Question

plz use Excel and word to complete this question with detailed report to explain?

Case 3 David Jones is planning to buy a new van for his work as a trady. After narrowing his choices down to three models (A, B, and C) within his budget, he is having difficulty in deciding which one to purchase. David has compared each model against one another on the basis of four criteria: price, safety, economy, and comfort. His comparisons are summarised below: Price Safet 1/3 1/4 1/2 Econom Comfort 1/3 1/4 David wants to incorporate all of the four criteria into his final decision. However, the criteria are not equally important. The following matrix summarises his comparisons of the importance of the criteria Criteria Price Safety 1/6 Comfort Economy 1/3 Price Safety Economy Comfort 1/5 1/4 1/2 1/3 Use analytic hierarchy process to compute the overall score for each van. What do the results suggest?

Answer 1

Step 1. Determine the priority of the factors which are taken into the consideration. The factors taken into consideration for the van here are – price, safety, economy, and comfort.

How to find the priority-

1. Find the geometric mean of all the factors, of their rank factors. GM = (factor 1*factor 2*..factor n) ^ (1/n)

2. 

3. Find the priority vector for each factor, priority vector = GM of the factor/ (Sum of all GMs). See below. This gives the actual priority values of all the factors. But now we also need to check the consistency of the data, consistency means that the data is valid to use, for this we need to find the Consistency Ratio

4. 

5. Finding the CR- Find the sum of all columns as below-

6. 

   Price Safety Economy Comfort GM 0.2 0.324668 0.061042 2 2.632148 0.494876 1 0.333333 0.7071070.132945 1 1.654875 0.311137 1 0.166667 0.333333 4 Price Safety Econo Comfort SUM- SUM PV 0.25 0.5 15 1.916667 8.3333333.533333 5.318798 0.915624 0.948513 1.1078741.099351

7. Now we multiply the sum of columns of the factors into their respective PVs. See below

8. 

1. Now we find the sum of all the Sum PV values, this sum will be the value calFled lambda max

2. 

   Price Safety Economy Comfort GM 1 0.166667 0.333333 6 Price Safety EconO Comfort SUM- SUM PV Lambda max 0.2 0.324668 0.061042 2 2.632148 0.494876 1 0.333333 0.7071070.132945 1 1.654875 0.311137 0.25 0.5 15 1.916667 8.3333333.533333 5.318798 0.915624 0.948513 1.1078741.099351 10 4.071362

1. Now we find Consistency Index; CI; CI= (lamda max- n)/(n-1); n= number of factors; 4 here. See below. CI=0.024

2. 

3. There is a term random index (RI) corresponding to number of fators; for n=4; RI=0.9. CR=CI/RI/ See below. If CR is below 0.1; then data is consistent and can be used. The CR value is .0264; hence the data is consistent

4. 

5. Now, we find the same CR for all the other 4 matrices; that is Van A,B,C against Price, safety, economy and comfort. Find the PVs of all the Vans against all the factors, using the same procedure described above. Check their consistency at all levels. Use RI for n=3 as 0.58. See below-

6. 

7. 

8. 

1. You see that for comfort and economy, the CR is above 0.1; hence the data is inconsistent and should be disregarded, but here we can continue to solve the question.

1. Now we make the final matrix, to find the final rank. For all the Van, A,B,C, write their PV values against the corresponding 4 factors; which we found above. Also write the PV values we found of the four factors.

2. 

1. Now, multiply the PV of the factor, to the corresponding PV of the respective Van, and find the final score of each van. For eg; for Van A; score = D40*D39 + E40*E39 + F40*F39 + G40*G39; and do so for all the Vans. See below

2. 

Here we see that final score for Van B is max; hence we should buy Van B

If you have any doubts regarding the answer, or want clarifications on any point or concept,or have any queries on any of the concepts used, please comment below. Thank you