The Analytic Hierarchy Process (AHP) is a mathematical theory for measurement and decision making...

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 ProcessA Structured Judgmental Forecasting Method

“AHP”

Analytic Hierarchy ProcessA Structured Judgmental Forecasting Method

AHP Steps to a Decision/Forecast

Setting the Framework:Goals, Criteria, & Alternatives

F orecas t S cen ario 1

C rite rion 1

F orecas t S cen ario 2 F orecas t S cen ario 3

C rite rion 2

F orecas t S cen ario n

C rite rion n

G oa l

Linear Hierarchy

component,cluster(Level)

element

A loop indicates that eachelement depends only on itself.

Goal

Subcriteria

Criteria

Alternatives

Feedback Network with components having Inner and Outer Dependence among Their Elements

C4

C1

C2

C3

Feedback

Loop in a component indicates inner dependence of the elements in that component with respect to a

common property.

Arc from componentC4 to C2 indicates the

outer dependence of the elements in C2 on theelements in C4 with

respectto 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 ComparisonsSize

Apple A Apple B Apple C

SizeComparison

Apple A Apple B Apple C

Apple A 1 2 6 6/10 A

Apple B 1/2 1 3 3/10 B

Apple C 1/6 1/3 1 1/10 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.

ResultingPriority Eigenvector

Relative Sizeof 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.