JeromeQuah Ex2 AHP

OVERVIEW	PROXIMITY	CRITERION SCORES	AHP	SUITABILITY

The Analytical Hierarchical Process (AHP) is a multi-criteria decision-making method to derive the relative weight of a number of criteria affecting for a decision to be made via the pair-wise comparison matrix. In this case, we will be applying the AHP in our decision-making for the suitable site to build the CDQC in Gombak, with the criteria being the Health Risk Factor, Accessibility Factor, Natural Conservation Factor and Economic Factor. Before utilising the AHP, the priority for the mentioned factors for the suitability map with its rationale are as follows: Order of Priority for Criteria (1 - Most Important, 4 - Least Important) Priority Number Factor Rationale 1 Health Risk When taking into account the purpose of the CDQC which would be to house those who are ill with contagious diseases, the well-being and health of the rest of the Gombak population is of the utmost importance. 2 Accessibility With the health of the unaffected Gombak population being the most important, the second would be the ease of transportation of materials during the construction phase of the CDQC and also the diseased post-construction. This is to ensure that the diseased are able to arrive at the CDQC as quick as possible, and to prevent the spread of the disease to others within the area after discovery of the disease. 3 Natural Conservation After health and accessibility comes the protection of the diseased in the CDQC from wildlife or fauna which could incur further illness and hygiene issues within both the internal and external parameters of the CDQC. 4 Economic Developmental costs are considered to be detrimental to the budget of the CDQC during its construction, but cost should not be a priority when it comes to building the facility that puts the health of its users first.

AHP FUNDAMENTAL SCALE

The following fundamental scale is utilized for the pair-wise comparison matrix for each of the criteria involved.

AHP Fundamental Scale (Row vs Column)
Extremely Less Important		1/9
		1/8
Very Strongly Less Important		1/7
		1/6
Strongly Less Important		1/5
		1/4
Moderately Less Important		1/3
		1/2
Equal Importance		1
		2
Moderately More Important		3
		4
Strongly More Important		5
		6
Very Strongly More Important		7
		8
Extremely More Important		9

MATRIX INPUT

Based on the factor priorities, the AHP Template provided by SCB Associates is utilized to perform the pair-wise comparison matrix. As shown below, it is based on the format of comparing the Row Factor with the Column Factor.

Factor Priorities for Communicable Disease Quarantine Centre in Gombak - Pairwise Comparison Matrix
Row vs. Column	Economic Factor	Accessibility Factor	Health Risk Factor	Natural Conservation Factor
Economic Factor	1	1/7	1/9	1/3
Accessibility Factor	7	1	1	3
Health Risk Factor	9	1	1	7
Natural Conservation Factor	3	1/3	1/7	1
Column Totals	20.00	2.48	2.25	11.33

Legend
Automatic Calculation by Matrix	Red
Self-Input into Matrix	Yellow

The value of each cell in the matrix is then normalized via dividing the cell's value by its Column Total. From this, the normalized values for each of the factors is totaled by the row of the matrix, and then divided by 4 to get the average of all the weights for that factor. This returns the AHP Value for the respective factor. These values represent the respective Criteria's Weights in the decision-making of selecting of the suitable site for the CDQC in Gombak. The values are shown in the Results Report below.

RESULTS REPORT

Normalised Column Weights (2 d.p.)
Row vs. Column	Economic Factor	Accessibility Factor	Health Risk Factor	Natural Conservation Factor	Criteria Weights (%)
Economic Factor	0.05	0.06	0.05	0.03	4.7
Accessibility Factor	0.35	0.40	0.44	0.26	36.6
Health Risk Factor	0.45	0.40	0.44	0.62	47.9
Natural Conservation Factor	0.15	0.13	0.06	0.09	10.9

CONSISTENCY CHECKING

Lastly, to ensure that the accuracy of the Criterion Weights of the factors, the Consistency of the values are calculated via multiplying the Criteria Weights to the non-normalised values of the columns pair-wise comparison matrix that tallies with their respective factors. For further clarity: Column Cell Value for Economic Factor * 4.7% Column Cell Value for Accessibility Factor * 36.6% Column Cell Value for Health Risk Factor * 47.9% Column Cell Value for Natural Conservation Factor * 10.9% The results are then totaled by row to acquire the Weighted Sum Value for each of the Criteria. Following that, each Weighted Sum Value is then divided by the respective Criteria Weight of the criteria to acquire the Lambda for each criteria. The following shows the pair-wise comparison matrix with the mentioned calculations for Consistency.

Pairwise Comparison Matrix - Consistency Checking Calculations (3 d.p.)
Row vs. Column	Economic Factor	Accessibility Factor	Health Risk Factor	Natural Conservation Factor	Weighted Sum Value	Lambda
Economic Factor	0.047	0.052	0.053	0.036	0.189	4.108
Accessibility Factor	0.329	0.366	0.479	0.327	1.501	4.101
Health Risk Factor	0.423	0.366	0.479	0.763	2.031	4.240
Natural Conservation Factor	0.141	0.122	0.068	0.109	0.440	4.041

Lambda Maximum or ΛMax is then calculated via the averaging of all the Lambda Column Values for each of the criteria. This value will be then be used to calculate the Consistency Index (CI) ΛMax = (4.108 + 4.101 + 4.240 = 4.041) ÷ 4 = 4.100 (3.d.p.) CI = (ΛMax − n) ÷ (n − 1) = (4.100 − 3) ÷ (4 − 1) = 0.033 (3.d.p.) Lastly, the Consistency Ratio (CR) is calculated with CI ÷ Random Index (RI) when n = 4. The RI is the CI of randomly generated pairwise matrices. With the following values I have obtained when utilizing the SCB Template, I have arrived with the CR of 0.06 (3.d.p.) ΛMax = 4.152 CI = 0.05 RI when n = 4: 0.9 CR = 0.06 or 6% My Input Values of the SCB Template can be downloaded here

Consistency Check (CR)

6%

This means that the CR = 6% for the proportion of inconsistent CRs is less than the standard value of 10%. From this, we can assume that our pairwise matrix used is reasonably consistent, in which we can continue with the decision-making process for the CDQC in Gombak with the following criteria weights for the involved factors. Health Risk Factor: 47.9% Accessibility Factor: 36.6% Natural Conservation: 10.9% Economic Factor: 4.7% These values will be utilized when deriving our Suitability Map in the next section for the CDQC area in Gombak.

REFERENCES

2 Aug 2018, Saaty's Analytic Hierarchy Process by Manoj Matthew. Accessed 8th November 2019