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VIKOR method
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VIKOR method
The VIKOR method is a multi-criteria decision making (MCDM) method. It was originally developed by Serafim Opricović in 1979 to solve decision problems with conflicting and noncommensurable (different units) criteria. It assumes that compromise is acceptable for conflict resolution and that the decision maker wants a solution that is the closest to the ideal, so the alternatives are evaluated according to all established criteria. VIKOR then ranks alternatives and determines the solution named compromise that is the closest to the ideal.
The idea of compromise solution was introduced in MCDM by Po-Lung Yu in 1973, and by Milan Zeleny.
Opricović had developed the basic ideas of VIKOR in his Ph.D. dissertation in 1979, and an application was published in 1980. The name VIKOR appeared in 1990 from Serbian: VIšeKriterijumska Optimizacija I Kompromisno Rešenje 'Multicriteria Optimization and Compromise Solution'. The real applications were presented in 1998. The paper in 2004 contributed to the international recognition of the VIKOR method. (The most cited paper in the field of Economics, Science Watch, Apr.2009).
The MCDM problem is stated as follows: Determine the best (compromise) solution in multicriteria sense from the set of J feasible alternatives , evaluated according to the set of n criterion functions. The input data are the elements of the performance (decision) matrix, where is the value of the i-th criterion function for the alternative .
The VIKOR procedure has the following steps:
Step 1. Determine the best fi* and the worst fi^ values of all criterion functions, i = 1,2,...,n; fi* = max (fij,j=1,...,J), fi^ = min (fij,j=1,...,J), if the i-th function is benefit; fi* = min (fij,j=1,...,J), fi^ = max (fij,j=1,...,J), if the i-th function is cost.
Step 2. Compute the values Sj and Rj, j=1,2,...,J, by the relations: Sj=sum[wi(fi* - fij)/(fi*-fi^),i=1,...,n], weighted and normalized Manhattan distance; Rj=max[wi(fi* - fij)/(fi*-fi^),i=1,...,n], weighted and normalized Chebyshev distance; where wi are the weights of criteria, expressing the DM's preference as the relative importance of the criteria.
Step 3. Compute the values Qj, j=1,2,...,J, by the relation Qj = v(Sj – S*)/(S^ - S*) + (1-v)(Rj-R*)/(R^-R*) where S* = min (Sj, j=1,...,J), S^ = max (Sj, j=1,...,J), R* = min (Rj, j=1,...,J), R^ = max (Rj, j=1,...,J),; and is introduced as a weight for the strategy of maximum group utility, whereas 1-v is the weight of the individual regret. These strategies could be compromised by v = 0.5, and here v is modified as = (n + 1)/ 2n (from v + 0.5(n-1)/n = 1) since the criterion (1 of n) related to R is included in S, too.
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VIKOR method
The VIKOR method is a multi-criteria decision making (MCDM) method. It was originally developed by Serafim Opricović in 1979 to solve decision problems with conflicting and noncommensurable (different units) criteria. It assumes that compromise is acceptable for conflict resolution and that the decision maker wants a solution that is the closest to the ideal, so the alternatives are evaluated according to all established criteria. VIKOR then ranks alternatives and determines the solution named compromise that is the closest to the ideal.
The idea of compromise solution was introduced in MCDM by Po-Lung Yu in 1973, and by Milan Zeleny.
Opricović had developed the basic ideas of VIKOR in his Ph.D. dissertation in 1979, and an application was published in 1980. The name VIKOR appeared in 1990 from Serbian: VIšeKriterijumska Optimizacija I Kompromisno Rešenje 'Multicriteria Optimization and Compromise Solution'. The real applications were presented in 1998. The paper in 2004 contributed to the international recognition of the VIKOR method. (The most cited paper in the field of Economics, Science Watch, Apr.2009).
The MCDM problem is stated as follows: Determine the best (compromise) solution in multicriteria sense from the set of J feasible alternatives , evaluated according to the set of n criterion functions. The input data are the elements of the performance (decision) matrix, where is the value of the i-th criterion function for the alternative .
The VIKOR procedure has the following steps:
Step 1. Determine the best fi* and the worst fi^ values of all criterion functions, i = 1,2,...,n; fi* = max (fij,j=1,...,J), fi^ = min (fij,j=1,...,J), if the i-th function is benefit; fi* = min (fij,j=1,...,J), fi^ = max (fij,j=1,...,J), if the i-th function is cost.
Step 2. Compute the values Sj and Rj, j=1,2,...,J, by the relations: Sj=sum[wi(fi* - fij)/(fi*-fi^),i=1,...,n], weighted and normalized Manhattan distance; Rj=max[wi(fi* - fij)/(fi*-fi^),i=1,...,n], weighted and normalized Chebyshev distance; where wi are the weights of criteria, expressing the DM's preference as the relative importance of the criteria.
Step 3. Compute the values Qj, j=1,2,...,J, by the relation Qj = v(Sj – S*)/(S^ - S*) + (1-v)(Rj-R*)/(R^-R*) where S* = min (Sj, j=1,...,J), S^ = max (Sj, j=1,...,J), R* = min (Rj, j=1,...,J), R^ = max (Rj, j=1,...,J),; and is introduced as a weight for the strategy of maximum group utility, whereas 1-v is the weight of the individual regret. These strategies could be compromised by v = 0.5, and here v is modified as = (n + 1)/ 2n (from v + 0.5(n-1)/n = 1) since the criterion (1 of n) related to R is included in S, too.