The VIKOR Method

1. Introduction

The VIKOR method was developed to solve multi-criteria decision-making (MCDM) problems with conflicting criteria. The name is an acronym for Višekriterijumska Optimizacija I Kompromisno Rešenje.

The fundamental logic of VIKOR is to find a compromise ranking. It focuses on how close an alternative is to the “Ideal” solution. It uses two main concepts:

• Maximum Group Utility: Pleasing the majority.
• Minimum Individual Regret: Reducing the dissatisfaction of the “opponent.”

2. Mathematical Method

Step 1: Normalization

Determine the best \( f_i^* \) and worst \( f_i^- \) values for each criterion \( i \):

Step 2: Calculate \( S \) and \( R \)

For each alternative \( j \), compute the weighted normalized distance:

Where \( w_i \) is the weight of the criterion.

Step 3: Calculate VIKOR Value \( Q \)

The final index is computed as:

Where:

• \( S^* = \min_j S_j, \quad S^- = \max_j S_j \)
• \( R^* = \min_j R_j, \quad R^- = \max_j R_j \)
• \( v \) is the weight for the strategy of “the majority of criteria” (usually \( 0.5 \)).

3. Numerical Solution

Consider 3 alternatives (A, B, C) evaluated against two criteria: Cost (w=0.6) and Quality (w=0.4).

Resulting Calculations

After applying the formulas, we obtain the following results:

Conclusion: Alternative C is the best compromise solution because it has the lowest \( Q \) value, representing the minimum distance from the ideal.