Question

A company is deciding between 2 foreign firms to provide its call center services. A factor-rating method is used. Factors are rated on a scale of 1-10, with 1 being the best score.

1. If the factors are weighted equally (respective weights of .333), what is the factor-rating score for each firm and which firm is preferred
2. Suppose a consultant recommended that Factor 3 be twice as important as Factor 1, while Factor 2 should be twice as important as Factor 3. Using the weighted method, what is the factor-rating scorer for each firm and which firm is preferred? (Round your weights to the third decimal place.) Show all work by hand (not excel), thank you!

3. Firm	Factor 1	Factor 2	Factor 3
   A	8	7	5
   B	4	8	7

Answer 1

a) If the factors are weighted equally,

score for Firm A = (0.333*8) + (0.333*7) + (0.333*5) = 2.664 + 2.331 + 1.665 = 6.660

score for Firm B = (0.333*4) + (0.333*8) + (0.333*7) = 1.332 + 2.664 + 2.331 = 6.327

Since score for Firm B is lower, Firm B will be preferred.

b) It is given that, weight of factor 3 (w₃) = 2* weight of factor 1 (w₁)

Also weight of factor 2 (w₂) = 2*w₃

We know, w₁ + w₂ + w₃ = 1

0.5 w₃ + 2 w₃ + w₃ =1

w₃ = 0.286

Hence, w₁ = 0.5 w₃ = 0.143

and, w₂ = 2 w₃ = 0.572

Given these weights,

Score for Firm A = (0.143*8) + (0.572*7) + (0.286*5) = 1.144 + 4.004 + 1.430 = 6.578

Score for Firm B = (0.143*4) + (0.572*8) + (0.286*7) = 0.572 + 4.576 + 2.002 = 7.15

In this case, Firm A has a lower score, therefore, Firm A will be preferred.