How is the score of an alternative found in a weighted decision matrix?

Sum of (rating x criterion weight) over all criteria

Highest single rating of the alternative

Why can a weighted decision matrix mislead?

Ratings and weights are subjective, and a very poor rating on a critical criterion can be hidden by high ratings elsewhere

It cannot handle more than two criteria

It always favours the cheapest option

It gives the same total for every alternative

Practice · 6 marks

Weighted decision matrix for drive selection

Short answer

Multiplying ratings by weights gives scores: A 106, B 99, C 97, D 95. Best choice is V-belt drive (A). Limitations: subjective weights/ratings can change ranking, and linear addition may hide a very poor rating on a critical criterion.

A conveyor needs a speed-reduction drive, and four alternatives are to be evaluated: A (V-belt drive), B (chain drive), C (separate gearbox) and D (integral gear-motor). The criteria weights are: initial cost 5, reliability 4, ease of maintenance 3, compactness 2. The ratings given by the design team (scale 1 to 10, 10 best) in the order [cost, reliability, maintenance, compactness] are: A = [7, 8, 9, 6], B = [8, 6, 7, 7], C = [9, 5, 6, 7], D = [6, 8, 5, 9]. (a) Use a weighted decision matrix to rank the alternatives and state the best choice. (b) State two limitations of this method of evaluating alternatives.

A weighted decision matrix multiplies the rating of each alternative on every criterion by the weight of that criterion, and the totals are compared.

(a) Ranking

Weights: cost 5, reliability 4, maintenance 3, compactness 2 (sum = 14). Maximum possible score = 10 x 14 = 140.

Score of A $= 5(7) + 4(8) + 3(9) + 2(6) = 35 + 32 + 27 + 12 = 106$

Score of B $= 5(8) + 4(6) + 3(7) + 2(7) = 40 + 24 + 21 + 14 = 99$

Score of C $= 5(9) + 4(5) + 3(6) + 2(7) = 45 + 20 + 18 + 14 = 97$

Score of D $= 5(6) + 4(8) + 3(5) + 2(9) = 30 + 32 + 15 + 18 = 95$

Alternative	Cost x5	Reliab. x4	Maint. x3	Compact x2	Total	Share of max
A V-belt	35	32	27	12	106	0.76
B Chain	40	24	21	14	99	0.71
C Gearbox	45	20	18	14	97	0.69
D Gear-motor	30	32	15	18	95	0.68

Ranking: A > B > C > D.

Answer: Alternative A (V-belt drive) is the best choice with a score of 106 out of 140.

(b) Limitations

The ratings and weights are subjective; a small change in weights can change the ranking (here B, C and D are within 4 points).
The method treats the criteria as independent and adds them linearly, so a very poor rating on one critical criterion (for example safety) can be hidden by high ratings elsewhere. Important constraints must be checked separately as pass/fail.

✓ Answer checked by Claude Opus 5.5 (high effort)

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Weighted decision matrix for drive selection

(a) Ranking

(b) Limitations

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