This is a worked-through example showing the use of the analytic hierarchy process (AHP) in a practical decision situation.
In AHP, values like price, weight, or area, or even subjective opinions such as feelings, preferences, or satisfaction, can be translated into measurable numeric relations.
It involves factors from the tangible and precisely measurable (purchase price, passenger capacity, cargo capacity), through the tangible but difficult to measure (maintenance costs, fuel costs, resale value) to the intangible and totally subjective (style).
If there are published safety ratings, for example, or manufacturer's specs for cargo capacity, they should be gathered as part of the process.
Also note that the structure of the vehicle-buying hierarchy might be different for other families (ones who don't limit themselves to Hondas, or who care nothing about style, or who drive less than 5,000 miles (8,000 km) a year, etc.).
It would definitely be different for a 25-year-old playboy who doesn't care how much his cars cost, knows he will never wreck one, and is intensely interested in speed, handling, and the numerous aspects of style.
When the pairwise comparisons are as numerous as those in our example, specialized AHP software can help in making them quickly and efficiently.
But on the other hand, the family has a limited amount of money to spend, no member has ever had a major accident, and Hondas are known as very safe cars.
In spite of the difficulty in comparing money to potential injury or death, the Jones family needs to determine its judgment about cost vs. safety in the car they are about to buy.
In this case the judgments showed acceptable consistency, and the software used the family's inputs to assign these new priorities to the criteria: You can duplicate this analysis at this online demonstration site; use the Line by Line Method by clicking its button, and don't forget to enter a negative number if the Criterion on the left is less important than the one on the right.
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.
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.
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.
The global priorities show how much the Safety of each model contributes to the overall goal of choosing the best car for the Jones family.
The global priorities show how much the passenger capacity of each model contributes to the overall goal of choosing the best car for the Jones family.
After careful consideration, the Jones family believes that no matter which car they buy, they will drive it the same number of miles per year.
The global priorities show how much the fuel cost of each model contributes to the overall goal of choosing the best car for the Jones family.
These estimated "residual values" are used for leasing, and are typically based on a limit of 12,000 miles (19,000 km) driven per year.
After some thought and discussion, they decide that, when comparing residual values, they want to look at the higher one as a percentage of the lower, and assign their intensities on that basis.
The global priorities show how much the resale value of each model contributes to the overall goal of choosing the best car for the Jones family.
The Jones family researched maintenance costs for the cars under consideration, but they didn't find any hard figures.
The global priorities show how much the maintenance cost of each model contributes to the overall goal of choosing the best car for the Jones family.
It also has videos, commercials, rotatable 360° views, color chips, and more, all available to help family members evaluate the Style of each car.
The family can compare their alternatives two-by-two on Style, using the tools on the web site to help them make their judgments.
The global priorities show how much the Style of each model contributes to the overall goal of choosing the best car for the Jones family.
The Cargo Capacity of each alternative, measured in cubic feet, is listed in the manufacturer's specifications for each vehicle.
The Joneses don't really know how it is calculated, but they trust that it's a good indication of how much cargo can be packed into a vehicle.
The global priorities show how much the cargo capacity of each model contributes to the overall goal of choosing the best car for the Jones family.
Each alternative has a global priority corresponding to its "fit" to all the family's judgments about all those aspects of Cost, Safety, Style and Capacity.
The Analytic Hierarchy Process has shown the Joneses that the Odyssey Minivan best satisfies all their criteria and judgments, followed closely by the Accord Sedan.
AHP hierarchy for the car buying decision
. The goal is green, the criteria and subcriteria are yellow, and the alternatives are pink. All the alternatives (three different models of Honda) are shown below the lowest level of each criterion. Later in the process, each alternative (each model) will be rated with respect to the criterion or subcriterion directly above it.
Alternatives for the car buying decision
. To save space in the diagrams, we have represented them as stacks of papers.
AHP hierarchy for the Jones family car buying decision
. Can you see the six possible comparisons in the Criteria row?
Alternatives for the Jones family car buying decision
. These six models are pairwise compared with each of the covering criteria. First do them with respect to purchase price, then with respect to fuel costs, and so on until the end, with passenger capacity.
Judgments made by the Jones family and entered into the AHP software
. Throughout this article, the family's judgments are shown with a green background. The orange and yellow colors show which alternative predominates.
AHP hierarchy for the Jones family car buying decision.
The Criteria have been pairwise compared, and their new priorities are shown. (Before the comparisons, each Criterion had a default priority of 0.250.) Note that the priorities still total 1.000, and the priorities for the subcriteria have not changed. The family has said that Cost is quite important to them, Style is relatively unimportant, and Safety and Capacity are each roughly half as important as Cost, with Safety having a slight edge over Capacity. Family members can look at these priorities and see how they feel about them. If they are uncomfortable about something, they can redo their pairwise comparisons.
AHP hierarchy for the Jones family car buying decision, showing LOCAL priorities.
The items in each group of Subcriteria have been pairwise compared, and their resulting priorities are shown. The priorities in each group total 1.000. These are called
local priorities
.
AHP hierarchy for the Jones family car buying decision, showing GLOBAL priorities.
The priority of the Goal is 1.000, as always. The global priorities shown in red for the Criteria and Subcriteria also add up to 1.000. Each item with a red global priority contributes that amount to the priority of the Goal.
The Jones Family's alternatives
, with purchase prices.
The Jones family's purchase price worksheet
.
Purchase price judgments entered by the Jones family
, with the rationale for their choices. From the Fundamental Scale,
1
expresses that A and B are equally preferred,
3
that A is moderately preferred to B,
5
that A is strongly preferred,
7
that A is very strongly preferred, and
9
that A is extremely preferred to B. Intensities 2, 4, 6, and 8 express intermediate values.
Safety data
to be evaluated by the Jones family. Curb Weight is from manufacturer's literature. Crash Ratings are from NHTSA and are given for various classes of vehicle. For each class, they include Frontal Impact, Driver's Side; Frontal Impact, Passenger's Side; Side Impact, Front Occupant; Side Impact, Rear Occupant; and Rollover Rating. Ratings are from one to five stars, with five stars being the best.
Safety judgments entered by the Jones family
, with the intensity and rationale for each. From the Fundamental Scale,
1
expresses that A and B are equally preferred,
3
that the better of the pair is moderately preferred to the worse,
5
that the better is strongly preferred,
7
that the better is very strongly preferred, and
9
that the better is extremely preferred to the worse. Intensities 2, 4, 6, and 8 express intermediate values.
Passenger Capacity
of the Jones family's alternatives.
Passenger Capacity judgments entered by the Jones family
. The rationale is that four passengers is barely enough, five is perfect for their needs, and eight is just a little bit better than five.
Fuel consumption figures
for the Jones family's alternatives.
Fuel Cost judgments entered by the Jones family
. Judgments are inversely proportional to the MPG ratings of the cars being compared.
The Jones rationale for comparing residual values
. It is based on the higher residual value as a percentage of the lower one.
Resale Value comparisons entered by the Jones family
. They are based on the rationale shown above.
Jones family worksheet for Maintenance Costs.
Plus signs indicate good maintenance history; the more plus signs, the lower the maintenance costs.
Maintenance Cost judgments entered by the Jones family
. From the Fundamental Scale,
1
means that A and B are equally preferred,
3
that A is moderately preferred, and
5
that A is strongly preferred. Intermediate numbers express intermediate preferences.
Style judgments entered by the Jones family
. The family looked at each pair of cars as shown in detail on a web site, decided which of the two they preferred, then entered the intensity of their preference according to the Fundamental Scale.
Cargo Capacity
of the Jones' alternatives.
Cargo Capacity judgments entered by the Jones family
. The rationale is that 14 cubic feet (0.40 m
3
) is totally satisfactory, five times that much (70 cu. ft.) is slightly better, and ten times that much (140 cu. ft.) is moderately better than 14.
Global priorities for the Jones family car buying decision
. Note that the priorities for each group of children total that of their parent.
