Multi-Criteria Decision Analysis (MCDA)

Overview

Multi-Criteria Decision Analysis (MCDA) is a family of structured methods used to support decision-making when multiple, often conflicting, criteria must be considered.

It helps convert qualitative and quantitative criteria into a transparent, repeatable evaluation that ranks, scores, or selects alternatives.

Key Concepts

Decision alternatives are the options being compared (projects, sites, designs, investments). Criteria are attributes used to evaluate alternatives (cost, risk, benefit, accessibility, environmental impact). Weights are the relative importance assigned to each criterion. Performance/score matrix are values of alternatives on each criterion. Normalization is converting different units/scales into a common scale. Aggregation rule is the mathematical method for combining criteria (e.g., weighted sum). Sensitivity/robustness analysis is checking how results change with different weights or assumptions.

Common MCDA Methods

• Weighted Sum Model (WSM / MAUT / MAVT)
  • Simple and widely used; aggregate normalized scores with weights.
• Analytic Hierarchy Process (AHP)
  • Pairwise comparisons to derive weights and derive priorities; checks consistency.
• TOPSIS (Technique for Order Preference by Similarity to Ideal Solution)
  • Ranks alternatives by closeness to an ideal best and farthest from an ideal worst.
• ELECTRE (ELimination Et Choix Traduisant la REalité)
  • Outranking method; handles incomparabilities and veto thresholds.
• PROMETHEE
  • Outranking with preference functions and net flow scores.
• Multi-Attribute Utility Theory (MAUT)
  • Builds utility functions to represent stakeholder preferences, often used when risk attitudes matter.

Workflow

graph LR
    A[Define the decision problem and objectives] --> B[Identify feasible alternatives]
    B --> C[Select and define criteria]
    C --> D[Measure or estimate performance of each alternative against each criterion]
    D --> E[Choose weighting method and elicit weights]
    E --> F[Normalize criterion scores if needed]
    F --> G[Aggregate scores using chosen MCDA method]
    G --> H[Rank alternatives and perform sensitivity/robustness checks]
    H --> I[Present results and support decision with documentation of assumptions]

• Define the decision problem and objectives.
• Identify feasible alternatives.
• Select and define criteria (ensure coverage and independence where possible).
• Measure or estimate performance of each alternative against each criterion.
• Choose weighting method and elicit weights (stakeholder elicitation, AHP, direct rating).
• Normalize criterion scores if needed.
• Aggregate scores using chosen MCDA method.
• Rank alternatives and perform sensitivity/robustness checks.
• Present results and support decision with documentation of assumptions.

Core Mathematics

• Weighted Sum (WSM/MAUT):
  • Given alternatives $i$ and criteria $j$: $S_i={\sum }_j{w}_j{x}_{ij}$, where $w_j$ are weights and $x_{ij}$ are normalized scores.
• Normalization examples:
  • Min–max: ${\tilde{x}}_{ij}=\frac{x_{ij}-{\min }_i{x}_{ij}}{{\max }_i{x}_{ij}-{\min }_i{x}_{ij}}$.
  • Benefit/cost direction handling: reverse scale for cost criteria.
• AHP weight derivation:
  • Pairwise comparison matrix $A$, eigenvector method: find $w$ such that $Aw={\lambda }_{\max }w$.

Simple worked example (weighted sum)

• Criteria: Cost (weight 0.6, lower is better), Quality (weight 0.4, higher is better).
• Alternatives A and B:
  • Cost: A = 80, B = 60 (lower better)
  • Quality: A = 70, B = 60 (higher better)
• Normalize (min–max, invert cost):
  • Cost normalized (benefit form): $c_i^{\prime }=1-\frac{cos{t}_i-60}{80-60}$ so A: $1-\frac{20}{20}=0$, B: $1-\frac{0}{20}=1$.
  • Quality normalized: A: $\frac{70-60}{70-60}=1$, B: $\frac{60-60}{10}=0$.
• Scores: $S_A=0.6\cdot 0+0.4\cdot 1=0.4$; $S_B=0.6\cdot 1+0.4\cdot 0=0.6$ → B preferred.

Weighting and stakeholder involvement

• Weight elicitation methods:
  • Direct rating (point allocation), swing weighting, pairwise comparisons (AHP), rank-order centroid, budget allocation.
• Document who set weights, how trade-offs were elicited, and provide alternate weight scenarios for transparency.

Sensitivity and robustness

• Test how rankings change under:
  • Perturbations of weights (one-at-a-time, Monte Carlo sampling).
  • Different normalization or aggregation rules.
  • Alternative performance estimates (uncertain data).
• Report stability: if rankings flip under small changes, decision is fragile.

Strengths and limitations

• Strengths:
  • Makes multiple criteria and trade-offs explicit.
  • Flexible: handles qualitative and quantitative data.
  • Supports stakeholder participation and transparent documentation.
• Limitations:
  • Results depend on choice of criteria, normalization, and weights.
  • Some methods (e.g., AHP) can be sensitive to inconsistent judgments.
  • Outranking methods can produce incomparabilities that require interpretation.

Applications (examples)

• Urban planning and site selection (GIS-integrated MCDA).
• Environmental impact assessment and resource management.
• Supplier selection and procurement.
• Portfolio selection in finance and real estate.
• Policy evaluation and health technology assessment.

Practical tips for implementation

• Keep criteria few and meaningful; avoid redundant criteria.
• Separate measurement scales and directions clearly (benefit vs cost).
• Use visualizations: scorecards, radar charts, sensitivity plots.
• Record assumptions and all intermediate matrices so results are reproducible.
• For GIS MCDA, use raster or vector overlays with weighted combination but be careful with scale and normalization.

Suggested note structure in this vault

• • Purpose / Summary
  • Key concepts
  • Methods (create sub-notes): e.g., Analytic Hierarchy Process (AHP), TOPSIS, ELECTRE, PROMETHEE
  • Workflow / Checklist
  • Worked examples and templates
  • References and further reading

References and further reading (selection)

• Keeney, R. L., & Raiffa, H. (1976). Decisions with Multiple Objectives: Preferences and Value Tradeoffs.
• Saaty, T. L. (1980). The Analytic Hierarchy Process.
• Hwang, C.-L., & Yoon, K. (1981). Multiple Attribute Decision Making: Methods and Applications.
• Belton, V., & Stewart, T. J. (2002). Multiple Criteria Decision Analysis: An Integrated Approach.

Appendix

Created: 2025-12-13 | Modified: 2025-12-13

See Also

• Geographic Information System (GIS)
• Analytic Hierarchy Process (AHP)
• TOPSIS
• ELECTRE
• PROMETHEE
• Normalization

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