Does VIKOR require an AI model?

No. It is a decision-analysis method that can be applied manually or in software.

No. That is a common compromise setting, but other choices and variants exist and should be stated.

Can the result include several alternatives?

Yes. Failure of the recommendation conditions can lead to a compromise set rather than a single winner.

AI Glossary / Mathematics and optimization / Advanced

VIKOR method

Definition

The VIKOR method is a multicriteria decision-making method that ranks alternatives and identifies compromise choices using their shortfalls from ideal criterion values. It combines an aggregate weighted shortfall with the largest individual weighted shortfall, then checks whether the leading alternative has sufficient advantage and stability to recommend it alone.

What it means

An alternative may perform well overall while falling badly behind on one important criterion. VIKOR makes both aspects visible. Its ideal is assembled from the best available value of each criterion, even when no single alternative achieves that entire combination.

The method supports decisions among specified alternatives with competing criteria. It does not discover missing alternatives, decide which criteria are legitimate, or establish that stakeholders agree with the weights. A mathematically calculated compromise is a decision aid, not proof of unanimous acceptance or objective superiority independent of modeling choices.

How it works

Arrange alternatives in a performance table, identify benefit and cost criteria, and set nonnegative criterion weights summing to one. Convert each performance to a normalized shortfall from the criterion's best value, using its best-to-worst range.

For each alternative, calculate S, the sum of weighted shortfalls, and R, their maximum. Normalize these two measures across alternatives and combine them into Q using a strategy parameter v between zero and one. Smaller values are preferred.

The leading Q alternative is checked for acceptable advantage over the runner-up and for also leading S or R. When those checks fail, the standard procedure can recommend a compromise set. Constant criteria or zero ranges in S or R require explicit handling rather than division by zero.

Three practical examples

1. Technology selection: compare tools across measured processing time, cost, and task quality after applying mandatory eligibility requirements.

2. Facility planning: assess feasible locations against several planning criteria, documenting how criterion weights represent agreed priorities.

3. Product procurement: examine whether an otherwise attractive supplier has an especially large weighted shortfall on one evaluated dimension.

Think of it this way

Think of a report card that considers both the overall shortfall from target grades and the weakest weighted subject. An option with one excellent mark cannot automatically hide every weakness elsewhere.

The analogy is limited: VIKOR uses a particular normalization, weighting, and compromise rule. Its largest weighted shortfall is not a universal veto, and a criterion with a small weight can still exert limited influence despite a poor raw result.

Worked example

Three alternatives have two penalty criteria to minimize: A=(0,10), B=(4,4), and C=(10,0). Assign equal criterion weights, 0.5 each. Each criterion ranges from 0 to 10.

The normalized shortfalls are A=(0,1), B=(0.4,0.4), and C=(1,0). After weighting, A and C have S=0.5 and R=0.5. B has S=0.4 and R=0.2.

Choose v=0.5. The normalized S and R measures are both zero for B and both one for A and C. Therefore Q(B)=0 and Q(A)=Q(C)=1.

With three alternatives, the standard acceptable-advantage threshold is 1/(3-1)=0.5. The gap from B to either runner-up is 1, so it passes. B also has the smallest S and R, satisfying the stability check. Thus B is the single compromise recommendation under these stated inputs.

This hand calculation does not show that B is cheapest on either criterion. It illustrates a balanced choice whose conclusion depends on the alternatives, values, and equal weights.

Illustrative case study

Fictional case: a company compares three document-processing services using validated error rate, processing delay, and a defined cost measure. It first excludes services that fail mandatory requirements.

The evaluation team agrees on criterion directions and weights, then calculates S, R, and Q. Instead of presenting only a ranked list, it shows the source measurements and explains which criterion drives each service's largest shortfall.

Before choosing, the team varies plausible weights and checks whether the recommendation changes. If several services remain close, it presents a compromise set for further testing. This scenario illustrates a review process; it reports no actual supplier performance or business savings.

Common misconceptions and mistakes

Do not confuse criterion weights with the strategy parameter v. The former express relative criterion importance; the latter balances the two aggregate measures.

VIKOR does not measure regret relative to unknown future states in the same way as a minimax-regret decision table. Here, individual regret refers to a criterion-based weighted shortfall.

Normalization does not remove judgment. Adding an extreme alternative can alter observed ranges and therefore normalized comparisons.

Avoid claiming that the lowest Q alone always warrants a unique recommendation. The advantage and stability checks are part of the compromise procedure, and implementation conventions should be documented.

Business use

VIKOR can help a procurement or planning team explain why an alternative offers a compromise across conflicting measures. The useful output includes criterion data, weights, S, R, Q, and the recommendation checks.

Define mandatory constraints before ranking so that an unacceptable option cannot compensate for a disqualifying weakness elsewhere. Record data uncertainty and compare results across plausible settings. If priorities are disputed, expose the disagreement instead of treating a spreadsheet score as a substitute for deciding those priorities.

Check your understanding

In the worked example, why is B selected even though it is not best on either individual criterion?

Answer: It has the smallest total weighted shortfall and smallest maximum weighted shortfall. Its combined score also passes the advantage and stability checks under the chosen settings.

Related terms

Normalization
Sensitivity analysis
Multicriteria decision-making
compromise programming
TOPSIS
Pareto efficiency
criterion weighting
decision matrix

Learn next

Recalculate the example with unequal criterion weights and track S and R separately. Then add an alternative with an extreme penalty and inspect the normalization changes. Study sensitivity analysis before using a ranking to support a consequential organisational choice.

Sources

Primary author paper appendix read: Opricović, Compromise in cooperative game and the VIKOR method: https://doiserbia.nb.rs/ft.aspx?id=0354-02430902225O . The appendix specifies the measures and recommendation conditions. Its wording about decreasing-order ranking conflicts with its explicit minimum-Q rule; this entry consistently uses smaller-is-better scores. The example uses v=0.5 and original data, not the paper's modified strategy setting or empirical results.

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