# AHP-TOPSIS-2N Example

## Introduction

##### Multicriteria Decision Analysis (MCDA) and the AHP-TOPSIS-2N method.

The objective of MCDA is to assist in decisions with multiple criteria. Multicriteria methods can be useful in several problems in business and even in personal life. AHP-TOPSIS-2N is a hybrid method build from the AHP (Analytic Hierarchy Process) and TOPSIS-2N (Technique for Order of Preference by Similarity to Ideal Solution - with two normalizations).

AHP-TOPSIS-2N uses the AHP to calculate the criteria weights and uses TOPSIS twice to generate rankings, each time with a different kind of normalization. This can allow the comparison of results and the analysis of the robustness. A consistency ratio is calculated, and when it is higher than 10%, it is required to check judgments on criteria comparison.

## Example

As an example, this vignette uses a case of row material supplier evaluation. The goal is to choose among A, B, and C suppliers based on the product cost, product quality (1 to 5), and the lead time. Below we have the decision matrix (alternatives x criteria).

Alternatives Cost Quality Lead Time
A1 1100 5 25
A2 850 3.5 10
A3 950 4 30

After defining the decision matrix, it’s time to define a matrix with a pairwise comparison of the criteria, using the Saaty scale (1-9).

Cost Quality Lead Time
Cost 1 1 3
Quality 1 1 5
Lead Time 1/3 1/5 1

The criteria comparison matrix can be read like this: “Cost is so important as Quality, Cost has moderate importance over Lead Time, Quality has strong importance over Lead Time.”

library(ahptopsis2n)

# define the decision matrix
decision<-matrix(c(1100, 5, 25,
850, 3.5, 10,
950, 4, 30), ncol=3, byrow=TRUE)

rownames(decision)<- c("A1", "A2", "A3")

#define criteria matrix with pairwise comparison
criteria<-matrix(c(1, 1, 3,
1, 1, 5,
1/3, 1/5, 1), ncol=3, byrow=TRUE)

# define each criterion objective
minmax<-c("min", "max", "min")

# associate the objects to the function arguments and run the function
ahptopsis2n(decision=decision, criteria=criteria, minmax=minmax)
#> [[1]]
#>            [,1]
#> [1,] 0.02505497
#>
#> [[2]]
#>       values ranking
#> A1 0.5754562       1
#> A2 0.4553086       2
#> A3 0.3517222       3
#>
#> [[3]]
#>       values ranking
#> A1 0.5374991       1
#> A2 0.4669885       2
#> A3 0.4359941       3

As we can see, the result is a list with a consistency ratio and two data frames with priority sorting of the alternatives.

### References

De Souza, L. P., Gomes, C. F. S. and De Barros, A. P. (2018). Implementation of New Hybrid AHP–TOPSIS-2N Method in Sorting and Prioritizing of an it CAPEX Project Portfolio. International Journal of Information Technology & Decision Making. DOI: 10.1142/S0219622018500207.

Saaty, T.L. The Analytic Hierarchy Process. McGraw-Hill, New York. (1980)