MGMT20005 Chap.4 Scoring Models and AHP
Scoring Models and AHP
Week 4 handles choices that depend on several conflicting criteria. A direct scoring model assigns each criterion a weight, rates each alternative, multiplies weight by rating and sums the contributions. The analytic hierarchy process derives priorities from pairwise judgments instead. An AHP hierarchy places the decision goal above criteria and alternatives.
Each reciprocal comparison matrix has ones on the diagonal and inverse values across the diagonal. Column normalisation followed by row averages gives an approximate priority vector. The consistency calculation converts the original matrix and priorities into lambda max, CI and CR; the course accepts judgments below the 0.10 CR threshold and asks for revision above it.
Final alternative priorities combine criterion priorities with local alternative priorities and should sum to one.
What this chapter covers
- 01
Weighted scoring with separate weights and ratings
- 02
AHP goals, criteria and alternatives
- 03
Reciprocal pairwise comparison matrices
- 04
Column normalisation and row-average priorities
- 05
Lambda max, consistency index and consistency ratio
- 06
Overall priorities and defensible recommendations
Worked example · free
Normalise a consistent comparison matrix
- 2Column totals are 1.75, 3.50 and 7.00. Divide each entry by its own column total.
- 2Every normalised column is 0.5714, 0.2857 and 0.1429, so the row-average priority vector is the same and sums to one.
- 2Multiplying the original matrix by the priorities gives weighted sums about 1.7142, 0.8571 and 0.4287. Dividing by the corresponding priorities gives 3 each, so lambda max is 3.
- 2CI = (3 minus 3)/(3 minus 1) = 0. With RI(3) = 0.58, CR = 0/0.58 = 0, which is below 0.10.
Key terms
- Criterion weight
- The importance assigned to a criterion across the full decision.
- Alternative rating
- A score describing how well one alternative performs on one criterion.
- Pairwise comparison
- A judgment of the relative importance or preference of one item against another.
- Priority vector
- A set of derived AHP weights that sum to one within a comparison matrix.
- Consistency index
- An AHP measure based on the difference between lambda max and the matrix size.
- Consistency ratio
- The consistency index divided by the random index for the matrix dimension.
Scoring Models and AHP FAQ
What is the difference between scoring and AHP?
A scoring model accepts criterion weights and alternative ratings directly, multiplies them and sums contributions. AHP derives priorities from reciprocal pairwise judgments, checks the consistency of those judgments, repeats the process for alternatives under each criterion and then combines the local priorities. Both produce rankings, but their input structures differ.
Why must a pairwise matrix be reciprocal?
A comparison and its reverse describe the same judgment from opposite directions. If A is three times as important as B, B must be one-third as important as A. Entering independent values on both sides can make each item appear to dominate the other and breaks the meaning of the comparison scale.
What happens when the consistency ratio is too high?
The course method treats a CR above 0.10 as a signal to revisit the judgments. Do not force a final ranking from contradictory comparisons. Identify which pairwise entries produce the tension, ask decision makers to reconsider them, then recalculate priorities and consistency from the revised matrix.
How should a close final ranking be reported?
Report the closeness and identify the criterion contributions driving each alternative rather than presenting a narrow lead as certainty. A small change to a contested weight may reverse the order. That sensitivity is decision information and should guide discussion about which judgment deserves review.
Exam move
Separate the two methods from the first line. For a scoring model, write the weight vector, the rating matrix and each weight-by-rating contribution. For AHP, draw the hierarchy, build reciprocal matrices, sum columns, normalise entries and average rows. Keep at least four decimal places until the final ranking.
Use the original matrix for the consistency calculation, obtain lambda max from weighted-sum-to-priority ratios, then compute CI and CR with the random index for the correct matrix size. Only after the judgments pass should local alternative priorities be combined with criterion priorities. Finish by naming the preferred alternative and the contribution that drives its result.
If totals tie or nearly tie, say so and identify the weight that could change the decision. Add a verbal audit after every matrix calculation. Identify the most important criterion, the strongest local alternative and whether the final rank agrees with those priorities. If it does not, inspect the other weighted contributions rather than changing a judgment to fit the desired answer.
For scoring models, test one reasonable weight change and explain whether the ranking is robust or fragile.
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