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Decision Making Processes Using Analytic Hierarchy Process

Choosing an insurance company

-project-


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TABLE OF CONTENTS :

1) Contexta) Presentation of the problem

2) Developing the survey

3) Interpretation of answersa) Linguistic scaleb) Saatys scalec) Ma Zhengs scaled) Superdecisions

4) Conclusions


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1. ContextThis projects aim is to find a solution to a problem using the Analytic Hierarchy Process

(AHP), which is choosing an insurance company. In fig.1, three criteria were taken into account,

namely the price of insurance, the benefits given by the insurer and the amount of money

refunded in case of an accident. The alternatives represent the companies considered an option

for the insured. These companies might be ASIROM, GENERALI or OMNIASIG .

Problem: Choosing an insurance company

Criteria

Alternatives

Fig.1. AHP model

2. Developing the surveyFor answering to the problem in question, a survey was conducted. Two respondents

answered to the questions in order to find out which is their main option when considering

choosing an insurance company.

First, they were required to choose among the criteria which they considerimportant and also mention the intensity of their choice.

Choosing an

insurance company

PriceAmount of mo ney

being refunded in

case of an accidennt

Benefits

ASIROMGENERALIOMNIASIG


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The second step was to choose between the companies by taking intoconsideration one of the criterion.

All three criteria were used and pairwise comparisons were made. Also, the intensity of their

preference was required.

The criteria had been denoted as following:

C1- Price

C2- Benefits

C3- Amount of money refunded in case of an accident

The alternatives had been represented as:

A1- ASIROM

A2- GENERALI

A3- OMNIASIG

Survey sample:

- Choosing between two criteria:What criterion is more important among PRICE and BENEFITS?

PRICE BENEFITS

- Choosing between two alternatives by taking into consideration the price:In terms of PRICE, what do you prefer between ASIROM and OMNIASIG?

ASIROM OMNIASIG

-Choosing between two alternatives by taking into consideration the BENEFITS:In terms of BENEFITS, what do you prefer between ASIROM and OMNIASIG?


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ASIROM OMNIASIG

- Choosing between two alternatives by taking into consideration the amount of moneybeing refunded in case of an accident

- In terms of AMOUNT OF MONEY, what do you prefer between ASIROM andGENERALI?

ASIROM OMNIASIG

- Choosing the intensity of the preference:On a scale from 1 to 9 (1-equally important, 9 extremely important) by how much you

think is more important the alternative you chose to the other one?

Equal

important

Not much

moreimportant

A little

moreimportant

Sufficiently

moreimportant

Moderately

moreimportant

More

important

Strongly

moreimportant

Very

stronglymoreimportant

Extrem

importa

X

3. Interpretation of the answersIn order to perform a deeper analysis of the problem, I used three different measuring

scales: Saatys scale, the linguistic scale and Ma-Zhengs scale. The answers are presented for

both the respondents. Further on, the results have been interpreted with the help of two programs,

Gauss and Super Decisions. After this analysis, the final choices of the two persons interviewed

will be obtained, according to the answers they provided in the survey.


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Gauss:Respondent 1 Respondent 2

Linguistic scale

C1 C2 C3 C1 C2 C3

C1 s0 s7 s1 C1 s0 s8 s-5

C2 s-7 s0 s-4 C2 s-8 s0 s-6

C3 s-1 s4 s0 C3 s5 s6 s0

C1 A1 A2 A3 C1 A1 A2 A3

A1 s0 s-5 s-3 A1 s0 s3 s2

A2 s5 s0 s4 A2 s-3 s0 s-1

A3 s3 s-4 s0 A3 s-2 s1 s0

C2 A1 A2 A3 C2 A1 A2 A3

A1 s0 s-6 s-5 A1 s0 s1 s0

A2 s6 s0 s3 A2 s-1 s0 s-2

A3 s5 s-3 s0 A3 s0 s2 s0

C3 A1 A2 A3 C3 A1 A2 A3

A1 s0 s2 s1 A1 s0 s8 s7

A2 s-2 s0 s-1 A2 s-8 s0 s-6

A3 s-1 s1 s0 A3 s-7 s6 s0

Saatys scale

C1 C2 C3 C1 C2 C3

C1 1 8 2 C1 1 9 0.167

C2 0.125 1 0.200 C2 0.111 1 0.143

C3 0.500 5 1 C3 6 7 1

C1 A1 A2 A3 C1 A1 A2 A3

A1 1 0.167 0.250 A1 1 4 3

A2 6 1 5 A2 0.250 1 0.500

A3 4 0.200 1 A3 0.333 2 1

C2 A1 A2 A3 C2 A1 A2 A3

A1 1 0.143 0.167 A1 1 2 1

A2 7 1 4 A2 0.500 1 0.333

A3 6 0.250 1 A3 1 3 1


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C3 A1 A2 A3 C3 A1 A2 A3

A1 1 3 2 A1 1 9 8

A2 0.333 1 0.500 A2 0.111 1 0.143

A3 0.500 2 1 A3 0.125 7 1

Resp1 C1 C2 C3 Resp2 C1 C2 C3

0.615 0.072 0.313 0.135 0.095 0.769

A1 0.089 0.07 0.544 A1 0.629 0.398 0.79A2 0.739 0.726 0.168 A2 0.145 0.17 0.079

A3 0.171 0.203 0.287 A3 0.224 0.431 0.129

The final priority vectors for the two respondents in Saatys scale are:

A1: 0.230047 A1: 0.730235

A2: 0.559341 A2: 0.096476

A3: 0.209612 A3: 0.170386

Ma-Zhengs scale

C1 C2 C3 C1 C2 C3

C1 1 4.500 1.125 C1 1 9 0.444

C2 0.222 1 0.556 C2 0.111 1 0.333


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C3 0.889 0.556 1 C3 2.250 3 1

C1 A1 A2 A3 C1 A1 A2 A3

A1 1 0.444 0.667 A1 1 1.500 1.286

A2 2.250 1 1.800 A2 0.667 1 0.889

A3 1.500 0.556 1 A3 0.778 1.125 1

C2 A1 A2 A3 C2 A1 A2 A3

A1 1 0.333 0.444 A1 1 1.125 1

A2 3 1 1.500 A2 0.889 1 0.778

A3 2.250 0.667 1 A3 1 1.286 1

C3 A1 A2 A3 C3 A1 A2 A3

A1 1 1.286 1.125 A1 1 9 4.500

A2 0.778 1 0.889 A2 0.111 1 0.333

A3 0.889 1.125 1 A3 0.222 3 1

Resp1 C1 C2 C3 Resp2 C1 C2 C3

0.479 0.154 0.366 0.278 0.137 0.583

A1 0.21 0.159 0.374 A1 0.409 0.346 0.749A2 0.5 0.5 0.293 A2 0.275 0.293 0.078

A3 0.289 0.34 0.331 A3 0.315 0.36 0.17

The final priority vectors for the two respondents in Ma-Zhengs scale are:


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A1: 0.261960 A1: 0.597771

A2: 0.423738 A2: 0.162065

A3: 0.311937 A3: 0.236000

Super Decisions:

Respondent 1:


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Respondent 2:


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