Are MCDM methods useful? A critical review of Analytic Hierarchy Process (AHP) and Analytic Network Process (ANP)

Figures & data

Table 1. Saaty’s scale

Rank	Description
1	equally important
3	moderately important
5	strongly important
7	significantly important
9	extremely important

Table 2. Consistency of random matrices

Matrix order	1	2	3	4	5	6	…
RI	0	0	0.52	0.89	1.11	1.25	…

Table 3. Initial weights of the criteria

	Quality	Price	Delivery	Local Weights
Quality	1	2	3	0.529
Price	1/2	1	2	0.309
Delivery	1/3	1/2	1	0.162
	${\lambda }_{max}$= 3.009		CR = 0.008

Table 4. Alternatives with respect to quality

	Supplier A	Supplier B	Supplier C	Local Weights
Supplier A	1	1	1	0.333
Supplier B	1	1	1	0.333
Supplier C	1	1	1	0.333
	${\lambda }_{max}$= 3.000		CR = 0.000

Table 5. Alternatives with respect to price

	Supplier A	Supplier B	Supplier C	Local Weights
Supplier A	1	3	2	0.529
Supplier B	1/3	1	1/2	0.162
Supplier C	1/2	2	1	0.309
	${\lambda }_{max}$= 3.009		CR = 0.008

Table 6. Alternatives with respect to delivery

	Supplier A	Supplier B	Supplier C	Local Weights
Supplier A	1	1/9	1/8	0.056
Supplier B	9	1	1	0.495
Supplier C	8	1	1	0.450
	${\lambda }_{max}$= 3.002		CR = 0.002

Table 7. The AHP ranking

	Quality 0.529	Price 0.309	Delivery 0.162	Global Weights	Rank
Supplier A	0.333	0.529	0.056	0.349	1
Supplier B	0.333	0.162	0.495	0.306	3
Supplier C	0.333	0.309	0.450	0.345	2

Figure 1. ANP, clusters, elements and dependencies

Table 8. The importance weights of the criteria

	Most to least important	Normalised weights
Quality	1.400	0.389
Price	1.200	0.333
Delivery	1.000	0.278

Table 9. Alternatives with respect to price

	Price
Supplier A	1.3
Supplier C	1.1
Supplier B	1

Table 10. Alternatives with respect to criteria

	Quality	Price	Delivery
Supplier A	1	1.3	1
Supplier B	1	1	3.9
Supplier C	1	1.1	4.7

Table 11. The ranking of the general MCDM method

	Quality	Price	Delivery	Weights	Rank
Supplier A	0.130	0.127	0.029	0.286	3
Supplier B	0.130	0.098	0.113	0.341	2
Supplier C	0.130	0.108	0.136	0.373	1

Note that the above tables are not too sensitive with regard to the selected scores. For instance, changing the numbers in the last column of Table 10 from ‘1, 3.9, and 4.7ʹ to ‘1, 4.7, and 4.7ʹ, or to ‘1, 2, and 3ʹ does not change the ranking. In the next section, the ranking of AHP in Table 7 is compared with the above table, Table 11.

Table 12. Perfect pairwise comparisons using AHP

	Quality	Price	Delivery	Local Weights
Quality	1	2	4	0.571
Price	1/2	1	2	0.286
Delivery	1/4	1/2	1	0.143
	${\lambda }_{max}$= 3.000		CR = 0.000