# Analytic Hierarchy Process

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## Abstract

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## Introduction

### History

The Analytic hierarchy process is a multi-criteria decision making (MCDM) method (Ishizaka, 2009) utilized to analyse, solve and prioritize complex decision, by rating and comparing multiple criteria and scenarios against each other. It was Thomas Saaty, regarded as one of the pioneers of Operations research which developed the Analytic Hierarchy Process throughout the 1970s.

### The objective of the method

The Analytic Hierarchy Method compares criteria, or alternatives with respect to a criterion in a pairwise manner (Forman, Exposition). Each criteria and alternative is rated, based on a predetermined scale which has shown to capture individual preferences with respect to quantitative and qualitative attributes (Saaty 1980, 1994, “from Forman”). The Analytic Hierarchy Method has been acknowledged for combining psychology and mathematics well in decision making (rewrite and find reference).

## Methodology

### A step-by-step approach

When applying the Analytic Hierarchy Process to a multi-criteria decision, there are some basic pre-defined steps that should be followed:

#### Define the Problem

The decision making should be driven by a stated problem. The problem should be well defined and the objectives of the problem should be broadened to consider all actors, objectives and possible outcomes (Vaidy&Kumar, p2). All criteria that influence the solution, the chosen outcome, are then to be identified.

#### Define the Problem Hierarchy

The factors which effect the final decision are then arranged in an hierarchic structure. This serves two purposes:

1. It helps to structure the problem and thereby understanding the complex relations between all considered factors.

2. It helps the decision maker to visually assess whether the issues stated in each level in the hierarchy are at the same level of importance and magnitude. This is important so factors can be considered accurately and of similar manner.

The hierarchy is sorted from the overarching goal at the top, to criteria and eventual sub-criteria, and then lastly the possible alternatives that are to be considered. (saaty, 2002)