Analytic Hierarchy Process

A technique for organizing and analyzing complex multi-objective decisions

Analytic Hierarchy Process (AHP) is a simple technique, developed by Thomas L. Saaty in the 1970s, for organizing and analyzing complex multi-objective decisions. It combines both quantitative and qualitative analysis elements and it finds application in group decision making. The philosophy of the technique is to decompose problem into a hierarchy of more easily understood sub-problems, each of which can be analyzed independently. Once the hierarchy is built, the decision makers systematically evaluate its various elements by comparing them to one another two at a time, with respect to their impact on an element above them in the hierarchy. The AHP converts these evaluations to numerical values that can be processed and compared over the entire range of the problem. A numerical weight is derived for each element of the hierarchy, allowing diverse and often incommensurable elements to be compared to one another in a rational and consistent way. In the final step of the process, numerical weights are calculated for each of the decision alternatives. These weights represent the alternatives' relative ability to achieve the goal.

The function facilitates the following:

• Simple AHP implementation

• Multiple decision makers

• Analytic Network Process (ANP): The generalization of the AHP, which incorporates dependences and feedbacks between decision criteria and options.

• Fuzzy AHP and ANP: This are special versions of the simple AHP and ANP, which find application in fuzzy environments, where the relative importance of the decision criteria and the alternatives is uncertain.

• Simulation: A Monte-Carlo simulation-based approach of AHP and ANP, which allows to compare distributions of weights and performs sensitivity analysis.

• Cost-Benefit analysis: The benefit (AHP weights) in relationship with the cost of the respective option.

• Optimization: In case of a resource allocation problem, the function estimates the optimal feasible combination of alternatives subject to the resources’ constraints.

• Prediction combination: In case this is a forecasting combination problem, the function generates a weighted average forecast, using the combination weights and the individual forecasts as inputs.