The Analytic Hierarchy Process (AHP) is a mathematical theory for measurement and decision making that was developed by Dr. Thomas L. Saaty during the mid-1970's when he was teaching at the Wharton Business School of the University of Pennsylvania. Applications of the Analytic Hierarchy Process can be classified into two major categories: (1) Choice -- the evaluation or prioritization of alternative courses of action, and (2) Forecasting -- the evaluation of alternative future outcomes. “AHP” Analytic Hierarchy Process A Structured Judgmental Forecasting Method

AHP Steps to a Decision/Forecast

Setting the Framework: Goals, Criteria, & Alternatives

Linear Hierarchy component, cluster (Level) element A loop indicates that each element depends only on itself. Goal Subcriteria Criteria Alternatives

Feedback Network with components having Inner and Outer Dependence among Their Elements C4C4 C1C1 C2C2 C3C3 Feedback Loop in a component indicates inner dependence of the elements in that component with respect to a common property. Arc from component C 4 to C 2 indicates the outer dependence of the elements in C 2 on the elements in C 4 with respect to a common property.

Sample Hierarchy/Network Structures for Modeling

Side Note: The Use of the Flow Chart is a Very Useful Device to Conceptualize Your Modeling and Forecasting Problem.

Consider a Simple Hierarchy Example

Six Types of Scales Nominal Positional Ordinal Arbitrary Relative or Ratio Absolute

Nominal Scale Nominal scales are primarily intended for identification or coding purposes. For example, a list of employee numbers or social security numbers.

Positional Scale Positional scales are a refinement of the nominal scale whereby it provides locational or positional information without necessarily implying ordering. Examples include: home addresses, geographic positions (latitude or longitude), altitude, musical scale.

Ordinal Scale Ordinal scales are a way of classifying (for example: hot, warm, tepid, cool, cold) and imply a magnitude of measurement.

Arbitrary Scale Arbitrary scales are a way of classifying responses (for example: 1, 2, 3, 4, 5 -- which is known as unipolar or a bipolar version, for example: -3, -2, -1, 0, 1, 2, 3) and imply a degree of strength. It can also take the form of a survey response, where say, strongly agree (=5), agree (=4), etc.

Relative or Ratio Scale Relative or ratio scales have uniform interval but with no absolute zero. The zero point is arbitrary (say, distance from the office or home). The Saaty pairwise rankings is a form of this scale.

Absolute Scale Absolute scales has uniform intervals and an absolute zero. (For example, money in a bank account.) This can be used in the AHP model.

Absolute Scale

Relative Scale

20 Pairwise Comparisons Size Apple AApple BApple C Size Comparison Apple A Apple B Apple C Apple A /10 A Apple B 1/2 1 33/10 B Apple C 1/6 1/3 11/10 C When the judgments are consistent, as they are here, any normalized column gives the priorities. Also, the judgments can be obtained by forming the appropriate ratios from the priority vector. That is not true if the judgments are inconsistent. Resulting Priority Eigenvector Relative Size of Apple

For example, in comparing option 1 to option 2 you might assign a ranking of 5 for option 1 relative to option 2. By transitivity, option 2 is assigned a ranking of [1/5 = 0.20] relative to option 1.