Best-Worst Method (BWM)
BWM is a comparison-based method used to calculate the weights of criteria. It requires fewer comparisons than AHP and produces more reliable results by focusing on the Best and Worst attributes.
1. Select Best (\(C_B\)) and Worst (\(C_W\)) criteria.
2. Best-to-Others (BO) Vector:
\( A_B = (a_{B1}, a_{B2}, …, a_{Bn}) \)
\( A_B = (a_{B1}, a_{B2}, …, a_{Bn}) \)
3. Others-to-Worst (OW) Vector:
\( A_W = (a_{1W}, a_{2W}, …, a_{nW})^T \)
\( A_W = (a_{1W}, a_{2W}, …, a_{nW})^T \)
4. Optimization Model:
\[ \min \xi \] \[ \text{s.t. } |w_B – a_{Bj}w_j| \le \xi \] \[ |w_j – a_{jW}w_W| \le \xi \] \[ \sum w_j = 1, w_j \ge 0 \]
\[ \min \xi \] \[ \text{s.t. } |w_B – a_{Bj}w_j| \le \xi \] \[ |w_j – a_{jW}w_W| \le \xi \] \[ \sum w_j = 1, w_j \ge 0 \]
Solved Example: Laptop Selection
Criteria: Price, Performance, Battery, Design.
Step 1: Best and Worst selection
Best: Performance | Worst: Design
Best: Performance | Worst: Design
Step 2: Comparisons (Scale 1-9)
Best-to-Others (BO): [Price: 3, Performance: 1, Battery: 2, Design: 8]
Others-to-Worst (OW): [Price: 4, Performance: 8, Battery: 5, Design: 1]
Best-to-Others (BO): [Price: 3, Performance: 1, Battery: 2, Design: 8]
Others-to-Worst (OW): [Price: 4, Performance: 8, Battery: 5, Design: 1]
Step 3: Solved Weights (\(w\))
Solving the optimization yields:
– Price: 0.23 | Performance: 0.48 | Battery: 0.23 | Design: 0.06
Solving the optimization yields:
– Price: 0.23 | Performance: 0.48 | Battery: 0.23 | Design: 0.06
Step 4: Alternative Ranking (Simple Weighted Sum)
| Alt | Price | Perf. | Bat. | Des. | Score |
|---|---|---|---|---|---|
| L1 | 0.8 | 0.9 | 0.7 | 0.5 | 0.815 |
| L2 | 0.5 | 0.8 | 0.9 | 0.9 | 0.766 |
Result: L1 is the best choice based on the derived weights.
Interactive BWM Calculator
1. Define weights using Best/Worst comparison.
2. Evaluate 4 Alternatives below.
Weight Determination
| Criteria | BO (Best-to-j) | OW (j-to-Worst) |
|---|---|---|
| Attr 1 | ||
| Attr 2 (Best) | ||
| Attr 3 | ||
| Attr 4 (Worst) |
Decision Matrix (Alternatives)
| Alt | Attr 1 | Attr 2 | Attr 3 | Attr 4 |
|---|---|---|---|---|
| A1 | ||||
| A2 | ||||
| A3 | ||||
| A4 |
Designed by: Dr. M.U. Mirza
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