Solving Multi Criteria Decision Making Problems

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There are several methods to solve multi-criteria decision-making problems. Analytic Hierarchy Process (AHP) and Analytic Network Process (ANP) are two methods created by Tomas Saaty. AHP endeavor to solve the decision making problem by formed it in a hierarchy while ANP is used when the problem is so complex that cannot be formed as a hierarchy. This complexity happens because of the effect of criteria between each other or the effect of alternatives on criteria. Generally we can say The Analytic Network Process is a generalization of the Analytic Hierarchy Process. The ANP approach can be comprises in to four steps [87]:
Step 1: Model construction and problem structuring: The problem should be stated clearly and decomposed into a rational system like a network
Step 2: Pairwise comparisons and priority vectors: In ANP, like AHP, pairs of decision elements at each cluster are compared with respect to their importance towards their control criteria. Furthermore, interdependencies among criteria of a cluster must also be treated pairwise; thus the influence of each element on other elements can be represented by an eigenvector. The relative importance values are determined with Saaty’s nine scales.
Step 3: Supermatrix structure: 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
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