The Analytic Hierarchy Process (AHP) and Analytic Network Process (ANP) are techniques for multi-criteria decision making. AHP structures decisions as a hierarchy, while ANP structures them as a network to account for interdependencies. Both use pairwise comparisons to measure weights and rank alternatives. The four major steps of ANP are: 1) model construction, 2) pairwise comparison matrices to derive local priorities, 3) supermatrix formation to obtain global priorities, and 4) selection of the best alternative based on overall priorities. The document then provides an example case study of applying ANP to analyze strengths, weaknesses, opportunities, and threats for an insurance company in Iran.

2. Analytic Hierarchy Process
(AHP)
1
The Analytic Hierarchy Process (AHP) is a structured
technique for organizing and analyzing complex
decisions, based on mathematics and psychology. It
was developed by Thomas L. Saaty in the 1970s and
has been extensively studied and refined since then.

3. Analytic Hierarchy Process
4 Major Steps of AHP:
2

4. Analytic Hierarchy Process
3

5. Saati Scale
4

6. Analytic Network Process
(ANP)
The Analytic Network Process (ANP) is a more general form of the
analytic hierarchy process (AHP) used in multi-criteria decision analysis.
AHP structures a decision problem into a hierarchy with a goal,
decision criteria, and alternatives, while the ANP structures it as a
network. Both then use a system of pairwise comparisons to measure
the weights of the components of the structure, and finally to rank the
5
alternatives in the decision.

7. Analytic Network Process
6
In a hierarchy, alternatives affect (depend on) the criteria, criteria affect
goal. It is assumed that:
– Criteria do not affect alternatives
– Criteria do not depend on each other
– Alternatives do not depend on each other
In complex decisions there may be dependence and feedback.
Network model with dependence and feedback improves the priorities
derived from judgments and makes prediction much more accurate

8. Analytic Network Process
4 Major Steps of ANP:
7
Step1: Model Construction and Problem Structuring
Step2: Pairwise Comparison Matrices and Priority Vectors
Step3: Supermatrix Formation
Step4: Selection of The Best Alternatives

9. Analytic Network Process
8
Step1: Model Construction and Problem Structuring
The problem should be stated clearly and be
decomposed into a rational system, like a network. This
network structure can be obtained by decision-makers
through brainstorming or other appropriate methods.

10. Analytic Network Process
9
Step2: Pairwise Comparison Matrices and Priority Vectors
Similar to the comparisons performed in AHP, pairs
of decision elements at each cluster are compared with
respect to their importance towards their control
criteria. The clusters themselves are also compared
pairwise with respect to their contribution to the
objective. Decision-makers are asked to respond to a
series of pairwise comparisons of two elements
or two clusters to be evaluated in terms of their
contribution to their particular upper level criteria.

11. Analytic Network Process
10
Step2: Pairwise Comparison Matrices and Priority Vectors
In addition, interdependencies among elements of a
cluster must also be examined pairwise;
the influence of each element on other elements can be
represented by an eigenvector. The relative
importance values are determined with Saaty’s 1–9 scale
,where a score of 1 represents equal
importance between the two elements and a score of 9
indicates the extreme importance of one element
(row cluster in the matrix) compared to the other one
(column cluster in the matrix).

12. Analytic Network Process
11
Step2: Pairwise Comparison Matrices and Priority Vectors
A reciprocal like with AHP, pairwise comparison in ANP is
performed in the framework of a matrix, and a local
priority vector can be derived as an estimate of the relative
importance associated with the elements (or clusters)
being compared by solving the following equation:
Where A is the matrix of pairwise comparison, w is the eigenvector,
and λ max is the largest eigenvalue of A.
Saaty proposes several algorithms to approximate w. In this paper,
Expert Choice is used to compute the eigenvectors from the pairwise
comparison matrices and to determine the consistency ratios.

13. Analytic Network Process
12
Step3: Supermatrix Formation
The Supermatrix concept is similar to the Markov chain
process.To obtain global priorities in a system with
interdependent influences, the local priority vectors are
entered in the appropriate columns of a matrix. As a result,
a supermatrix is actually a partitioned matrix, where each
matrix segment represents a relationship between two
clusters in a system.The local priority vectors obtained in
Step 2 are grouped and placed in the appropriate positions
in a supermatrix based on the flow of influence from one
cluster to another, or from a cluster to itself, as in the loop.

14. Analytic Network Process
13
Step4: Selection of The Best Alternatives
If the supermatrix formed in Step 3 covers the whole network, the
priority weights of the alternatives can be found in the column of
alternatives in the normalized supermatrix. On the other hand, if a
supermatrix only comprises clusters that are interrelated,
additional calculations must be made to obtain the overall
priorities of the alternatives. The alternative with the largest
overall priority should be selected, as it is the best alternative as
determined by the calculations made using matrix operations.

15. Case Study
14
به کارگیری تکنیک فرآیند تحلیل شبکه ای در تحلیل
نقاط قوت، ضعف، فرصت و تهدید
)مطالعه موردی شرکت سهامی بیمه ایران(

16. Case Study
15
AHP ANP

17. Case Study
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18. Case Study
17

19. Case Study
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20. Case Study
19

21. Case Study
20
ماتریس مقایسه زوجی گروه
SWOT های

22. Case Study
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وابستگی های درونی گروه
SWOT های

23. Case Study
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24. Case Study
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25. Case Study
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.
.

26. Case Study
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ماتریس درجه اهمیت استراتژی
های جایگزین

27. Case Study
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اولویت های نهایی
گزینه های استراتژی
SO>WO>ST>WT