Question

Based on three criteria of Performance, Price, and Brand, we want to decide to by a computer. According to our preferences, the weights of the criteria are 0.581, 0.309, and 0.110, respectively. A study comparing three personal computers of hp. Asus, and Apple resulted in the following pairwise comparison matrix for the performance criterion:

Apple 12 1/2 Performance ap Asus Apple Asus 3 1/3 1/2 According to the Analytical Hierarchy Process (AHP) method, (use three decimals in your calculations, for example: 10.256

a Determine the priorities for the three computers relative to the Performance criterion (calculate the priority vector regarding the Performance criterion).

b. Compute the consistency ratio. Are the judgments regarding Performance consistent? Explain. Consider the Random Index (RI) amounts as follows: 3. 4 6. 7. RI 0.58 0.9 1.12 1.24 1.32 1.41

c. Based on the priority vector you calculated in part a (Performance priority vector), and [0.239) supposing that the Price priority vector and Brand priority vector are given as 0.623 and lo.137] [0.309] 0.110 . respectively, what is your recommended decision" lo.581.

Answer 1

Answer:-

Given That:-

Based on three criteria of Performance, Price, and Brand, we want to decide to by a computer.

Given,

Weights of citeria

Performance price brand

Comparison matrix for performance criteria

Performance hp Asus Apple

Normalising matrix:

Divide each element of column with irs column sum and calculate AM for each row

If the performance matrix is consistent so AM is the priority vector, so we need to check consistency Ratio for consistency of the matrix.

First we need to calculate maximum eigen value

= 3.0117

= 0.0058

Therefore n = 3 is the order of square matrix,

Consistency index CI = 0.0058

Consistence Ratio = Consistency Index/Random Index

= CI/RI

RI(3) = 0.58

So

CR = 0.0058/0.58

= 0.01

= 1.0% < 10%

So the given performance matrix is consistent. therefore the arithmatic mean vector is the priority vector of performance.

a) Determine the priorities for the three computers relative to the Performance criterion

Performance Priority vector

First Priority of performance

Third Priority

Second Priority

b. Compute the consistency ratio. Are the judgments regarding Performance consistent? Explain.

Consistency Ratio LR = 0.01

= 1%

So performance priority vector is consistent.

c. Based on the priority vector you calculated in part a and supposing that the Price priority vector and Brand priority vector. what is your recommended decision?

Decision vector = Priority Matrix * Criteria Vector

Priority matrix performance price brand * criteria

Decision vector

hp Asus Apple

frist priority computer

second priority computer

Third priority computer

Because hp has highest priority so i will recommend (on the basis of this information) hp computer.

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