1,b1,c1,d1) and B= (a2,b2,c2,d2) are two
the methodology                                                                                                                                                          trapezoidal fuzzy numbers. Then the operations [+,-
                                                                                                                                                                         ,×,÷] are expressed (Kaufmann and Gupta 1991) as.
            III. METHOD OF SOLUTION
2.1 Fuzzy sets                                                                                                                                                           Let
A fuzzy set A can denoted by Ai = {(x, fA(x)) |x U}, where                                                                                                                             A  B   a1 , b1 , c1 , d1 )  ( a2 , b2 , c2 , d 2                                  
U is universe of discourse, x is an element in U, A is a                                                                                                                                                  a1  a2 , b1  b2 , c1  c2 , d1  d 2                               
fuzzy set in fA(x) is the membership function of A x
(Kaufmann & gupta, 1991) the larger fA(x), the stronger the
                                                                                                                                                                                       A  B  ( a1 , b1 , c1 , d1 )  ( a2 , b2 , c2 , d 2 )
grade of membership for x in A
                                                                                                                                                                                                          a1  d 2 , c1  b2 , c1  b2 , d1  a2                       
2.2 Fuzzy numbers
A real fuzzy number A is described as any fuzzy subset of
the real line R with membership function fA which                                                                                                                                      A  B   a1 , b1 , c1 , d1   ( a2 , b2 , c2 , d 2 )
possesses the following properties (Dubois & Prade, 1978                                                                                                                                                  a1  a2 , b1  b2 , c1  c2 , d1  d 2                           
                                                                                        Triangular L-R Fuzzy Number
                                                   1.0                                                                                                                                 A
                                                                                                                                                                                         
                                                                                                                                                                                            a1. b1 , c1 , d1 
                                                                                                                                                                                       B  a2 , b2 , c2 , d 2 
                                                   0.9

                                                   0.8
                               Membership Value




                                                   0.7

                                                   0.6                                                                                                                                         a b c d 
                                                   0.5                                                                                                                                         1 , 1 , 1 , 1 
                                                   0.4
                                                                                                                                                                                                d 2 c2 b2 a2 
                                                   0.3

                                                   0.2                                                                                                                         µ (X)
                                                                                                                                                                                A


                                                   0.1

                                                   0.0
                                                         0.0         0.1          0.2          0.3          0.4     0.5     0.6       0.7     0.8          0.9     1.0                 Very Low            Low    More or Less Low   Medium   More or Less High   High               Very High
                                                                                  A                                 B                         C
                                                                                                       X (Input space)



                                                                                   Trapezoidal L-R Fuzzy Number
                                            1.0

                                             0.9

                                             0.8
            Membership Value




                                             0.7

                                             0.6

                                             0.5
                                                                     Left                                                                           Right
                                             0.4

                                             0.3

                                             0.2
                                                                                                                                                                                    0.0           0.1      0.2   0.3         0.4      0.5     0.6         0.7     0.8            0.9             1.0

                                             0.1
                                                                                                                                                                                                                                   WEIGHT
                                             0.0
                                                   0.0         0.1          0.2          0.3          0.4         0.5     0.6     0.7       0.8        0.9       1.0
                                                               A                         B                                        C                    D
                                                                                                     X (Input space)
                                                                                                                                                                            Fig. 2: Graphical representation of fuzzy numbers for
                                                                                                                                                                                             linguistic variables.
   A fuzzy number is defined as a continuous fuzzy set
  that contains convexity with one distinct peak and                                                                                                                     For the selection of location, seven fuzzy numbers are taken
                                                                                                                                                        www.ijmer.com                                                                                                    4190 | Page
International Journal of Modern Engineering Research (IJMER)
                 www.ijmer.com         Vol.2, Issue.6, Nov-Dec. 2012 pp-4189-4194       ISSN: 2249-6645
to describe the level of performance on decision criteria, to             Step – 4:
avoid difficulties for an performance makers in
distinguishing subjectively between more than seven                             The normalized weight for each criteria (Ci) is
alternatives Salty (1977)                                              obtained as Wj, Where J=1, 2… n. The normalized weight
Table 1 shows the fuzzy numbers associated with the                    for each criterion is obtained by dividing the Defuzzified
corresponding linguistic variables and the same is                     scores of each criterion by the total of all the criteria.
graphically represented in figure3.                                    Rating of Suitable Locations:
                                                                                In similar way as procedure adopted for the
Table 1: Fuzzy numbers and corresponding linguistic                    calculation of weight criteria, the rating of suitable location
variables                                                              is derived as:
       Linguistic Variable    Fuzzy Number                             •        Locations suitable on each of the criteria are to
        VL (Very low)               (0.0, 0.0, 0.1, 0.2)                        be rated in the linguistic variables by the
                                                                                performance makers, which is converted into
             L (low)                (0.1, 0.2, 0.3, 0.4)                        fuzzy numbers and the same is represented in
                                                                                the matrix form (Fuzzy Decision Matrix).
 ML/LL (more or less low )          (0.2, 0.3, 0.4, 0.5)               •        The average fuzzy score matrix for each
     M ( Medium)                    (0.4, 0.5, 0.5, 0.6)                        locations are obtained.
 MH/LH (more or less high)          (0.5, 0.6, 0.7, 0.8)               •        The crisp score (Defuzzified value) for each
                                                                                location are obtained and same is represented in
        H( High)                    (0.6, 0.7, 0.8, 0.9)
                                                                                the matrix form as Xij, where i= 1,2 , m and J=
       VH (Very high)               (0.8, 0.9, 1.0, 1.0)                        1,2, , n. Where, m is the number of locations, n is
                                                                                the number of criteria.
                                                                       •        Total aggregated score for locations against
Step – 1:                                                                       each criteria is obtained as
The linguistic variables assigned by the experts for each
criteria is translated into fuzzy numbers and the same is                    TS = {Xij} {Wj}
represented in the matrix (Fuzzy Decision Matrix).
                                                                                v11v12  v1 j  v1m   w1 
  Step – 2:                                                                                            
Let Ajar be the fuzzy number assigned to an vendor AI by                        v21v22  v2 j  v2 m   w2 
                                                                                                     
the Perfomanance makers (Pk) for the decision criterion.
                                                                           TS                             v  w t
Cj, the average of fuzzy numbers is given as                                    vi1vi 2  vij  vim   w j 
                                                                                                       
     Aij 
             1
                 a j i1  a j i 2  ......  a j ik  ; k                                          
             p                                                                  vn1vn 2  vnj  vnm   wn 
                                                                                                       

                           =1,2………….p.                                           On the basis of the total score obtained for
                                                                       each location against decision criteria, overall scores are
 The average fuzzy score matrix for each criteria is                   obtained, using simple average method, which provide
obtained.                                                              final ranking of locations.
                                                                                           V. CASE STUDY
   Step – 3:
                                                                             Steel industries purposed methodology allows the
The crisp score (Defuzzified values) for each criteria is
                                                                       experts to rank the suitable vendor reelection for a
obtained. Defuzzification of fuzzy numbers is an operation
                                                                       magnum steel limited Gwalior (India) companies on the
that produces a non fuzzy crisp value. Defuzzified value is
                                                                       basis of different decision criteria in a more realistic
given by the following equation (Kaufman and Gupta,
                                                                       manner. The advantage of fuzzy set theory facilitates the
1991).
                                                                       assessment to be made on the basic of linguistic manner,
                                                                       which corresponded to the real lie situations in a much
Trapezoidal fuzzy number
                                                                       better way for simplicity five perfomanance makers E1,
        E
              a  b  c  d                                          E2,, E3, E4, E5 vendor selection projects, were consulted
                       4                                               to get the linguistic variables in terms of importance of
                                                                       each of the delusion criteria used to rank the vendor for
Triangular fuzzy number                                                each criteria’s (V1, V2, V3, V4, V5).

         E
                a  2b  c                                           1. material cost(C1)
                                                                       2. Semi –Raw material cost (C2)
                       4
                                                       www.ijmer.com                                                      4191 | Page
International Journal of Modern Engineering Research (IJMER)
                      www.ijmer.com         Vol.2, Issue.6, Nov-Dec. 2012 pp-4189-4194       ISSN: 2249-6645
3.    Transportation cost (C3)                                                   30      33        30         0           9
4.    Inventory and storage cost (C4)
                                                                       C5        0.6     0.7       0.8        0.93        0.80      0.253
5.     Production Process cost (C5)                                              70      67        70         0           9
6.    On time delivery (C6)
                                                                       C6        0.5     0.6       0.7        0.80        0.67      0.211
7.    Percentage waste items (C7)                                                60      34        20         0           8
8.    Flexibility in service (C8)                                      C7        0.2     0.3       0.4        0.50        0.35      0.110
9.    Financial position (C9)                                                    00      00        00         0           0
10.   Inspection (quality control) (C10)                               C8        0.5     0.6       0.7        0.83        0.67      0.211
                                                                                 41      20        20         1           8
Table. 2 show the linguistic variables assigned by the                 C9        0.4     0.5       0.6        0.72        0.59      0.184
Perfomanance makers to each of the decision criteria are                         22      80        42         0           1
define in the table -1                                                 C10       0.4     0.5       0.6        0.72        0.60      0.190
                                                                                 70      67        70         0           7
Table 3: Linguistic variables assigned by the Perfomanance
                          maker’s                                                Rating of alternatives (venders) on criterion (Xi j)
 Criteria                   perfomanance maker’s                       Suitability of venders against each criteria are to be rated
                                                                       and linguistic variables are assigned by the experts to the
                 E1         E2         E3      E4      E5              venders table-3 are define in table-1 the linguistic variables
 C1              H          M          H       H       VH              are converted into fuzzy numbers
 C2              H          H          H       VH      H
                                                                              Table 5: Linguistics variables for alternatives
 C3              MH         H          H       VH      VH
                                                                    C1           V1           M          L           M        L         M
 C4              MH         MH         M       M       M
                                                                                 V2           H          M           VH       H         M
 C5              M          M          MH      M       M                         V3           VH         M           M        VH        VH
 C6              H          H          VH      H       M                         V4           VH         VH          H        VH        VH

 C7              MH         VH         M       MH      M                         V5           H          H           M        H         H
                                                                    C2           V1           VH         VH          VH       VH        VH
 C8              M          MH         MH      M       M
                                                                                 V2           H          H           H        VL        L
 C9              VH         H          VH      M       H
                                                                                 V3           H          VH          VH       VH        VH
 C10             MH         MH         M       VH      M                         V4           M          M           VH       H         VH
                                                                                 V5           VH         VH          M        H         H
The average fuzzy scores, defuzzifled values and                    C3           V1           L          M           M        M         M
normalized weight of criteria are obtained and given in table
3                                                                                V2           L          M           H        M         H
         Table 3: Normalized weight of criteria                                  V3           H          VH          H        H         VH
 criter    Parameter of average fuzzy          Defu    Norma                     V4           VH         H           H        H         VH
 ia        scores                              zz      lized                     V5           M          VH          H        VH        H
                                               ifled   weight       C4           V1           VH         VH          M        H         H
                                               Valu                                           VL         M           M        H         VH
                                               e
                                                                                 V2
                                                                                 V3           VH         VH          H        H         M
 C1        0.6        0.7        0.8    0.89   0.80    0.250
                                                                                 V4           M          H           H        VH        M
           70         67         70     0      0
                                                                                 V5           VH         H           M        VH        VH
 C2        0.4        0.5        0.6    0.72   0.60    0.190
           70         67         70     0      6                    C5           V1           M          H           M        L         M

 C3        0.6        0.7        0.8    0.92   0.80    0.253                     V2           H          L           VL       L         M
           70         68         70     0      7                                 V3           M          M           VL       H         H
 C4        0.5        0.6        0.7    0.78   0.66    0.209                     V4           H          VH          M        M         H

                                                       www.ijmer.com                                                              4192 | Page
International Journal of Modern Engineering Research (IJMER)
                   www.ijmer.com         Vol.2, Issue.6, Nov-Dec. 2012 pp-4189-4194       ISSN: 2249-6645

            V5         H       M        H       M        VH              V2       0.480   0.530   0.633     0.730   0.593
 C6         V1         VH      H        VL      H        M               V3       0.470   0.567   0.670     0.720   0.607
                       VH      H        M       M        H               V4       0.330   0.433   0.530     0.450   0.436
            V2                                                           V5       0.400   0.500   0.600     0.700   0.550
            V3         L       VL       M       VL       L         C4    V1       0.733   0.830   0.930     0.980   0.868
            V4         L       L        L       H        H               V2       0.267   0.370   0.470     0.520   0.407
            V5         VH      H        H       H        VH              V3       0.400   0.500   0.600     0.700   0.550
 C7         V1         VL      M        L       VL       L               V4       0.400   0.500   0.600     0.700   0.550
            V2         VL      M        M       M        H               V5       0.533   0.630   0.730     0.801   0.494
            V3         M       M        VL      VL       L         C5    V1       0.200   0.300   0.400     0.500   0.350
                                                                         V2       0.730   0.833   0.930     0.980   0.856
            V4         H       H        L       L        VL
                                                                         V3       0.670   0.767   0.870     0.920   0.807
            V5         H       VH       VH      M        M
                                                                         V4       0.470   0.470   0.567     0.720   0.557
 C8         V1         VH      M        L       H        H
                                                                         V5       0.530   0.633   0.730     0.820   0.679
            V2         VL      VL       L       M        M
                                                                   C6    V1       0.470   0.567   0.670     0.720   0.607
            V3         H       M        H       H        H
                                                                         V2       0.470   0.567   0.670     0.700   0.602
            V4         L       M        H       M        H
                                                                         V3       0.130   0.233   0.330     0.460   0.289
            V5         M       M        H       H        H
                                                                         V4       0.530   0.630   0.730     0.820   0.678
 C9         V1         L       M        L       L        L
                                                                         V5       0.470   0.570   0.670     0.720   0.608
            V2         H       M        H       M        L
                                                                   C7    V1       0.730   0.830   0.930     0.950   0.860
            V3         L       M        VH      H        M
                                                                         V2       0.530   0.630   0.730     0.820   0.678
            V4         M       VL       L       L        L
                                                                         V3       0.400   0.500   0.600     0.700   0.550
            V5         H       H        M       M        VL
                                                                         V4       0.330   0.430   0.500     0.670   0.483
 C10        V1         H       VL       L       VL       VL
                                                                         V5       0.530   0.630   0.730     0.820   0.678
            V2         L       H        H       H        M
                                                                   C8    V1       0.470   0.570   0.670     0.720   0.608
            V3         L       L        VL      VL       VL
                                                                         V2       0.730   0.830   0.930     0.980   0.868
            V4         M       L        VL      M        VL
                                                                         V3       0.670   0.767   0.870     0.890   0.800
            V5         M       L        VL      M        H
                                                                         V4       0.470   0.470   0.567     0.620   0.532
                                                                         V5       0.530   0.633   0.730     0.820   0.679
      Table 6: Average fuzzy scores and Defuzzified scores
                                                                   C9    V1       0.470   0.567   0.670     0.720   0.606
criteria   Vendo     Average Fuzzy scores               Defuzz
           r                                              ied            V2       0.470   0.567   0.670     0.720   0.607
                                                         score           V3       0.130   0.233   0.330     0.460   0.289
C1         V1        0.670    0.767    0.870   0.890    0.799            V4       0.530   0.630   0.730     0.820   0.678
           V2        0.470    0.567    0.670   0.710    0.605            V5       0.470   0.570   0.670     0.720   0.608
           V3        0.670    0.767    0.870   0.880    0.797      C10   V1       0.730   0.830   0.930     0.960   0.863
           V4        0.530    0.633    0.730   0.800    0.674            V2       0.530   0.630   0.730     0.830   0.680
           V5        0.670    0.767    0.870   0.900    0.802            V3       0.400   0.500   0.600     0.700   0.550
C2         V1        0.530    0.633    0.730   0.820    0.679            V4       0.330   0.430   0.500     0.640   0.476
           V2        0.200    0.300    0.400   0.500    0.350            V5       0.530   0.630   0.730     0.820   0.678
           V3        0.730    0.833    0.930   0.980    0.869            V4       0.467   0.567   0.667     0.767   0.617
           V4        0.670    0.767    0.870   0.910    0.805            V5       333     0.433   0.530     0.620   0.479
           V5        0.600    0.700    0.800   0.900    0.750
C3         V1        0.530    0.633    0.730   0.850    0.686

                                                       www.ijmer.com                                           4193 | Page
International Journal of Modern Engineering Research (IJMER)
                   www.ijmer.com         Vol.2, Issue.6, Nov-Dec. 2012 pp-4189-4194       ISSN: 2249-6645
 The total scores for each vendor can be calculated matrix
                         as follows                                                VII.     ACKNOWLEDGEMENT
     V        V2       V3       V4           V5        Wj                         Authors would like to thank to Vimal steel
      1
                                                                         corporation ltd., for providing data’s to create decision
     C1  0.800     0.605   0.797    0.674    0.802  0.250            criteria & also thank to Perfomanance maker’s for
     C2  0.679     0.350   0.869    0.805    0.750  0.190            providing linguistic variables to apply fuzzy multi criteria
                                                            
     C3  0.686     0.593   0.607    0.436    0.550   0.253           decision approach for selecting the best vendor for a
                                                                     companies.
     C4  0.868     0.407   0.550    0.550    0.494  0.209 
     C5  0.350     0.856   0.807    0.557    0.679  0.254 
                                                                                         REFERENCES
     C6 0.607      0.602   0.289    0.678    0.608   0.213
TS                                                                    [1]   Alexios-patapios kontis and vassilionvyagotis,
     C7  0.860     0.678   0.550    0.483    0.678     0.110 
                                                                           supplier Selection problem multi-criteria approaches
     C8  0.608     0.808   0.800    0.532    0.629  0.212 
                                                                               based on DEA,international Scientific Advances in
     C9  0.606     0.607   0.289    0.678    0.608   0.185 
                                                                           Management & Applied Economics, vol1.1,no.2,207-
     C10  0.863    0.680   0.550    0.476    0.678  0.190                  219(2011)
                                                            
                                                                     [2]   Shyur &Shih, 2006.Evaluating vendors many criteria
         
                                                    
                                                             
                                                                                 Including quantitative, as well as qualitative, a
                                                                               considerable Number of decision making European
Total scores for vender (V1) on criteria is obtained as-
                                                                               Journal of Operation Research, Vol.50, 5-10(2009)
(0.800×0.250)+(0.679×0.190)+(0.686×0.253)+(0.868×0.20
                                                                         [3]   Kaufmann, A.,& Gupta, M.M, Introduction to Fuzzy
9)+(0.350×0.254)+(0.607×0.213)+(0.860×0.110)+(0.608×0
                                                                               Arithmetic theory & application, Van No strand
.212)+(0.606×0.185)+(0.863×0.190)= 1.4035
                                                                               Reinhold, Newyork.vol.1; 5-18 (1991)
Similarly, total scores for venders (V2), (V3),(V4),(V5)are
                                                                         [4]   Dickson, Weber, Multi objective linear model for
obtained and provided in table-7In the selection of suitable
                                                                               Vendor Selection criteria and methods, European
vendor for any company , initial investment, qualitative
                                                                               Journal of
criteria each has equal weight age. Hence t h e final
                                                                               Operational Research, Vol.50, 2-18(1991)
s c o r e s a n d r a n k i n g o f venders are given in table.6
                                                                         [5]   Buffa and Jackson and Sharma, Multi decision making
                                                                               used linear and non-linear programming, Total
        Table 7: Final scores and ranging of venders.
                                                                               Quality Environmental Management Vol.3 (4); 521-
Vendors V1               V2           V3          V4        V5                 530(1994)
 Final                                                                   [6]   Tu-chung Chu, Rangnath varma, Evaluating suppliers
Scores 1.4035          1.2859       1.29900   1.2489     1.3353                via a multiple criteria decision making method under
 Rank      1              4         000001
                                        3        5           2                 fuzzy Enviroment,
                                                                               nternationalJournalofcomputers&Industrial
           VI. RESULTS CONCLUSION                                               Engineering vol, 62; 653-660(2012)
         This paper, presented the fuzzy multi criteria                  [7]   Swanson’s., 2001.Linking maintenance strategies
decision approach, the order odd ranking of vendor’s for                       To performance. International Journal of Production
the company’s are as V1>V5>V3>V2>V4. The result                                Economics70, 237-244. (2001)
show V1 is the best location for the company. Has been                   [8]   Shyur &Shih, 2006.Evaluating vendors many criteria
highlighted to solve multi-criteria decision making                            Including quantitative, as well as qualitative, a
problems through a case study of vendor selection. The                         considerable Number of decision making European
Study demonstrates the effectiveness of the said MCDM                          Journal of Operational Research,Vol.50,5-10(2009)
techniques in solving such a vendor selection problem.




                                                         www.ijmer.com                                                   4194 | Page

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A Fuzzy Logic Multi-Criteria Decision Approach for Vendor Selection Manufacturing System

  • 1. International Journal of Modern Engineering Research (IJMER) www.ijmer.com Vol.2, Issue.6, Nov-Dec. 2012 pp-4189-4194 ISSN: 2249-6645 A Fuzzy Logic Multi-Criteria Decision Approach for Vendor Selection Manufacturing System Harish Kumar Sharma1 National Institute of Technology, Durgapur (WEST BENGAL) - 1713209 Abstract: The success of an industry depends on decision making ( MCDM) are coherently derived to optimization of product cost and for achieving above goal manage the problem ( Shyur &Shih, 2006).Evaluating Internal selection should be efficient. In the present study vendors many criteria including quantitative, such as cost, an efficient Multi-Criteria Decision Making (MCDM) price as well as qualitative, a considerable number of approach has been proposed for quality evaluation and decision models have been developed based on the MCDM performance appraisal in vendor selection. Vendor theory. selection is a Multi-Criteria Decision Making (MCDM) To resolve the problem, this paper suggests problem influenced by several parameters which are in evaluating vendor using a multiple levels multiple criteria linguistic. Multiple.Performance criteria/attributes. These decision making method under fuzzy logic method criteria attributes may be both qualitative as well as maintenance alternative for industries planning of the basis quantitative. Qualitative criteria estimates are generally of quantitative and qualitative factors formula are clearly based on previous experience and perfomanance maker’s displayed. Classified to benefit and cost criteria has the opinion on suitability. Therefore to quantity the linguistic larger the better, ratings of vendor and importance weights variables fuzzy logic and set theory is used. The fuzzy set of all the criteria are assessed in linguistic values theory helps in vagueness of the system. a fuzzy decision represented by fuzzy numbers. approach is developed where are resourcing of vendors to  Selection of fuzzy number & their membership select suitable vendor for materials is made MCDM method functions. has been illustrated in this reporting through a case study.  Fuzzy logic of the scale function  Averaging the fuzzy numbers as given by the Keywords: Vendor’s selection Fuzzy sets, Decision matrix, performance makers in terms linguistics variables. Rank, Multiple criteria decision making, weight  Determinations of fuzzy normalize weight.  Overall ranking of alternatives. I. Introduction  Finally result of multi criteria decision making Iron and steel industry is an important basic In this paper the vendor selection by a MCDM for industry for any industrial economy providing the primary these logic method identified a criteria based on product, material for construction, automobile machinery and other cost ,quality ,service etc. these criteria short out the vendor industries. the importance of maintenance function has by using the performance makers P1,P2,P3,P4,P5, and PN increased due to its role in keeping and improving the these performance makers gives the data in a logistics availability, product quality cost-effectiveness levels. variable weight of the criteria then we find the suitable Maintenance costs constitute an important part of the vendor material operating budget of manufacturing firms. Maintenance selection is one of the most critical activities for many II. REVIEW OF PREVIOUS WORK industries. The selection of an appropriate maintenance may [1]The vendor selection a focus area of research reduce the purchasing cost and also improve since the 1966s.literature (Dickson,1966; Weber competitiveness. ,1991)several dimensions are mentioned that are important It is impossible for a company to successfully for the multiple vendor produce, low-cost, high-quality products without selectiondecision.nmaking,price,quality,delivery,performan satisfactory maintenance. The selection of appropriate ce,history,capacity,service Production facilities and maintenance has been one of the most important function technical capabilities etc. the problem is how to select for a industries. If the relationship between a supplier and vendor that perform optimally on the desired dimensions.[2] manufacturing industries. Many studies have pointed out Weber et al.(1991) reviewed 74 vendor(supplier) that key is to set effective evaluation criteria for the supplier selection articles from 1966 to 1991 and showed that more selection than 63% of them were in a multi criteria decision making. Vendor selection is a common problem for acquiring other researchers also endorsed using a weighted linear the necessary materials to support the output of method of multiple for the VSP. Gaballa (1974) is the organizations. The problem is to find and evaluate first author who applied mathematical programming to a periodically the best or most suitable vendor for the vendor selection problem in a real case. He used a mixed organization based on various vendor. Due to the fact that integer programming .model to minimize the total the evaluation always involves conflicting performance discounted price of it misallocated to the VSP. Weber criteria of vendors. The techniques of multiple criteria www.ijmer.com 4189 | Page
  • 2. International Journal of Modern Engineering Research (IJMER) www.ijmer.com Vol.2, Issue.6, Nov-Dec. 2012 pp-4189-4194 ISSN: 2249-6645 and Current (1993) developed a multi objective MIP for normality with at least one element with degree of vendor selection and order allocation among the selected vendors .they applied the proposed model in a proposed  x  a   x  a  model in a practical case.[3] Buffa and Jackson (1983) and  a  x  b  a  xb Sharma et al. (1989), respectively, used linear and non-  b  a    b  a  linear mixed-integer goal programming (GP) for price, c  x    1b  x  c      x    b  x  c    x     c  a  x  d  c  x  d  service level, delivery and quality goals. Failure base  maintenance (FBM) is performed when a failure or 0   c  d   breakdown occurs, no action is taken to detect the onset of     or to present failure. The maintenance related costs are      0   usually high, but it may be considered cost effective in certain cases.[4] fuzzy multi agent system is proposed for (a) fA is a continuous mapping from R to [0, 1]; ta-chung chu,Rangnath varma (2011),developed to depict (b) fA(x) = 0,∀ x ∈ (-∞,a ] the relationship among parent criteria and their sub-criteria (c) fA is strictly increase on [a, b]; and criteria and the weight of all criteria,[5] amit karami (d) fA (x) = 1, x e [b, c]; and zhiling Gua We demonstrate that the fuzzy logic (e) fA is strictly decreasing on [c, d];(f) fA(x) = 0,∀ x ∈[d,∞); approach provides a robust analysis for vendor selection, Where a, b, c and d are real numbers. We may let a -1, or a=b, [6]eleonona botani ,Antonio Rizzi (2007) An adapted multi or b=c or c=d or d= +1 –criteria approach to suppliers and products selection An application oriented to lead-time reduction. An extensive IV. OPERATIONS ON FUZZY NUMBERS case study is presented to show the practical application of Let A=(a1,b1,c1,d1) and B= (a2,b2,c2,d2) are two the methodology trapezoidal fuzzy numbers. Then the operations [+,- ,×,÷] are expressed (Kaufmann and Gupta 1991) as. III. METHOD OF SOLUTION 2.1 Fuzzy sets Let A fuzzy set A can denoted by Ai = {(x, fA(x)) |x U}, where A  B   a1 , b1 , c1 , d1 )  ( a2 , b2 , c2 , d 2  U is universe of discourse, x is an element in U, A is a   a1  a2 , b1  b2 , c1  c2 , d1  d 2  fuzzy set in fA(x) is the membership function of A x (Kaufmann & gupta, 1991) the larger fA(x), the stronger the A  B  ( a1 , b1 , c1 , d1 )  ( a2 , b2 , c2 , d 2 ) grade of membership for x in A   a1  d 2 , c1  b2 , c1  b2 , d1  a2  2.2 Fuzzy numbers A real fuzzy number A is described as any fuzzy subset of the real line R with membership function fA which A  B   a1 , b1 , c1 , d1   ( a2 , b2 , c2 , d 2 ) possesses the following properties (Dubois & Prade, 1978   a1  a2 , b1  b2 , c1  c2 , d1  d 2  Triangular L-R Fuzzy Number 1.0 A   a1. b1 , c1 , d1  B  a2 , b2 , c2 , d 2  0.9 0.8 Membership Value 0.7 0.6 a b c d  0.5  1 , 1 , 1 , 1  0.4  d 2 c2 b2 a2  0.3 0.2 µ (X) A 0.1 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 Very Low Low More or Less Low Medium More or Less High High Very High A B C X (Input space) Trapezoidal L-R Fuzzy Number 1.0 0.9 0.8 Membership Value 0.7 0.6 0.5 Left Right 0.4 0.3 0.2 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0.1 WEIGHT 0.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 A B C D X (Input space) Fig. 2: Graphical representation of fuzzy numbers for linguistic variables. A fuzzy number is defined as a continuous fuzzy set that contains convexity with one distinct peak and For the selection of location, seven fuzzy numbers are taken www.ijmer.com 4190 | Page
  • 3. International Journal of Modern Engineering Research (IJMER) www.ijmer.com Vol.2, Issue.6, Nov-Dec. 2012 pp-4189-4194 ISSN: 2249-6645 to describe the level of performance on decision criteria, to Step – 4: avoid difficulties for an performance makers in distinguishing subjectively between more than seven The normalized weight for each criteria (Ci) is alternatives Salty (1977) obtained as Wj, Where J=1, 2… n. The normalized weight Table 1 shows the fuzzy numbers associated with the for each criterion is obtained by dividing the Defuzzified corresponding linguistic variables and the same is scores of each criterion by the total of all the criteria. graphically represented in figure3. Rating of Suitable Locations: In similar way as procedure adopted for the Table 1: Fuzzy numbers and corresponding linguistic calculation of weight criteria, the rating of suitable location variables is derived as: Linguistic Variable Fuzzy Number • Locations suitable on each of the criteria are to VL (Very low) (0.0, 0.0, 0.1, 0.2) be rated in the linguistic variables by the performance makers, which is converted into L (low) (0.1, 0.2, 0.3, 0.4) fuzzy numbers and the same is represented in the matrix form (Fuzzy Decision Matrix). ML/LL (more or less low ) (0.2, 0.3, 0.4, 0.5) • The average fuzzy score matrix for each M ( Medium) (0.4, 0.5, 0.5, 0.6) locations are obtained. MH/LH (more or less high) (0.5, 0.6, 0.7, 0.8) • The crisp score (Defuzzified value) for each location are obtained and same is represented in H( High) (0.6, 0.7, 0.8, 0.9) the matrix form as Xij, where i= 1,2 , m and J= VH (Very high) (0.8, 0.9, 1.0, 1.0) 1,2, , n. Where, m is the number of locations, n is the number of criteria. • Total aggregated score for locations against Step – 1: each criteria is obtained as The linguistic variables assigned by the experts for each criteria is translated into fuzzy numbers and the same is TS = {Xij} {Wj} represented in the matrix (Fuzzy Decision Matrix). v11v12  v1 j  v1m   w1  Step – 2:     Let Ajar be the fuzzy number assigned to an vendor AI by v21v22  v2 j  v2 m   w2      the Perfomanance makers (Pk) for the decision criterion. TS         v  w t Cj, the average of fuzzy numbers is given as vi1vi 2  vij  vim   w j      Aij  1   a j i1  a j i 2  ......  a j ik  ; k     p vn1vn 2  vnj  vnm   wn      =1,2………….p. On the basis of the total score obtained for each location against decision criteria, overall scores are The average fuzzy score matrix for each criteria is obtained, using simple average method, which provide obtained. final ranking of locations. V. CASE STUDY Step – 3: Steel industries purposed methodology allows the The crisp score (Defuzzified values) for each criteria is experts to rank the suitable vendor reelection for a obtained. Defuzzification of fuzzy numbers is an operation magnum steel limited Gwalior (India) companies on the that produces a non fuzzy crisp value. Defuzzified value is basis of different decision criteria in a more realistic given by the following equation (Kaufman and Gupta, manner. The advantage of fuzzy set theory facilitates the 1991). assessment to be made on the basic of linguistic manner, which corresponded to the real lie situations in a much Trapezoidal fuzzy number better way for simplicity five perfomanance makers E1, E a  b  c  d  E2,, E3, E4, E5 vendor selection projects, were consulted 4 to get the linguistic variables in terms of importance of each of the delusion criteria used to rank the vendor for Triangular fuzzy number each criteria’s (V1, V2, V3, V4, V5). E  a  2b  c  1. material cost(C1) 2. Semi –Raw material cost (C2) 4 www.ijmer.com 4191 | Page
  • 4. International Journal of Modern Engineering Research (IJMER) www.ijmer.com Vol.2, Issue.6, Nov-Dec. 2012 pp-4189-4194 ISSN: 2249-6645 3. Transportation cost (C3) 30 33 30 0 9 4. Inventory and storage cost (C4) C5 0.6 0.7 0.8 0.93 0.80 0.253 5. Production Process cost (C5) 70 67 70 0 9 6. On time delivery (C6) C6 0.5 0.6 0.7 0.80 0.67 0.211 7. Percentage waste items (C7) 60 34 20 0 8 8. Flexibility in service (C8) C7 0.2 0.3 0.4 0.50 0.35 0.110 9. Financial position (C9) 00 00 00 0 0 10. Inspection (quality control) (C10) C8 0.5 0.6 0.7 0.83 0.67 0.211 41 20 20 1 8 Table. 2 show the linguistic variables assigned by the C9 0.4 0.5 0.6 0.72 0.59 0.184 Perfomanance makers to each of the decision criteria are 22 80 42 0 1 define in the table -1 C10 0.4 0.5 0.6 0.72 0.60 0.190 70 67 70 0 7 Table 3: Linguistic variables assigned by the Perfomanance maker’s Rating of alternatives (venders) on criterion (Xi j) Criteria perfomanance maker’s Suitability of venders against each criteria are to be rated and linguistic variables are assigned by the experts to the E1 E2 E3 E4 E5 venders table-3 are define in table-1 the linguistic variables C1 H M H H VH are converted into fuzzy numbers C2 H H H VH H Table 5: Linguistics variables for alternatives C3 MH H H VH VH C1 V1 M L M L M C4 MH MH M M M V2 H M VH H M C5 M M MH M M V3 VH M M VH VH C6 H H VH H M V4 VH VH H VH VH C7 MH VH M MH M V5 H H M H H C2 V1 VH VH VH VH VH C8 M MH MH M M V2 H H H VL L C9 VH H VH M H V3 H VH VH VH VH C10 MH MH M VH M V4 M M VH H VH V5 VH VH M H H The average fuzzy scores, defuzzifled values and C3 V1 L M M M M normalized weight of criteria are obtained and given in table 3 V2 L M H M H Table 3: Normalized weight of criteria V3 H VH H H VH criter Parameter of average fuzzy Defu Norma V4 VH H H H VH ia scores zz lized V5 M VH H VH H ifled weight C4 V1 VH VH M H H Valu VL M M H VH e V2 V3 VH VH H H M C1 0.6 0.7 0.8 0.89 0.80 0.250 V4 M H H VH M 70 67 70 0 0 V5 VH H M VH VH C2 0.4 0.5 0.6 0.72 0.60 0.190 70 67 70 0 6 C5 V1 M H M L M C3 0.6 0.7 0.8 0.92 0.80 0.253 V2 H L VL L M 70 68 70 0 7 V3 M M VL H H C4 0.5 0.6 0.7 0.78 0.66 0.209 V4 H VH M M H www.ijmer.com 4192 | Page
  • 5. International Journal of Modern Engineering Research (IJMER) www.ijmer.com Vol.2, Issue.6, Nov-Dec. 2012 pp-4189-4194 ISSN: 2249-6645 V5 H M H M VH V2 0.480 0.530 0.633 0.730 0.593 C6 V1 VH H VL H M V3 0.470 0.567 0.670 0.720 0.607 VH H M M H V4 0.330 0.433 0.530 0.450 0.436 V2 V5 0.400 0.500 0.600 0.700 0.550 V3 L VL M VL L C4 V1 0.733 0.830 0.930 0.980 0.868 V4 L L L H H V2 0.267 0.370 0.470 0.520 0.407 V5 VH H H H VH V3 0.400 0.500 0.600 0.700 0.550 C7 V1 VL M L VL L V4 0.400 0.500 0.600 0.700 0.550 V2 VL M M M H V5 0.533 0.630 0.730 0.801 0.494 V3 M M VL VL L C5 V1 0.200 0.300 0.400 0.500 0.350 V2 0.730 0.833 0.930 0.980 0.856 V4 H H L L VL V3 0.670 0.767 0.870 0.920 0.807 V5 H VH VH M M V4 0.470 0.470 0.567 0.720 0.557 C8 V1 VH M L H H V5 0.530 0.633 0.730 0.820 0.679 V2 VL VL L M M C6 V1 0.470 0.567 0.670 0.720 0.607 V3 H M H H H V2 0.470 0.567 0.670 0.700 0.602 V4 L M H M H V3 0.130 0.233 0.330 0.460 0.289 V5 M M H H H V4 0.530 0.630 0.730 0.820 0.678 C9 V1 L M L L L V5 0.470 0.570 0.670 0.720 0.608 V2 H M H M L C7 V1 0.730 0.830 0.930 0.950 0.860 V3 L M VH H M V2 0.530 0.630 0.730 0.820 0.678 V4 M VL L L L V3 0.400 0.500 0.600 0.700 0.550 V5 H H M M VL V4 0.330 0.430 0.500 0.670 0.483 C10 V1 H VL L VL VL V5 0.530 0.630 0.730 0.820 0.678 V2 L H H H M C8 V1 0.470 0.570 0.670 0.720 0.608 V3 L L VL VL VL V2 0.730 0.830 0.930 0.980 0.868 V4 M L VL M VL V3 0.670 0.767 0.870 0.890 0.800 V5 M L VL M H V4 0.470 0.470 0.567 0.620 0.532 V5 0.530 0.633 0.730 0.820 0.679 Table 6: Average fuzzy scores and Defuzzified scores C9 V1 0.470 0.567 0.670 0.720 0.606 criteria Vendo Average Fuzzy scores Defuzz r ied V2 0.470 0.567 0.670 0.720 0.607 score V3 0.130 0.233 0.330 0.460 0.289 C1 V1 0.670 0.767 0.870 0.890 0.799 V4 0.530 0.630 0.730 0.820 0.678 V2 0.470 0.567 0.670 0.710 0.605 V5 0.470 0.570 0.670 0.720 0.608 V3 0.670 0.767 0.870 0.880 0.797 C10 V1 0.730 0.830 0.930 0.960 0.863 V4 0.530 0.633 0.730 0.800 0.674 V2 0.530 0.630 0.730 0.830 0.680 V5 0.670 0.767 0.870 0.900 0.802 V3 0.400 0.500 0.600 0.700 0.550 C2 V1 0.530 0.633 0.730 0.820 0.679 V4 0.330 0.430 0.500 0.640 0.476 V2 0.200 0.300 0.400 0.500 0.350 V5 0.530 0.630 0.730 0.820 0.678 V3 0.730 0.833 0.930 0.980 0.869 V4 0.467 0.567 0.667 0.767 0.617 V4 0.670 0.767 0.870 0.910 0.805 V5 333 0.433 0.530 0.620 0.479 V5 0.600 0.700 0.800 0.900 0.750 C3 V1 0.530 0.633 0.730 0.850 0.686 www.ijmer.com 4193 | Page
  • 6. International Journal of Modern Engineering Research (IJMER) www.ijmer.com Vol.2, Issue.6, Nov-Dec. 2012 pp-4189-4194 ISSN: 2249-6645 The total scores for each vendor can be calculated matrix as follows VII. ACKNOWLEDGEMENT V V2 V3 V4 V5 Wj Authors would like to thank to Vimal steel 1 corporation ltd., for providing data’s to create decision C1  0.800 0.605 0.797 0.674 0.802  0.250  criteria & also thank to Perfomanance maker’s for C2  0.679 0.350 0.869 0.805 0.750  0.190  providing linguistic variables to apply fuzzy multi criteria     C3  0.686 0.593 0.607 0.436 0.550   0.253 decision approach for selecting the best vendor for a     companies. C4  0.868 0.407 0.550 0.550 0.494  0.209  C5  0.350 0.856 0.807 0.557 0.679  0.254      REFERENCES C6 0.607 0.602 0.289 0.678 0.608   0.213 TS   [1] Alexios-patapios kontis and vassilionvyagotis, C7  0.860 0.678 0.550 0.483 0.678  0.110      supplier Selection problem multi-criteria approaches C8  0.608 0.808 0.800 0.532 0.629  0.212  based on DEA,international Scientific Advances in C9  0.606 0.607 0.289 0.678 0.608   0.185      Management & Applied Economics, vol1.1,no.2,207- C10  0.863 0.680 0.550 0.476 0.678  0.190  219(2011)         [2] Shyur &Shih, 2006.Evaluating vendors many criteria         Including quantitative, as well as qualitative, a considerable Number of decision making European Total scores for vender (V1) on criteria is obtained as- Journal of Operation Research, Vol.50, 5-10(2009) (0.800×0.250)+(0.679×0.190)+(0.686×0.253)+(0.868×0.20 [3] Kaufmann, A.,& Gupta, M.M, Introduction to Fuzzy 9)+(0.350×0.254)+(0.607×0.213)+(0.860×0.110)+(0.608×0 Arithmetic theory & application, Van No strand .212)+(0.606×0.185)+(0.863×0.190)= 1.4035 Reinhold, Newyork.vol.1; 5-18 (1991) Similarly, total scores for venders (V2), (V3),(V4),(V5)are [4] Dickson, Weber, Multi objective linear model for obtained and provided in table-7In the selection of suitable Vendor Selection criteria and methods, European vendor for any company , initial investment, qualitative Journal of criteria each has equal weight age. Hence t h e final Operational Research, Vol.50, 2-18(1991) s c o r e s a n d r a n k i n g o f venders are given in table.6 [5] Buffa and Jackson and Sharma, Multi decision making used linear and non-linear programming, Total Table 7: Final scores and ranging of venders. Quality Environmental Management Vol.3 (4); 521- Vendors V1 V2 V3 V4 V5 530(1994) Final [6] Tu-chung Chu, Rangnath varma, Evaluating suppliers Scores 1.4035 1.2859 1.29900 1.2489 1.3353 via a multiple criteria decision making method under Rank 1 4 000001 3 5 2 fuzzy Enviroment, nternationalJournalofcomputers&Industrial VI. RESULTS CONCLUSION Engineering vol, 62; 653-660(2012) This paper, presented the fuzzy multi criteria [7] Swanson’s., 2001.Linking maintenance strategies decision approach, the order odd ranking of vendor’s for To performance. International Journal of Production the company’s are as V1>V5>V3>V2>V4. The result Economics70, 237-244. (2001) show V1 is the best location for the company. Has been [8] Shyur &Shih, 2006.Evaluating vendors many criteria highlighted to solve multi-criteria decision making Including quantitative, as well as qualitative, a problems through a case study of vendor selection. The considerable Number of decision making European Study demonstrates the effectiveness of the said MCDM Journal of Operational Research,Vol.50,5-10(2009) techniques in solving such a vendor selection problem. www.ijmer.com 4194 | Page