Project name: School Project Prioritization and Implementation
Date: 6/18/2025 11:28:02 PM

The VIKOR technique was first introduced by Opricovic in 1998 in order to solve multi-criteria decision making (MCDM) problems and obtain the best compromise solution. This method focuses on ranking and selecting from a set of alternatives in the presence of conflicting criteria. The main objective of the VIKOR method is to choose a solution that is closest to the ideal level in each criterion such that the alternatives are based on the particular measure of ‘‘closeness’’ to the ‘‘ideal’’ solution.

In this study there are 5 criteria and 5 alternatives that are ranked based on VIKOR method. The table below shows the type of criterion and weight assigned to each criterion.

Characteristics of Criteria

nametypeweight
1criterion1Positive0.2
2criterion2Positive0.2
3criterion3Positive0.2
4criterion4Positive0.2
5criterion5Positive0.2

The following table shows the decision matrix.

Decision Matrix

criterion1criterion2criterion3criterion4criterion5
alternative17.645.638.026.948.42
alternative28.385.287.237.157.63
alternative38.135.867.696.687.98
alternative46.757.328.357.737.48
alternative57.276.146.716.847.39

The VIKOR method involves the following steps:

The Steps of the VIKOR Method

STEP 1: Normalize the decision matrix

The following formula can be used to normalize.

The table below shows the normalized decision matrix.

Normalized Decision Matrix

criterion1criterion2criterion3criterion4criterion5
alternative10.4460.4140.4710.4390.483
alternative20.4890.3880.4240.4520.438
alternative30.4750.4310.4510.4220.458
alternative40.3940.5380.490.4880.429
alternative50.4250.4510.3940.4320.424

STEP 2: Determine the best and worst benefits of each criterion

The best and worse benefits can be determined by the following formula:

If the criterion is positive, then

If the criterion is negative, then

The positive ideal solution ( and negative ideal solution ( can be expressed as follows:

STEP 3: Calculate the and values

The values and , representing the group utility and individual regret, respectively, can be calculated by the formulas below :

Where denotes the weight of the criteria.

The following table shows the values and .

The values and

R S
alternative10.1660.447
alternative20.20.6
alternative30.20.54
alternative40.20.383
alternative50.20.821

STEP4: Calculate the value

The value , representing the VIKOR index for each alternative can be calculated by the following formula:

Where

And is the maximum group utility represented by value 0.5.

The values

Q
alternative10.074
alternative20.748
alternative30.679
alternative40.5
alternative51

STEP5: Rank the alternatives, sorting by the S, R and Q values

Alternatives are ranked by sorting the S, R, and Q, values in decreasing order such that the best rank is assigned to the alternative with the smallest VIKOR value. The results are three ranking lists.

The following table presents the ranking list for the alternatives based on the S, R, and Q values

The ranking list for the alternatives

R valueRank in R S valueRank in S Q valueRank in Q
alternative10.16610.44720.0741
alternative20.220.640.7484
alternative30.220.5430.6793
alternative40.220.38310.52
alternative50.220.821515

STEP 6: Propose a compromise solution

the alternative ( ), which is the best ranked by the measure Q (minimum) if the following two conditions are satisfied:

Condition 1 . Acceptable advantage: where is the alternative with first position and is the alternative with second position in the ranking list by Q. m is number of alternatives.

Condition 2 . Acceptable stability in decision making: The alternative must also be the best ranked by S or/and R.

If one of the conditions is not satisfied, then a set of compromise solutions is proposed, which consists of:

Solution 1. Alternatives if Condition 1 is not satisfied; Alternative is determined by for maximum M (the positions of these alternatives are ‘‘in closeness’’).

Solution 2. Alternatives and if only condition 2 is not satisfied.

Solution 3. Alternative with the minimum Q value will be selected as the best Alternative if both conditions are satisfied.

result of the conditions survey is shown in the following table.

result of the conditions survey

Acceptance

Condition 1

Acceptance

Condition 2

Solution 3

Selected solution

Therefore, alternative1 is selected as the final alternative.