Multi-criteria decision analysis

Multi-criteria decision analysis (MCDA) is a structured approach to evaluating alternatives against multiple conflicting criteria, enabling decision-makers to compare options systematically when no single alternative dominates on all dimensions (Belton V., Stewart T.J. 2002, p.2)^[1]. You're choosing a new factory location. Site A has lower costs but worse transportation access. Site B has better access but higher labor costs. Site C splits the difference but faces regulatory uncertainty. How do you compare? MCDA provides methods to structure such problems, weigh criteria, and reach defensible decisions.

The field emerged in the 1960s and 1970s as operations researchers sought to extend optimization techniques to problems without single objectives. Real decisions almost always involve tradeoffs—cost versus quality, speed versus safety, profit versus environmental impact. MCDA acknowledges this complexity rather than forcing artificial simplification into single-objective models.

Purpose

MCDA addresses fundamental decision challenges:

Multiple objectives. Organizations and individuals pursue many goals simultaneously, not just one.

Conflicting criteria. Improving on one criterion often means sacrificing on another. Better quality typically costs more^[2].

Subjective weights. How much one criterion matters relative to another reflects values, not just facts.

Complexity management. Structured methods help decision-makers handle information they couldn't process intuitively.

Process

MCDA follows systematic steps:

Problem structuring

Define the decision. What is being decided? What alternatives exist? What outcomes matter?

Identify criteria. What dimensions matter for evaluating alternatives? Criteria should be comprehensive, measurable, and independent^[3].

Specify alternatives. What options are being compared? These might be given or generated through the process.

Assessment

Score alternatives. How well does each alternative perform on each criterion? This may involve measurement, estimation, or expert judgment.

Assign weights. How important is each criterion relative to others? Weights reflect stakeholder values and priorities.

Synthesis

Combine evaluations. Using the chosen MCDA method, aggregate criterion-level assessments into overall evaluations^[4].

Rank alternatives. Determine which alternatives are preferred based on combined performance.

Sensitivity analysis

Test robustness. How do results change if weights or scores vary? Stable conclusions across reasonable variations provide confidence.

Major methods

Various techniques implement MCDA principles:

Weighted sum

Simple aggregation. Multiply each criterion score by its weight, sum across criteria. The alternative with the highest weighted sum wins.

Transparency. Easy to understand and explain, making it accessible to stakeholders^[5].

Limitation. Assumes criteria are comparable on common scales and that compensation between criteria is appropriate.

Analytic Hierarchy Process

Pairwise comparison. AHP, developed by Thomas Saaty, structures decisions hierarchically and uses pairwise comparisons to derive weights and scores.

Consistency checking. AHP includes mechanisms to identify inconsistent judgments.

TOPSIS

Ideal solutions. Technique for Order of Preference by Similarity to Ideal Solution compares alternatives to theoretical best and worst options.

Distance metrics. Alternatives closest to the ideal and farthest from the anti-ideal rank highest^[6].

ELECTRE

Outranking. The ELECTRE family of methods determines whether one alternative "outranks" another based on concordance and discordance analysis.

Partial ordering. ELECTRE may conclude that some alternatives are incomparable rather than forcing complete rankings.

PROMETHEE

Preference functions. PROMETHEE uses preference functions to model how decision-makers value differences between alternatives on each criterion.

Applications

MCDA serves diverse decisions:

Healthcare. Evaluating treatments considering effectiveness, side effects, cost, and patient preferences^[7].

Infrastructure. Selecting project alternatives balancing cost, environmental impact, and community benefit.

Supplier selection. Comparing vendors on price, quality, reliability, and capability.

Environmental management. Balancing ecological, economic, and social objectives in resource decisions.

Advantages

MCDA offers benefits:

Transparency. The decision process becomes explicit and auditable.

Stakeholder engagement. Structured processes enable meaningful participation in complex decisions.

Documentation. Rationale for decisions is recorded for future reference and accountability^[8].

Limitations

MCDA has constraints:

Garbage in. Results depend on criteria selection, alternative definition, scoring accuracy, and weight assignment.

Apparent objectivity. Mathematical methods may create false impressions of precision.

Complexity. Sophisticated methods may be difficult for stakeholders to understand and trust.

Multi-criteria decision analysis — recommended articles

Decision making — Operations research — Cost-benefit analysis — Risk analysis

References

• Belton V., Stewart T.J. (2002), Multiple Criteria Decision Analysis: An Integrated Approach, Springer.
• Saaty T.L. (1980), The Analytic Hierarchy Process, McGraw-Hill.
• Figueira J., Greco S., Ehrgott M. (2005), Multiple Criteria Decision Analysis: State of the Art Surveys, Springer.
• Ishizaka A., Nemery P. (2013), Multi-Criteria Decision Analysis: Methods and Software, Wiley.

Footnotes

1. ↑ Belton V., Stewart T.J. (2002), Multiple Criteria Decision Analysis, p.2
2. ↑ Figueira J. et al. (2005), State of the Art Surveys, pp.34-56
3. ↑ Saaty T.L. (1980), Analytic Hierarchy Process, pp.78-94
4. ↑ Ishizaka A., Nemery P. (2013), Methods and Software, pp.45-62
5. ↑ Belton V., Stewart T.J. (2002), Multiple Criteria Decision Analysis, pp.112-128
6. ↑ Figueira J. et al. (2005), State of the Art Surveys, pp.89-104
7. ↑ Saaty T.L. (1980), Analytic Hierarchy Process, pp.134-148
8. ↑ Ishizaka A., Nemery P. (2013), Methods and Software, pp.178-192

Author: Sławomir Wawak