Setting Up the MCDM Matrix
The Multi Criteria Decision Making (MCDM) methodology has proven to be a very effective tool when used to select one course of action from several alternatives. This section demonstrates the application of this approach to a simplified process of solar panel selection.
Three components constitute the MCDM technique: alternatives, criteria and weights for each criterion.
Alternatives
Alternatives are the different options among which a client can choose. In our example, the alternatives are different panel models, referred to as Panel 1, Panel 2 and Panel 3.
Criteria
Criteria are the properties of the alternatives that are of value to the decision maker. It is important to consider all properties that may significantly affect the decision maker, including potential repercussions on other current projects or on potential future projects. For simplicity of demonstration, only three criteria will be considered: price (dollar value), output (W) and physical weight (kg).
Weights
The relative importance of each criterion can be reflected by assigning each a different weight. It is customary to assign percentage weightings to each criterion, so that the in total they equal 100%. In our example we choose to assign the weighting as follows – cost: 50%, output: 40%, physical weight: 10%.
MCDM Matrix
Once the alternatives, criteria and weights have been identified, the decision matrix can be constructed. A matrix for our example:
| Weight | Panel 1 | Panel 2 | Panel 3 | |
| Cost | 50% | |||
| Output | 40% | |||
| Physical weight | 10% | |||
Total |
100% |
Assigning Scores and Interpretation
Each alternative is evaluated on a 10 point scale for each of the criterion. Then the scores are scaled in accordance to the weightings and summed up to create a final score. The final score received by an alternative corresponds to how far from ideal this alternative is, e.g., 7.9 means that the alternative is 79% ideal. Final scores are all-inclusive and can serve as a basis for decision making.
This method can be used based on rough estimates or on fine-tuned and sophisticated data, as needed, through the use of techniques employed to assign the scores. Picking the most appropriate technique for every situation is not always a straightforward process. The commonly used techniques are:
- If the category is quantitative, such as cost, the highest score is assigned to the lowest cost alternative and a lowest score to the highest cost alternative. The remaining alternatives are ranked in proportion to the difference between these two.
- If the category is qualitative, such as degree of risk or reputation, the scores are assigned using the expert judgment of the person or people who are completing the matrix.
Below is the completed MCDM matrix for the panel selection example.
| Weight | Panel 1 | Panel 2 | Panel 3 | ||||
| Assigned Rating |
Final (Weighted) Rating |
Assigned Rating |
Final (Weighted) Rating |
Assigned Rating |
Final (Weighted) Rating |
||
| Cost | 50% | 10 | 5 | 8 | 4 | 5 | 2.5 |
| Output | 40% | 6 | 2.4 | 6 | 2.4 | 10 | 4 |
| Physical weight | 10% | 4 | 0.4 | 6 | 0.6 | 10 | 1 |
| Total | 100% | 7.8 | 7 | 7.5 | |||
Sensitivity Analysis
Sensitivity analysis allows one to determine how robust the selected choice is, i.e., how sensitive that choice is to changing weights or scores. To demonstrate, we assume in our example that the balancing of weighting for output and physical size is uncertain. By changing the weights until the preferred alternative changes, we can determine how dependent the current choice is to the change in the weighing of a particular criterion:
| Weight | Panel 1 | Panel 2 | Panel 3 | |
| Cost | 50% | 10 (5) | 8 (4) | 5 (2.5) |
| Output | 25% | 6 (1.5) | 6 (1.5) | 10 (2.5) |
| Physical weight | 25% | 4 (1) | 6 (1.5) | 10 (2.5) |
| Total | 100% | 7.5 | 7 | 7.5 |
We can see that as long as output is weighted above 25%, the preferred solution will not change; however, if the weighting is further reduced, then Panel 3 becomes a better choice.
If a similar analysis is done with regard to cost and physical weight, we find that the preferred alternative changes very quickly. To alter the preferred alternative, it is enough to decrease the weight of the cost criterion to below 47.5%. Thus the cost category is very sensitive to change in weighting.