page_title: Analytic hierarchy process – car example
section_title: Purchase price
hierarchical_section_title: Analytic hierarchy process – car example / Pairwise comparing the Alternatives with respect to the Criteria / Purchase price
caption_attribution_description: Part of a series of images to illustrate an article on the Analytic Hierarchy Process
context_page_description: This is a worked-through example showing the use of the analytic hierarchy process in a practical decision situation.
  See Analytic hierarchy process#Practical examples for context for this example.
context_section_description: The family has established a budget of $25,000 for buying the new car, but they are willing to consider alternatives whose price exceeds their budget. To refresh your mind, here are the six cars they are considering—in AHP terminology, the six alternatives—along with their purchase prices:  
  Knowing that they will have a lot of pairwise comparisons to make, the family prepared this worksheet to help them. It shows comparative information about the price and budget status of each pair of cars:
  Now, what do they do?
  First they might compare the purchase price of the Accord Sedan to that of the Accord Hybrid. If they stick purely to arithmetic, they could say that the Sedan is favored by 1.5, since the Hybrid's price is about 1.5 times that of the Sedan, and a lower price is better. They could follow that pattern through all 15 of the comparisons, and it would give a mathematically consistent set of comparisons.
  But merely entering the numbers wouldn't take into account things like the $25,000 budget, or the value to the family of saving, say, $5,000 vs. $1,000 on a purchase. Things like that can be highly important in making decisions, and their importance can vary greatly with the situation and the people involved. Some families might never want to exceed their budget. Others might be willing to exceed it by a few dollars or a few per cent, but very unwilling to go further. Still others might not care much if they spend double their budget on the car. Because the AHP allows decision-makers to enter their judgments about the data, rather than just the data themselves, it can deal with all these situations and more.
  Let's say that the Jones family is willing to exceed their budget by up to $1,000, but anything more is unacceptable. They "never say never," however—budget-busting cars will score as low as possible on the purchase price, but won't be removed from the list of alternatives. And for cars priced under budget, a $1,000 difference in price doesn't matter much to the Joneses, but a $5,000 difference is strongly important, and a $10,000 difference is extreme. They might enter the following intensities into the AHP software (throughout this example, the judgments of decision-makers are shaded in green):
  You can follow the family's thinking by looking at the rationale for each judgment. Whenever a car that is under budget is compared with one that is over budget by more than $1,000, the former is extremely preferred. For cars under budget, a $1,000 less expensive car is slightly preferred, a $5,000 one is strongly preferred, and a $6,000 one is even more strongly preferred. When both cars are well over budget (comparison #6), they are equally preferred, which is to say they are equally undesirable. Because budget status and absolute price difference are enough to make each comparison, the ratio of prices never enters into the judgments.
  When the judgments shown above are entered, the AHP software returns the following priorities for the six alternatives with respect to Purchase Price:
  The local priorities show how much the purchase price of each model contributes to the subcriterion of Purchase Price. The global priorities show how much the purchase price of each model contributes to the overall goal of choosing the best car for the Jones family.
caption: The Jones Family's alternatives, with purchase prices.
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