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146 Proceedings of the 26 th Chinese Control Conference July 26-31, 2007, Zhangjiajie, Hunan, China VIKOR * , 071003 E-mail: [email protected] VIKOR VIKOR VIKOR VIKOR Selection of Suppliers based on VIKOR algorithm * Qi Jianxun, Zhang Zhiguang, Kong Feng School of Business and Administration, North China Electric Power University, Baoding 071003, P. R. China E-mail: [email protected] Abstract: Selection of suppliers is the precondition and foundation of supply chain operation. It is an important aspect to choose the best supplier for supply chain management. The VIKOR method was developed to solve MCDM problems with conflicting and with different units criteria, assuming that compromising is accepted for conflict resolution, the decision maker wants a solution that is the closest to the ideal, and the alternatives are evaluated according to all established criteria. VIKOR algorithm is applied to select the best supplier and weight is given to VIKOR by entropy-weighing method in this paper, an example was shown and validation was proved in Selection of Suppliers. Key Words: Selection of Supplier, VIKOR, Multi-attribute Decision Making, Entropy—weighing Method 1 (Introduction) 1 CIMS 1997 [1] , , 92.4% 69.7% , (quality)(cost)(time) (credit)(reliability) ABC AHP/DEA [2] TOPSIS [3] ANP [1] [4] VIKOR * 2 VIKOR (Selection of Suppliers Based on VIKOR Algorithm) 2.1 VIKOR (The Principle of VIKOR ) VIKOR [5-8] Opricovic 1998 VIKOR (Positive-ideal solu- tion)(Negative-ideal solution) VIKOR L p -metric 1/ * * 1 [ ( ) /( )] p n p pj i i ij i i i L w f f f f = = (1) 1 ; 1, 2, p j J = , pj L j a VIKOR VIKOR 1

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Page 1: [IEEE 2007 Chinese Control Conference - Zhangjiajie, China (2007.07.26-2007.06.31)] 2007 Chinese Control Conference - Selection of Suppliers based on VIKOR algorithm

146

Proceedings of the 26th Chinese Control ConferenceJuly 26-31, 2007, Zhangjiajie, Hunan, China

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Selection of Suppliers based on VIKOR algorithm *

Qi Jianxun, Zhang Zhiguang, Kong FengSchool of Business and Administration, North China Electric Power University, Baoding 071003, P. R. China

E-mail: [email protected]

Abstract: Selection of suppliers is the precondition and foundation of supply chain operation. It is an important aspect tochoose the best supplier for supply chain management. The VIKOR method was developed to solve MCDM problems withconflicting and with different units criteria, assuming that compromising is accepted for conflict resolution, the decisionmaker wants a solution that is the closest to the ideal, and the alternatives are evaluated according to all established criteria.VIKOR algorithm is applied to select the best supplier and weight is given to VIKOR by entropy-weighing method in thispaper, an example was shown and validation was proved in Selection of Suppliers.Key Words: Selection of Supplier, VIKOR, Multi-attribute Decision Making, Entropy—weighing Method

1 �(Introduction)1

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2 �� �� VIKOR �� (Selection ofSuppliers Based on VIKOR Algorithm)

2.1 VIKOR���� (The Principle of VIKOR )

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$'�#� ����N�'�+8$'&VIKOR��T��d������N*(Positive-ideal solu-tion)/�N*(Negative-ideal solution)�C�N*��J� �$Qd�G���e�������

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Page 2: [IEEE 2007 Chinese Control Conference - Zhangjiajie, China (2007.07.26-2007.06.31)] 2007 Chinese Control Conference - Selection of Suppliers based on VIKOR algorithm

147

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2.2 �� �� VIKOR ���� (The Steps of

VIKOR Algorithm for Suppliers Selection)

1) �Y"�JL��N*�#�N**

1 2[(max ),(min )]i j ij j ijf f i I f i I= ∈ ∈

1 2[(min ), (max )]i j ij j ijf f i I f i I− = ∈ ∈

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3) �Y�$Q�/0�W)'1 Q* *( ) /( )j jQ v S S S S−= − −

* *(1 )( ) /( )jv R R R R−+ − − − (7)�e

* min ;j jS S= max j jS S− = ; * min j jR R= ;

max j jR R− = ;23e� v$%+845��� v�" 0.5 $%�B�7�+6�$35�+8� vP7 0.5 $%�B.1�/05�+8� v8" 0.5 $%�1�/05�+8&d VIKORe%79� vS 0.5�:1!�����(����! ���&

4) �B jQ � jS � jR � ;���� ���5) ���!2<��!��B Q ����>

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3 ���� (Numerical Simulation)

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Page 3: [IEEE 2007 Chinese Control Conference - Zhangjiajie, China (2007.07.26-2007.06.31)] 2007 Chinese Control Conference - Selection of Suppliers based on VIKOR algorithm

148

� 1 ���� !"#

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A1 19 1 0.92 4 0.94 3 225 6A2 20 2 0.98 2 0.96 2 208 3A3 22 4 0.90 5 0.80 7 200 1A4 24 6 0.99 1 0.88 5 235 7A5 23 5 0.87 6 0.98 1 215 5A6 21 3 0.86 7 0.85 6 212 4A7 24 6 0.94 3 0.90 4 205 2

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1 0.93 0.96 0.890.95 0.99 0.98 0.960.86 0.91 0.82 10.79 1 0.90 0.850.83 0.88 1 0.930.90 0.87 0.87 0.940.79 0.95 0.92 0.98

V

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟

= ⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

2) �N*�8�N*9: S:* (1,1,1,1, )f = � (0.79,0.87,0.82,0.85)f − =

3) &B'((2)(4);Y<;A��B����2�; A � 5 � � � # T � [ " ( 2 S :w =(0.42,0.16,0.26,0.16)

4) &B'((5)-(7);Y"��� jS � jR � jQ)�4" 2&

5) �@��4" 3�C�; VIKOR;Y<�@ =>?S S2 @S1 @S6 @S3 @S5 @S7 @S4 �A

>?B

TOPSIS '�C57'L� +8'�>?�T F[9-10]&

� 2 $��� VIKOR!%#

A1 A2 A3 A4 A5 A6 A7S 0.26 0.18 0.65 0.72 0.56 0.61 0.62R 0.12 0.1 0.28 0.43 0.34 0.2 0.42Q 0.1 0 0.71 1 0.73 0.55 0.90

� 3 $��� VIKOR&'

A1 A2 A3 A4 A5 A6 A7S 2 1 6 7 3 4 5R 2 1 4 7 5 3 6Q 2 1 4 7 5 3 6

4 () (Conclusion)

VIKOR Y'dJL6<d./!�AB ��$'D$Q5�����:��<� �$Q&GS

;��+XEF�)��G+X!FHH��:6<

XIJ+8@���>?*&BK���N6'`4

TOPSIS'L�VIKORM<(X��P�N*�7�A��&BN�N*�BC4M)5�$Q����

:��� TOPSIS������P�$Q�cM�N*�P:M��N*���:;�f��� �

!�N6�6�,�5�VIKOR:0�#�� ��������$Q��&

TUW(X VIKORY'*+X�����9:�]^������� MCDM$'>?���abX VIKOR� �� �745+8$'&

*+,- (References)

[1] !"�#$%. �& ANP $'�����. '(��O�2005, 5(11).

[2] )P�*+. ,-���e����� AHPGDEA $'[J]��e'(���.�2002, 23(4): 29-31.

[3] /D0�1b2Q. �&3RZ��SIJ�����$'45 [J]�D6(����2004, 31(8): 132-134.

[4] ��. ����e�������GH' [J],������� , 2004, 20(2): 89-92.

[5] Opricovic S. Multicriteria Optimization of Civil EngineeringSystems, Faculty of civil ,Belgrade 1998.

[6] Opricovic S. Compromise Solution by MCDM methods: AComparative analysis of VIKOR and TOPSIS [J] EuropeanJournal of Operational Research, 2004, 156: 445-455.

[7] Opricovic S,Tzeng G H.Multicriteria planning of post-earthquake sustainable reconstruction [J]. The Journal ofComputer-Aided Civil and Infrastructure Engineering 2002,17 (3):211–220.

[8] DeLucchi M A, Murphy J J, McCubbin DR. The health andvisibility cost of air pollution: a comparison of estimationmethods[J]. Journal of Environmental Management 2002, 64(2): 139-152.

[9] �����D�����. ���e����$'���[J]��2���������2001, 18(8): 80-83.

[10] �W�. �������7�L� +8!_a��."����, 2006 (3).