Applied Statistics

Analytic Hierarchy Process (AHP) with the ahp Package

On my December to-do list, I had “write an R package to make analytic hierarchy process (AHP) easier” — but fortunately gluc beat me to it, and saved me tons of time that I spent using AHP to do an actual research problem. First of all, thank you for writing the new ahp package! Next, I’d like to show everyone just how easy this package makes performing AHP and displaying the results. We will use the Tom, Dick, and Harry example that is described on Wikipedia. – the goal is to choose a new employee, and you can pick either Tom, Dick, or Harry. Read the problem statement on Wikipedia before proceeding.

AHP is a method for multi-criteria decision making that breaks the problem down based on decision criteria, subcriteria, and alternatives that could satisfy a particular goal. The criteria are compared to one another, the alternatives are compared to one another based on how well they comparatively satisfy the subcriteria, and then the subcriteria are examined in terms of how well they satisfy the higher-level criteria. The Tom-Dick-Harry problem is a simple hierarchy: only one level of criteria separates the goal (“Choose the Most Suitable Leader”) from the alternatives (Tom, Dick, or Harry):

To use the ahp package, the most challenging part involves setting up the YAML file with your hierarchy and your rankings. THE MOST IMPORTANT THING TO REMEMBER IS THAT THE FIRST COLUMN IN WHICH A WORD APPEARS IS IMPORTANT. This feels like FORTRAN. YAML experts may be appalled that I just didn’t know this, but I didn’t. So most of the first 20 hours I spent stumbling through the ahp package involved coming to this very critical conclusion. The YAML AHP input file requires you to specify 1) the alternatives (along with some variables that describe the alternatives; I didn’t use them in this example, but I’ll post a second example that does use them) and 2) the goal hierarchy, which includes 2A) comparisons of all the criteria against one another FIRST, and then 2B) comparisons of the criteria against the alternatives. I saved my YAML file as tomdickharry.txt and put it in my C:/AHP/artifacts directory:

```#########################
# Alternatives Section
# THIS IS FOR The Tom, Dick, & Harry problem at
#
Alternatives: &alternatives
# 1= not well; 10 = best possible
# Your assessment based on the paragraph descriptions may be different.
Tom:
age: 50
experience: 7
education: 4
Dick:
age: 60
experience: 10
education: 6
Harry:
age: 30
experience: 5
education: 8
#
# End of Alternatives Section
#####################################
# Goal Section
#
Goal:
# A Goal HAS preferences (within-level comparison) and HAS Children (items in level)
name: Choose the Most Suitable Leader
preferences:
# preferences are defined pairwise
# 1 means: A is equal to B
# 9 means: A is highly preferable to B
# 1/9 means: B is highly preferable to A
- [Experience, Education, 4]
- [Experience, Charisma, 3]
- [Experience, Age, 7]
- [Education, Charisma, 1/3]
- [Education, Age, 3]
- [Age, Charisma, 1/5]
children:
Experience:
preferences:
- [Tom, Dick, 1/4]
- [Tom, Harry, 4]
- [Dick, Harry, 9]
children: *alternatives
Education:
preferences:
- [Tom, Dick, 3]
- [Tom, Harry, 1/5]
- [Dick, Harry, 1/7]
children: *alternatives
Charisma:
preferences:
- [Tom, Dick, 5]
- [Tom, Harry, 9]
- [Dick, Harry, 4]
children: *alternatives
Age:
preferences:
- [Tom, Dick, 1/3]
- [Tom, Harry, 5]
- [Dick, Harry, 9]
children: *alternatives
#
# End of Goal Section
#####################################
```

Next, I installed gluc’s ahp package and a helper package, data.tree, then loaded them into R:

```devtools::install_github("gluc/ahp", build_vignettes = TRUE)
install.packages("data.tree")

library(ahp)
library(data.tree)
```

Running the calculations was ridiculously easy:

```setwd("C:/AHP/artifacts")
Calculate(myAhp)
```

And then generating the output was also ridiculously easy:

```> GetDataFrame(myAhp)
Weight  Dick   Tom Harry Consistency
1 Choose the Most Suitable Leader 100.0% 49.3% 35.8% 14.9%        4.4%
2  ¦--Experience                   54.8% 39.3% 11.9%  3.6%        3.2%
3  ¦--Education                    12.7%  1.0%  2.4%  9.2%        5.6%
4  ¦--Charisma                     27.0%  5.2% 20.1%  1.7%        6.1%
5  °--Age                           5.6%  3.8%  1.5%  0.4%        2.5%
>
> print(myAhp, "weight", filterFun = isNotLeaf)
levelName     weight
1 Choose the Most Suitable Leader 1.00000000
2  ¦--Experience                  0.54756924
3  ¦--Education                   0.12655528
4  ¦--Charisma                    0.26994992
5  °--Age                         0.05592555
> print(myAhp, "weight")
levelName     weight
1  Choose the Most Suitable Leader 1.00000000
2   ¦--Experience                  0.54756924
3   ¦   ¦--Tom                     0.21716561
4   ¦   ¦--Dick                    0.71706504
5   ¦   °--Harry                   0.06576935
6   ¦--Education                   0.12655528
7   ¦   ¦--Tom                     0.18839410
8   ¦   ¦--Dick                    0.08096123
9   ¦   °--Harry                   0.73064467
10  ¦--Charisma                    0.26994992
11  ¦   ¦--Tom                     0.74286662
12  ¦   ¦--Dick                    0.19388163
13  ¦   °--Harry                   0.06325174
14  °--Age                         0.05592555
15      ¦--Tom                     0.26543334
16      ¦--Dick                    0.67162545
17      °--Harry                   0.06294121
```

You can also generate very beautiful output with the command below (but you’ll have to run the example yourself if you want to see how fantastically it turns out — maybe that will provide some motivation!)

```ShowTable(myAhp)
```

I’ll post soon with an example of how to use AHP preference functions in the Tom, Dick, & Harry problem.

6 replies »

1. Hi Nicole,

thanks for using my package! I am working hard on the next version, and you can peak-preview on the dev branch on github.

The main improvements are here: https://github.com/gluc/ahp/blob/dev/NEWS

The file format will change. As I didn’t expect anyone to do anything serious with the package yet, I didn’t plan backward compatibility. But now that I know I’m wrong, I might do it anyway if it’s not too complicated. Anyway, it would be great if you could add your example to the package. Ideally, you could do a pull request on the dev branch.

Anyway, thanks again for being an early adopter!

Best,

Chris

2. Suda says:

Hi Glur,
It is wonderful package, I it is pretty much easy.
As in example, I use for two decision maker, but making same for number of decision maker is really cumbersome. is there any other way to input for number of decision makers. like thorugh decision matrix

3. For those who want to run the Tom, Dick and Harry example here goes the new file format required for the current version (v0.3.0 candidate) of gluc/ahp:

#########################
Version: 2.0
#########################
# Alternatives Section
# THIS IS FOR The Tom, Dick, & Harry problem at
#
Alternatives: &alternatives
# 1= not well; 10 = best possible
# Your assessment based on the paragraph descriptions may be different.
Tom:
age: 50
experience: 7
education: 4
Dick:
age: 60
experience: 10
education: 6
Harry:
age: 30
experience: 5
education: 8
#
# End of Alternatives Section
#####################################
# Goal Section
#
Goal:
# A Goal HAS preferences (within-level comparison) and HAS Children (items in level)
name: Choose the Most Suitable Leader
preferences:
pairwise:
# preferences are defined pairwise
# 1 means: A is equal to B
# 9 means: A is highly preferable to B
# 1/9 means: B is highly preferable to A
– [Experience, Education, 4]
– [Experience, Charisma, 3]
– [Experience, Age, 7]
– [Education, Charisma, 1/3]
– [Education, Age, 3]
– [Age, Charisma, 1/5]
children:
Experience:
preferences:
pairwise:
– [Tom, Dick, 1/4]
– [Tom, Harry, 4]
– [Dick, Harry, 9]
children: *alternatives
Education:
preferences:
pairwise:
– [Tom, Dick, 3]
– [Tom, Harry, 1/5]
– [Dick, Harry, 1/7]
children: *alternatives
Charisma:
preferences:
pairwise:
– [Tom, Dick, 5]
– [Tom, Harry, 9]
– [Dick, Harry, 4]
children: *alternatives
Age:
preferences:
pairwise:
– [Tom, Dick, 1/3]
– [Tom, Harry, 5]
– [Dick, Harry, 9]
children: *alternatives
#
# End of Goal Section
#####################################