W2_Afra_Best Alternative using AHP

1.     Problem Recognition

      Manager or decision maker need to use an appropriate method to make a complex decision. One of those methods is AHP (Analytic Hierarchy Process). Rather than prescribing a "correct" decision, the AHP helps decision makers find one that best suits their goal.

AHP tool will be used on this blog to choose the best and correct Gas turbine depends on

some specifications and criteria.

2.     Feasible alternatives

They are four Gas turbines with different specification has been selected to choose between by using five criteria (most important and common) which are: manufacturer, output, heat rate, price, Efficiency and Shaft speed. The price of each gas turbine shows in the table below: 

(A, B, C, D are dummy names for gas turbine) 

A	332 Million dollars
B	234 Million dollars
C	222 Million dollars
D	123 Million dollars

Table 1: Gas Turbines Price

3.    Development of the outcome of Alternative

Decision hierarchical tree below places all criteria and alternative gas turbines. This decision hierarchical has three levels: the top level shows the overall decision which is to select the best gas turbine for a plant, the second level shows all criteria need to be considered while selecting the best turbine, the third level shows all four alternatives.

Figure 1: Decision hierarchical tree

4.  Selection Criteria

Pair-wise comparison will be used to select the best alternative, this technique the relative

priority for each criterion against each other criterion as well as the priority for each alternative

(gas turbine) against each other alternative. The Pair-wise comparison uses a scale that ranges

from equally preferred to extremely preferred. Here is the scale

Figure 2: Pair-wise comparison scale

5.   Analysis and comparison of the Alternative

The table below develops a weight for every single criterion by developing single Pair-wise comparison matrix for the criteria. all elements on the diagonal assign to 1 since When we compare any alternative against itself the judgment must be that they are equally preferred.

	Manufacturer	Output	Heat Rate	Shaft speed	Efficiency
Manufacturer	1	5	2	7	4
Output	1/5	1	2	4	2
Heat Rate	1/2	1/2	1	2	3
Shaft speed	1/7	1/4	1/2	1	3
Efficiency	1/4	1/2	1/3	1/3	1
Total	2.09	7.25	5.83	14.33	13.00

Table 2:  Pair-wise comparison matrix

The table below shows the normalized pairwise comparison matrix.  Along with the average for each row.

	Manufacturer	Output	Heat Rate	Shaft speed	Efficiency	Total	Average
Manufacturer	0.48	0.69	0.34	0.49	0.31	2.31	0.46
Output	0.10	0.14	0.34	0.28	0.15	1.01	0.20
Heat Rate	0.24	0.07	0.17	0.14	0.23	0.85	0.17
Shaft speed	0.07	0.03	0.09	0.07	0.23	0.49	0.10
Efficiency	0.12	0.07	0.06	0.02	0.08	0.35	0.07
Total	1	1	1	1	1

Table 3:  Normalized pairwise comparison matrix

Furthermore, to calculate consistency index, following formula will be used.

                CI = 0.0180. To identify the random index, the table below will be used.

RI value is equal to 1.12

According to above formula, CR is equal to 0.0161. Based on Saaty’s empirical suggestion that if C.R. < 0.10 is acceptable.

Table below is the alternative ranking matrix

	Manufacturer	Output	Heat Rate	Shaft speed	Efficiency
A	0.0882	0.2769	0.3728	0.1824	0.2459
B	0.3126	0.2403	0.3728	0.4759	0.2534
C	0.5154	0.1922	0.2052	0.2910	0.2624
D	0.0837	0.2906	0.0491	0.0507	0.2383

Table 4:  Alternative ranking matrix

The alternative ranking is the product between the alternative ranking matrix and criteria ranking.

A	0.19
B	0.32
C	0.36
D	0.13

Table 5:  Alternative ranking 

The alternative that having highest weights will be selected. Gas Turbine C is the highest ranked Turbine.

6.  Selection of the preferred Alternative

The mentioned criteria above are not enough to judge. After alternative ranking has been defined, we should compare with the price using benefit-cost ratio.

	Cost	Normalized Cost	Alternative ranking	Benefit-Cost Ratio
A	332 .000	0.36	0.19	0.53
B	234 .000	0.26	0.32	1.23
C	222 .000	0.24	0.36	1.5
D	123 .000	0.14	0.13	0.93
Total	911.000

Table 6:  Benefit-Cost Ratio

Based on benefit-cost analysis, Gas Turbine C has the highest ratio.

6.  Performance Monitoring and the Post Evaluation of result

      To find more accurate result, this tool needs to be done by someone who understands the problem and criteria very well. To make sure about the result I'll do another blog posting in coming weeks with the same problem but by using non-compensatory models.

References: 

1.       Suresh. (2017). Ahp calculations. Slideshare.net. Retrieved 13 November 2017, from https://www.slideshare.net/lakshanasuresh/ahp-calculationshttps://en.wikipedia.org/wiki/Analytic_hierarchy_process_%E2%80%93_car_example

2.       W5_WW_ Analytical Hierarchy Process. (2017). GARUDA AACE 2015. Retrieved 13 November 2017, from https://garudaaace2015.wordpress.com/2015/03/28/w5_ww_-analytical-hierarchy-process-2/

3.       How to make a decisions: The Analytic Hirerrchey Process. (1990) (pp. 15-19). North Holland. Retrieved from https://www.google.com.om/url?sa=t&rct=j&q=&esrc=s&source=web&cd=5&cad=rja&uact=8&ved=0ahUKEwiR9PH-
_bvXAhXQIOwKHfveC8YQFgg_MAQ&url=https:%2F%2Fwww.researchgate.net%2Ffile
.PostFileLoader.html%3Fid%3D5879e59e615e27bbf27ef4e3%26assetKey%3DAS%253
A450351808684035%25401484383646513&usg=AOvVaw0VtE6wBMM3Umm_zqlcjAw5

4. Ishizaka, A. (2017). Clusters and pivots for evaluating a large number of alternatives in AHP. Retrieved 13 November 2017, from http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0101-74382012000100006