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

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

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

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

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



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


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.


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

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