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# AHP Online System - AHP-OS

## Multi-criteria Decision Making Using the Analytic Hierarchy Process

This free web based AHP solution is a supporting tool for decision making processes. The programs can be helpful in your daily work for simple decision problems and also support complex decision making problems. Participate in a group session and try a practical example. Download the quick reference guide or the AHP-OS manual. For full functionality you need to login. Please register as new user, if you don't have an account yet. It's all free!

``` Goepel, K.D. (2018). Implementation of an Online Software Tool for the Analytic Hierarchy Process (AHP-OS). International Journal of the Analytic Hierarchy Process, Vol. 10 Issue 3 2018, pp 469-487, https://doi.org/10.13033/ijahp.v10i3.590 ```

### Introduction

AHP stands for Analytic Hierarchy Process. It is a method to support multi-criteria decision making, and was originally developed by Prof. Thomas L. Saaty. AHP derives ratio scales from paired comparisons of criteria, and allows for some small inconsistencies in judgments. Inputs can be actual measurements, but also subjective opinions. As a result, priorities (weightings) and a consistency ratio will be calculated. Internationally AHP is used in a wide range of applications, for example for the evaluation of suppliers, in project management, in the hiring process or the evaluation of company performance.

### Benefits of AHP

Using AHP as a supporting tool for decision making will help to gain a better insight in complex decision problems. As you need to structure the problem as a hierarchy, it forces you to think through the problem, consider possible decision criteria and select the most significant criteria with respect to the decision objective. Using pairwise comparisons helps to discover and correct logical inconsistencies. The method also allows to "translate" subjective opinions, such as preferences or feelings, into measurable numeric relations. AHP helps to makes decisions in a more rational way and to make them more transparent and better understandable.

### Method

Mathematically the method is based on the solution of an Eigen value problem. The results of the pair-wise comparisons are arranged in a matrix. The first (dominant) normalized right Eigen vector of the matrix gives the ratio scale (weighting), the Eigen value determines the consistency ratio.

### AHP Examples

In order to make the method easier to understand, and to show the wide range of possible applications, we give some examples for different decision hierarchies.

A simple introduction to the method is given here.