User:Louis F. Sander/Sandbox

Sections

• Lead/Introduction
• Where it is used
• How it works
• Criticisms (keep it short and objective)

Notes

Aspects of AHP

• Math
• Psychological
• Computerized now, with gadgets
• Disciplined look at a decision (focus on objectives, alternatives, more than voting)
• Handles rational, intuitive, irrational, all at the same time
• Lets you compare the alternatives and fiddle with them, vs. just giving the best one

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and has been successfully applied to many complex planning, resource allocation, and priority setting problems

Good Stuff

Problems with high stakes, involving human perceptions and judgements, and whose resolutions have long-term repercussions, call for a rational approach to their solution. (Bhushan promo)

You might also want to read the paper "The Analytic Hierarchy Process - An Exposition," E.J. Forman and S. I. Gass, Operations Research, 49, 4, July-August, 2001, pp. 469-486. (Saul Gass, U of MD)

Drafts

Pairwise Comparisons

In AHP, we rank a group of items by comparing them to each other in pairs. If the group has more than three items or so, this is much easier than trying to rank all the items at once.

As we consider the pairs of items, we express the importance of (or our preference for, etc.) one item versus the other by assigning it a weight from -9 to +9. To facilitate the assignment of numbers, we can use a verbal scale ranging from "Much Less Important" to "Of Equal Importance," to "Much More Important."

When we have finished all the comparisons, AHP's mathematical algorithm looks at our work and assigns the appropriate numerical weight to each item in the group. The higher the number, the more important (or preferred, etc.) to us is the item to which it is assigned. For convenience, the numbers are normalized so their total is 100 (or, sometimes, 1). The processing also gives a numeric indicator of the consistency of our rankings. (If we greatly prefer apples to oranges, and greatly prefer oranges to persimmons, it would be inconsistent to say that we slightly prefer persimmons to apples.)

Example

To illustrate the power of this technique, imagine that we would like to know how important each of these is to us in a prospective spouse: Brains, Looks, Personality, and Wealth. If we compare the factors two by two, AHP can use our comparisons to assign a numerical weight to each of them.

You can try it on THIS WEB SITE from the Canadian Conservation Institute. Here's what to do after opening the site:

1. On the first screen, enter the number 4, to specify how many criteria you will be comparing.
2. Click Continue, then enter the names of the criteria: Brains, Looks, Personality, and Wealth. (To facilitate our discussion, enter them in this order. Other than for that purpose, the order doesn't matter.)
3. Scroll down and select the Line-by-Line Method to facilitate entering the data.
4. Click Continue and begin your pairwise comparisons. (Note the bar chart showing that right now, all the criteria have equal importance.)
5. For each of the six pairs of items, compare the first to the second by entering a number between -9 and 9. Use the verbal scale to help you choose each number. (Example: If Brains are a little less important than Looks, enter a -3 for this pair. If Brains are very much more important, enter a 9.)
6. Click Calculate to see the results of your comparisons. The higher the number assigned to each criterion, the more important it is to you.
7. The Consistency Ratio is a measurement of the consistency of the data you entered. The higher it is, the less consistent were your entries. If it is greater than 0.100 or so, you might want to review your entries to see if they really reflect your thinking. (Don't worry too much about inconsistencies unless they are quite large -- inconsistency is a part of human nature, and we are dealing fairly closely with human nature here.)

The web site allows for easy modification of your judgments, and it can be instructive to change them and see how the changes affect the outcome.

If you'd like to experiment even more, enter a new problem with only three criteria: Brains, Looks, and Personality (to facilitate our example, enter them in that order). Imagine that Looks and Personality are each moderately less important to you than Brains. Further, you have no preference for Looks vs. Personality. You can indicate this by entering 5, 5, and 1 for the pairwise comparisons. The results will show your preference for brains, and will be perfectly consistent. If you modify your entries to show different preferences, you'll be able to see how the modifications alter your results. (The web site allows you to change your preferences, but this feature "times out" after a few minutes.)

As the number of criteria increases, it is harder to "see" the relationships, but the technique is every bit as valid. Imagine how difficult it would be for you, without the aid of AHP, to handle the consideration of Brains, Looks, Personality, Wealth, Age, and Religion. Try it with AHP and see how much easier it becomes.