VIKOR (VIšekriterijumsko KOmpromisno Rangiranje) is a multi-criteria decision-making method that was developed by Yugoslav researchers in the 1980s. It is a technique used to rank and select alternatives based on multiple criteria, where each criterion may have different units, scales, and importance weights. VIKOR seeks to identify a compromise solution that minimizes the maximum individual regret or dissatisfaction of all decision-makers with respect to the selected alternative. The method involves calculating a VIKOR index for each alternative, which takes into account both the distance from the ideal solution and the distance from the worst solution, as well as a measure of the relative importance of the criteria. The alternative with the highest VIKOR index is considered to be the best compromise solution.

## Step-by-step guide for using the VIKOR

### 1. Collect the decision matrix

The decision matrix is a table that lists the alternatives and criteria being evaluated. The size of the matrix depends on how many alternatives and criteria are under consideration. In each cell of the matrix, an alternative’s performance in a particular criterion is recorded.

\begin{equation*} X = (x_{ij})_{n\times m} \end{equation*}

In the above equation, n is the number of alternatives (or options) and m is the number of criteria.

### 2. Normalize the decision matrix

Normalizing the matrix involves transforming the raw data into a standard scale (usually from 0 to 1) so that it can be compared across different criteria. This is done by dividing each element of the matrix by the maximum value in the same column.

R = (r_{ij}) = \frac{x_{j}^{+} - x_{ij}}{x_{j}^+ - x_{j}^{-}}

### 3. Determine weights for each criterion

Deciding on the relative importance of each criterion is essential to the VIKOR method. Weights can be calculated using various approaches, such as the entropy method, which assigns weights based on how evenly the alternatives perform in each criterion.

w_j=(w_1,w_2,\dots,w_m)

### 4. Calculate the ‘utility’ and ‘regret’ of each alternative

The utility and regret measures are used to calculate the closeness coefficient of each alternative. The utility measure (S) represents how close an alternative is to the ideal solution, while the regret (R) measure represents how far away it is from the worst solution. Calculating these measures requires finding the distance between each alternative’s normalized values and the ideal or worst solutions.

a) To calculate the utility S_i of alternative i find the result by this formula:

S_i = \sum_{j=1}^{n} w_j \times r_{ij}

b) To calculate the cost R_i of alternative i, use this:

R_i = \max_j (w_j \times r_{ij})

### 5. VIKOR index (Q) calculation

The VIKOR index (Q) measures an alternative’s overall performance relative to all other alternatives and is based on its utility and cost measures. A lower value indicates better performance, and this value is used to rank the alternatives.

Q_i = \left ( v \times \frac{S_i-S^+}{S^- - S^+} \right ) + \left ( (1-v) \times \frac{R_i-R^+}{R^- - R^+} \right )

The weight of the strategy known as “the majority of criteria” or “the maximum group utility” is presented as v.

### 6. Rank the alternatives based on Vikor ranking method

Finally, the alternatives are ranked based on Vikor ranking strategy. You can find the details here.

## An easy-to-use VIKOR solver is available!

There are several solvers for the VIKOR algorithm, including online and offline software packages, but they often require specialized knowledge and tools, which can make it difficult for non-experts to use them effectively. To overcome this challenge, we recommend using our Orpida VIKOR Excel template, which is an affordable and user-friendly tool that simplifies the VIKOR process by providing an interactive spreadsheet interface. Users simply enter their data and preferences into the spreadsheet, and it automatically calculates the VIKOR scores and ranks the alternatives. To access the VIKOR Excel file, click on the link.