OCRA Algorithm
Operational Competitiveness Rating Analysis (OCRA) is an efficiency-based MCDM method. It calculates the relative performance of alternatives based on beneficial (outputs) and non-beneficial (inputs) criteria separately.
1. Beneficial Criteria Rating (\(\bar{I}\)):
\[ \bar{I}_{ij} = \frac{x_{ij} – \min(x_{j})}{\min(x_{j})} \] 2. Beneficial Aggregate Score (\(P_i\)):
\[ P_i = \sum_{j=1}^{n} w_j \bar{I}_{ij} \]
\[ \bar{I}_{ij} = \frac{x_{ij} – \min(x_{j})}{\min(x_{j})} \] 2. Beneficial Aggregate Score (\(P_i\)):
\[ P_i = \sum_{j=1}^{n} w_j \bar{I}_{ij} \]
3. Non-Beneficial Criteria Rating (\(\bar{O}\)):
\[ \bar{O}_{ij} = \frac{\max(x_{j}) – x_{ij}}{\min(x_{j})} \] 4. Non-Beneficial Aggregate Score (\(R_i\)):
\[ R_i = \sum_{j=1}^{n} w_j \bar{O}_{ij} \]
\[ \bar{O}_{ij} = \frac{\max(x_{j}) – x_{ij}}{\min(x_{j})} \] 4. Non-Beneficial Aggregate Score (\(R_i\)):
\[ R_i = \sum_{j=1}^{n} w_j \bar{O}_{ij} \]
5. Final Score (\(E_i\)):
\[ E_i = (P_i + R_i) – \min(P + R) \]
\[ E_i = (P_i + R_i) – \min(P + R) \]
Solved Example: Project Efficiency
Goal: Evaluate 4 Projects based on 4 Criteria: Revenue (B), Quality (B), Operational Cost (C), and Risk (C). Weights: 0.3, 0.2, 0.3, 0.2.
Step 1: Decision Matrix & Min/Max
| Alt | Rev (B) | Qual (B) | Cost (C) | Risk (C) |
|---|---|---|---|---|
| P1 | 500 | 80 | 200 | 10 |
| P2 | 600 | 85 | 250 | 15 |
| P3 | 450 | 90 | 180 | 12 |
| P4 | 700 | 75 | 300 | 20 |
| Min | 450 | 75 | 180 | 10 |
| Max | 700 | 90 | 300 | 20 |
Step 2: Calculating Ratings for P1
– Benefit (Rev): \((500 – 450) / 450 = 0.111\)
– Benefit (Qual): \((80 – 75) / 75 = 0.067\)
– Cost (Cost): \((300 – 200) / 180 = 0.556\)
– Cost (Risk): \((20 – 10) / 10 = 1.000\)
Step 3: Weighted Sums for P1
\(P_1 = (0.3 \times 0.111) + (0.2 \times 0.067) = 0.0467\)
\(R_1 = (0.3 \times 0.556) + (0.2 \times 1.000) = 0.3668\)
\(Total_1 = 0.0467 + 0.3668 = 0.4135\)
– Benefit (Rev): \((500 – 450) / 450 = 0.111\)
– Benefit (Qual): \((80 – 75) / 75 = 0.067\)
– Cost (Cost): \((300 – 200) / 180 = 0.556\)
– Cost (Risk): \((20 – 10) / 10 = 1.000\)
Step 3: Weighted Sums for P1
\(P_1 = (0.3 \times 0.111) + (0.2 \times 0.067) = 0.0467\)
\(R_1 = (0.3 \times 0.556) + (0.2 \times 1.000) = 0.3668\)
\(Total_1 = 0.0467 + 0.3668 = 0.4135\)
Step 4: Final Ranking
| Alt | P (Benefit) | R (Cost) | Sum | Final Score | Rank |
|---|---|---|---|---|---|
| P1 | 0.046 | 0.366 | 0.412 | 0.355 | 1 |
| P2 | 0.126 | 0.183 | 0.309 | 0.252 | 3 |
| P3 | 0.040 | 0.360 | 0.400 | 0.343 | 2 |
| P4 | 0.166 | 0.000 | 0.166 | 0.109 | 4 |
OCRA Interactive Calculator
| Weights | ||||
|---|---|---|---|---|
| Type | ||||
| A1 | ||||
| A2 | ||||
| A3 | ||||
| A4 |
Designed by: Dr. M.U. Mirza
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