MOORA Algorithm
The Multi-Objective Optimization by Ratio Analysis (MOORA) method is an objective ranking system that utilizes a ratio system to compare various alternatives against a set of criteria.
1. Normalization (Vector Method):
\[ x_{ij}^* = \frac{x_{ij}}{\sqrt{\sum_{i=1}^{m} x_{ij}^2}} \]
\[ x_{ij}^* = \frac{x_{ij}}{\sqrt{\sum_{i=1}^{m} x_{ij}^2}} \]
2. Weighted Assessment:
\[ y_i = \sum_{j=1}^{g} w_j x_{ij}^* – \sum_{j=g+1}^{n} w_j x_{ij}^* \] Where \(g\) are benefit criteria and the rest are cost criteria.
\[ y_i = \sum_{j=1}^{g} w_j x_{ij}^* – \sum_{j=g+1}^{n} w_j x_{ij}^* \] Where \(g\) are benefit criteria and the rest are cost criteria.
3. Final Ranking:
The alternative with the highest \(y_i\) is the best choice.
The alternative with the highest \(y_i\) is the best choice.
Solved Example: Factory Site Selection
Selecting the best location based on 4 criteria: Infrastructure (B), Skill Level (B), Land Cost (C), and Distance (C).
Weights: \(w = [0.3, 0.3, 0.2, 0.2]\).
Step 1: Decision Matrix
| Alt | Infra(B) | Skill(B) | Cost(C) | Dist(C) |
|---|---|---|---|---|
| Site 1 | 8 | 7 | 100 | 50 |
| Site 2 | 6 | 9 | 80 | 30 |
| Site 3 | 9 | 6 | 120 | 40 |
| Site 4 | 7 | 8 | 90 | 60 |
Step 2: Normalization Calculation
For Infrastructure: \(\sqrt{8^2+6^2+9^2+7^2} = \sqrt{230} = 15.16\)
Normalized Value (Site 1, Infra): \(8 / 15.16 = 0.527\)
Step 3: Final Solved Assessment (y)
Example for Site 1:
\(y_1 = (0.527 \times 0.3 + 0.463 \times 0.3) – (0.505 \times 0.2 + 0.542 \times 0.2)\)
\(y_1 = 0.297 – 0.209 = \mathbf{0.088}\)
| Alt | Benefit Sum | Cost Sum | Score (y) | Rank |
|---|---|---|---|---|
| Site 1 | 0.297 | 0.209 | 0.088 | 3 |
| Site 2 | 0.298 | 0.173 | 0.125 | 1 |
| Site 3 | 0.297 | 0.252 | 0.045 | 4 |
| Site 4 | 0.297 | 0.211 | 0.086 | 2 |
Interactive MOORA Calculator
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| Alt 4 |
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