Question

SMART

Andrea is house hunting with her husband. They are both 28 years old, have no children, and have a combined income of $110,000 per year. After looking at over 50 houses, they have narrowed their choices down to 4 located in the towns of Maynard, Stow, Hudson, and Bolton. The parameters that are important to them are commute, price, school system, and availability of good local Chinese food. After much soul-searching and discussion, they are able to construct the following table rating each option on each attribute (10 is best and 0 is worst):

	Maynard	Stow	Hudson	Bolton
Commute:	8	7	6	5
Price:	$275,000	$375,000	$250,000	$425,000
Schools:	5	7	4	7
Chinese Food:	6	8	7	6

Use the SMART technique to determine which house Andrea should buy, given the following relative weights: Commute: 5, Price: 20,   Schools: 10, Chinese Food: 25

       AHP

Keith is the manager of a food processing company and needs to replace a worn out packaging machine with a new one. He has a limited budget and has narrowed his choices down to three: (i) Aztec, (ii) Barton and (iii) Congress. The criteria that are important to him are depicted by the following hierarchy:

Keith has decided to use AHP to help him make his decision. He has conducted a pairwise comparison of the criteria as represented by the following table:

Pairwise Comparison	Most Important Criterion	How Much More Important?	Numerical Ranking
Reliability- After Sales Support	Reliability	Somewhat Strongly	4
Reliability-Speed of Delivery	Reliability	Strongly	5
Reliability-Customization	Reliability	Somewhat Strongly	4
After Sales Support-Speed of Delivery	After Sales Support	Weakly	3
After Sales Support-Customization	Customization	Very Weakly	2
Speed of Delivery-Customization	Customization	Weakly	3

Synthesize Keith’s rankings and compute the Consistency Ratio (CR). Show your work.

Finally, Keith has pairwise compared each of the alternatives in terms of Reliability, After Sales Support, Speed of Delivery and Customization as shown in the following four matrices.

Reliability

	Aztec	Barton	Congress
Aztec	1	3	4
Barton		1	2
Congress			1

After Sales Support

	Aztec	Barton	Congress
Aztec	1
Barton	2	1
Congress	3	4	1

Speed of Delivery

	Aztec	Barton	Congress
Aztec	1
Barton	2	1	4
Congress	3		1

Customization

	Aztec	Barton	Congress
Aztec	1	5	3
Barton		1	4
Congress			1

Synthesize the alternatives, compute an overall priority ranking for each and declare a winner. Show your work.

             

Answer 1

SMART

	Maynard	Stow	Hudson	Bolton
Commute:	8	7	6	5
Price:	$275,000	$375,000	$250,000	$425,000
Price Weighted*:	7.27	5.33	8.00	4.71
Schools:	5	7	4	7
Chinese Food:	6	8	7	6

* Based on the fact that lower cost is easier affordability, so the index is 2,000,000 divided by th.

By multiplying with the weights

	Maynard	Stow	Hudson	Bolton
Commute:	40	35	30	25
Price:	145	105	160	94
Schools:	50	70	40	70
Chinese Food:	150	200	175	150
Totals	385	410	405	339

Stow seems the location where Andrea should buy a house, given the following relative weights: Commute: 5, Price: 20,   Schools: 10, Chinese Food: 25

AHP

Reliability

	Aztec	Barton	Congress
Aztec	1	3	4	0.62
Barton	1/3	1	2	0.25
Congress	1/4	1/2	1	0.13
Totals	1 7/12	4 1/2	7	1.00

Aztec is the winner

After Sales Support

	Aztec	Barton	Congress
Aztec	1	1/2	1/3	0.14
Barton	2	1	1/4	0.25
Congress	3	4	1	0.61
Totals	6	5 1/2	1 7/12	1.00

Congress is the winner

Speed of Delivery

	Aztec	Barton	Congress
Aztec	1	1/2	1/3	0.14
Barton	2	1	4	0.54
Congress	3	1/4	1	0.32
Totals	6	1 3/4	5 1/3	1.00

Barton is the winner

Customization

	Aztec	Barton	Congress
Aztec	1	5	3	0.57
Barton	1/5	1	4	0.33
Congress	1/3	1/4	1	0.10
Total	1 8/15	6 1/4	8	1.00

Aztec is the winner

Combination of factors for priority

	Reliability	Customization	After Sales Support	Speed of Delivery
Reliability	1	4	4	5	0.52
Customization	1/4	1	2	3	0.23
After Sales Support	1/4	1/2	1	3	0.18
Speed of Delivery	1/5	1/3	1/3	1	0.07
Total	1 7/10	5 5/6	7 1/3	12	1.00

On multiplying the factors we get for Aztec
(0.62 x 0.52) + (0.57 x 0.23) + (0.14 x 0.18) + (0.14 x 0.07) = 0.4885

Similarly, for Barton 0.2887

and for Congress 0.2228

which shows Aztec to be the best among the three options.