Question

A manager is using the AHP to decide which of three computer maintenance firms (A, B and C) should be awarded a three-year contract. The manager decides to evaluate the companies on the basis of price (P), quality (Q) and after-sale services (S). The following pair-wise comparison matrices were developed based on the manager's preferences Criteria Price (P) 4 2 1/3 1/3 1/4 1/3 1/4 1/23 Quality (Q) After-sale Services (S) 4 1/2 1/4 1/3 1/4 1/2 What are the weights of the three criteria? [3 pts

Answer 1

Calculating the weights of criteria is the first step of AHP process.

Given a pairwise comparison matrix. we can calculate the weight of each criteria by taking the nth root of product of each item of a row which corresponds to that criteria, here n is the number of criterias.

So Wieght of P will be cuberoot(1*3*4) = 2.28

So Wieght of Q will be cuberoot(1/3*1*3) = 1

So Wieght of S will be cuberoot(1/4*1/3*1) = 0.437

After normalization i.e dividing by thier sum we get,

So Wieght of P will be cuberoot(1*3*4) = 2.28/3.717 = 0.613

So Wieght of Q will be cuberoot(1/3*1*3) = 1/3.717=0.269

So Wieght of S will be cuberoot(1/4*1/3*1) = 0.437/3.717=0.11