W7_YN_ Analytic Hierarchy Process

W7_YN_ Analytic Hierarchy Process

Opportunity Statement

As the spot market team grows, additional equipment must be procured for the use of the staff. This includes purchasing laptops for individual use. Up until now, the company has been procuring its laptops from a specific brand, but it’s not limited to this brand. There are many companies manufacturing laptops around the world. In this blog, we shall compare between three main providers of laptops. The brands chosen are ones that are available in the country, and are known for producing laptops for business use.

Feasible Alternatives

Three different laptop brands will be compared. Their names are not used and will be referred to as brands A, B, and C.

Outcomes of Feasible Alternatives

The alternatives will be compared using the Analytic Hierarchy Process (AHP) of the Multi-Attribute Decision Making Technique. AHP is useful when the criteria used to compare the alternatives are expressed in different units or are hard to quantify. The process enjoys mathematical properties that allows giving each of the criteria a weightage that represents its importance when compared to the other criteria.

Acceptable Criteria

Three criteria will be used to compare between the alternatives:

C1)  Design

C2)  Tech Support

C3)  Software

C4)  Customer Reviews

C5)  Cost

Analysis and Comparison of the Alternatives

All alternatives will be compared in terms of each of the criteria individually. The alternatives will be compared to each other to determine their relative importance or superiority in terms of each of the criteria. Figure 1 below shows the scale used for this step.

Figure 1: Scale of Relative Importance

A table of relative importance, or a judgement matrix, is created for each of the criteria as seen in tables 1-4 below. It is important to highlight that the alternatives will be initially compared in terms of all criteria except for cost. The cost of each of the alternatives will be used later to find the benefit-cost ratio to yield the amount of value we are receiving for the cost of the laptop.  

 Table 1: Judgement Matrix for C1

Table 2: Judgement Matrix for C2

Table 3: Judgement Matrix for C3

Table 4: Judgement Matrix for C4

Tables 1-4 above include the priority vector for each judgement matrix. The priority vector illustrates the relative importance of each alternative in terms of a specific criteria. This is calculated by multiplying the elements in each row of the matrix and taking the nth root, with n being the number of alternatives. Then, the numbers are normalized by dividing each of them by their sum.

The next step is to ensure the consistency of the pairwise comparisons. To do so, the eigenvalue (λmax) is calculated by taking the sum of the product of the priority vector and the sum of each of the columns in the judgement matrix. Next, the consistency index (CI) is calculated using the following equation:

Then the consistency ration (CR) is calculated by dividing (CI) by the random consistency index (RCI). RCI depends on the number of alternatives in the judgement matrix, and has values as shown in table 5 below.

Table 5: RCI values for different n values

Table 6 below summarizes the consistency values for each of the judgement matrices of C1-C4.

 

Table 6: Consistency Ratio of Pairwise Comparisons

The pairwise comparisons are considered adequately consistent if CR<0.1, which is the case for all of our cases as seen in the table above.
Since some of the criteria are more important than the others, AHP allows giving each criteria a relative weight in terms of its importance amongst all criteria. This is done in a similar manner to the pairwise comparisons of the alternatives in terms of a criteria. The results are seen in table 7 below.

Table 7: Pairwise Comparison of Criteria

The priority vector of the table above contains the relative importance or the weight of each of the criteria.

The final step is to create the decision matrix using the priority vectors from tables 1-4 & 7. The decision matrix combines the results in terms of all criteria and the weight of each criteria in order to yield a final priority vector. The final priorities represent the relative importance of each alternative in terms of all criteria considered. The results are shown in table 8 below. The final priority is calculated by taking the sum for all criteria of the product of the relative importance of an alternative and the weight the criteria. The numbers in green are the weight of each criteria, while the number in blue are the relative importance of alternatives in terms of each criteria.

 

Table 8: Decision Matrix

Now we take cost into account by calculating the benefit-cost ratio. The cost of each alternative is shown in table 9 below and are normalized using the sum of all costs.

Table 9: Costs Normalized

Finally, the benefit-cost ratio is calculated. The results are in table 10 below.

Table 10: Benefit-Cost Ratio

Preferred Alternative

As seen in tables 8 & 10 above, option A is the laptop brand we should go with when considering value on its own, and also when taking cost into consideration. This is due to the higher values of final priority and benefit-cost ratio of option A. Brand C is the next best option.

Tracking and Reporting

This analysis shall be repeated once the first shipment of brand A laptops is received, and used for a period of three months. The analysis will be updated for the criteria above in order to make the choice on whether the following shipment should be of the same brand or not.

References

1)      Mann, S. H., & Triantaphyllou, E. (1995). Using the Analytic Hierarchy Process for Decision Making in Engineering Applications: Some Challenges. International Journal of Industrial Engineering: Applications and Practice, 2(1), 35-44.

2)      W12_OAN_Car Selection using AHP – EMERALD AACE 2017 – WEEKLY BLOG. (2017, November 5). Retrieved from https://emeraldaace2017.com/2017/11/05/w12_oan_car-selection-using-ahp/

3)      W5_WW_ Analytical Hierarchy Process. (2015, March 28). Retrieved from https://garudaaace2015.wordpress.com/2015/03/28/w5_ww_-analytical-hierarchy-process-2/