# Common mistakes using the decision support matrix.

During the fifth step of the military decision-making process, staff members compare courses of action (COAs) in order to recommend a preferred COA. (1) One tool commonly used is a decision support matrix. A common mistake, the improper weighting of criteria, often reduces the value of the results of the decision support matrix by yielding incorrect results. This article addresses the issue by briefly discussing the concept behind decision support matrices and then identifying and correcting common problems in weighting criteria.

The purpose of a decision support matrix is to quantify the advantages of different COA options. COAs are ranked based on various criteria and for each criterion are assigned numerical "places" of 1 through the number of COAs that exist, with 1 being assigned to the most desirable COA for a particular criterion. (2) The criteria are developed by the staff and approved by the commander. The purpose of the decision support matrix is to measure the deviation of each COA from the ideal. Because lower numbers are assigned to the most desirable COA, smaller values within the matrix represent smaller deviations from the ideal. For this reason, smaller values represent better choices.

To reflect the relative importance of one criterion compared to others, weighted values are assigned to the criteria. (3) Assigning larger weighted values to the least-desired criteria keeps the number assigned to the more important criteria smaller; however, the proper weighting of individual criterion is actually counter-intuitive to the general rule that smaller is better. For a nonweighted criterion, the deviation between two COAs is equal to the difference in the values of their criterion rankings. By assigning a weight multiplier to a criterion, we increase the deviation range for that criterion.

The deviation between a COA that has been ranked as a 1 for a particular criterion and a COA that has been ranked as a 2 is equal to 1. The deviation for a weighted criterion is increased by multiples of the weighting value. For a criterion that is assigned a weight of 2, the COA with a rank of 1 would now have a value of 2 (1 x 2) and the COA with a rank of 2 would now have a value of 4 (2 x 2) for a deviation of 2. Weighting a criterion increases the penalty for deviating from the ideal within that criterion.

In Table 1, the most important criterion has been weighted higher. The nonweighted totals for each COA are equal; but when weighted, COA B deviates more from the ideal in the most important criterion and is therefore penalized more heavily. As shown in Table 2, more heavily weighting the least important criterion would cause the recommendation of the less favorable COA in our most important criterion.

Another facet of improperly weighting criteria when using the decision support matrix is over-weighting the criteria. The assignment of an excessively large value to the most important criterion causes the effect of any other criteria to be negated, and no matter how COAs rank in other criteria, the COA ranking most favorably in the highest-weighted criterion will be recommended. Table 3 shows that, even though COA B ranks more favorably in all other criteria, COA A is still recommended because the most important criterion is weighted too heavily.

To avoid this mistake, the highest weighting value used must be at least 1 less than the total of all other weighting values. In the Table 3 example, the highest weighting value is 6, and the total of all other weighting values is also 6. This weighting scheme returns a total value of 18 for both COAs, and the staff will recommend the COA that ranks better in the most important criterion. A weighting value of 5 for the most important criterion would have returned a total of 17 for COA A and 16 for COA B; COA B would be recommended.

Over-weighting is most commonly encountered when COAs are compared by three or fewer criteria. When any of the three criteria are weighted, the maximum valid weighting value is exceeded.

Commanders and staffs cannot rely simply on the results of the decision support matrix to reach a decision; inputs into the matrix are largely subjective evaluations and subject to change. (4) However, if staff officers understand the function of the matrix, it can be a very useful tool to help make informed decisions. A properly utilized matrix can assist staff officers in making recommendations in their commodity areas or in assisting in any decision that must be judged against multiple criteria. (5)

Captain Schropfer is the commander of Company C, 3d Battalion, 10th Infantry Regiment. He is a graduate of the CBRN Captain's Career Course, the CBRN Senior Staff Planners Course, and the Technical Escort Course. He holds a bachelor's degree in psychology from the University of Nebraska and a master's degree in environmental management from Webster University.

Endnotes:

(1) Field Manual 6-0, Commander and Staff Organization and Operations, 5 May 2014, pp. 9-40-9-41.

(2) Ibid.

(3) Ibid.

(4) Ibid, p. 9-41.

(5) Ibid.
```Table 1. Correct Weighting of Criteria

Criterion                  COA A   COA B

Most important criterion   1 (2)   1 (2)
(weighted times 2)

Least important criterion  2 (2)   1 (1)

Total                      3 (4)   3 (5)

Note: The value in parentheses is the weighted total of each
criterion.

Legend:
COA--course of action

Table 2. Weighting of Criteria Reversed

Criterion                  COA A   COA B

Most important criterion     1       2

Least important criterion  2 (4)   1 (2)
(weighted times 2)

Total                      3 (5)   3 (4)

Note: The value in parentheses is the weighted total of each
criterion.

Legend:
COA-course of action

Table 3. Most Important Criteria Over Weighted

Criterion                   COA A    COA B

Most important criterion    1 (6)    2 (12)
(weighted times 6)

More important criterion    2 (6)    1 (3)
(weighted times 3)

Less important criterion    2 (4)    1 (2)
(weighted times 2)

Least important criterion     2        1
Total                       7 (18)   5 (18)

Note: The value in parentheses is the weighted total of each
criterion.

Legend:
COA-course of action
```
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