The WASPAS Method: A Comprehensive Guide
The WASPAS (Weighted Aggregates Sum Product Assessment) method is an advanced decision-making tool. By integrating two distinct models, it achieves a high level of mathematical consistency.
Specifically, this approach combines the Weighted Sum Model (WSM) and the Weighted Product Model (WPM). Furthermore, it allows decision-makers to adjust a joint importance coefficient ($\lambda$). Consequently, this dual-verification process makes it one of the most reliable techniques in Multi-Criteria Decision Making (MCDM).
1. Mathematical Formulation
Initially, we must normalize the decision matrix to ensure all criteria are comparable. This process depends on whether a criterion is a “Benefit” or a “Cost.”
Normalization Formulas
For Benefit Criteria (e.g., Quality):
$$ \bar{x}_{ij} = \frac{x_{ij}}{\max_i x_{ij}} $$In contrast, for Cost Criteria (e.g., Price):
$$ \bar{x}_{ij} = \frac{\min_i x_{ij}}{x_{ij}} $$The Integrated Score
Ultimately, the final preference score ($Q_i$) is determined by merging the additive and multiplicative results:
$$ Q_i = 0.5 \sum_{j=1}^{n} \bar{x}_{ij} w_j + 0.5 \prod_{j=1}^{n} (\bar{x}_{ij})^{w_j} $$2. Numerical Example
To illustrate, let us evaluate three Software Providers based on Experience (w=0.6) and Cost (w=0.4). Experience is a benefit, while Cost is a cost.
| Alternative | Experience (Years) | Cost ($) |
|---|---|---|
| Provider A | 10 | 500 |
| Provider B | 15 | 800 |
| Provider C | 8 | 400 |
Step-by-Step Solution:
First, we normalize the values. For Provider A’s Experience: $10 / 15 = 0.667$. For Provider A’s Cost: $400 / 500 = 0.800$.
Next, we calculate the Weighted Sum (WSM). For Provider A: $(0.667 \times 0.6) + (0.800 \times 0.4) = 0.720$.
Additionally, we calculate the Weighted Product (WPM). For Provider A: $(0.667^{0.6}) \times (0.800^{0.4}) = 0.717$.
Finally, we average these two values to get the WASPAS score: 0.7185. Following this same logic for all providers reveals the best choice.
3. Interactive WASPAS Calculator
Use this tool to calculate scores for 3 alternatives. Note: Columns 1 & 3 are Benefits; Columns 2 & 4 are Costs.
Final Results ($Q_i$):
Designed by: Dr. M.U. Mirza
Mathematical Researcher & Educator