The weighted product method (WPM) is a multi-criteria decision-making approach that determines the ranking of alternatives based on the multiplication of their normalized performance values and the relative weights of criteria. For instance, in choosing a car, factors like cost and speed are considered, with cost being a non-preferred criterion. The method allows for a systematic comparison and ranking of alternatives, illustrated through a car selection example where Mercedes-Benz, Jaguar, and Toyota were evaluated.

1. Weighted Product Method
Dr. Mrinmoy Majumder
Course Name : Intro to Multi Criteria Decision Making Methods
Lecture No.08 out of 15
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2. What is Weighted Product Method
• In decision making problems, the Weighted Product Model or Method(WPM) is an
attempt to one alternative out ranking the other alternative.(Bridgman,1922)
• It is similar to the weighted sum model (WSM). The main difference is that instead of
addition in the main mathematical operation now there is multiplication
wj denotes the relative weight of importance of the criterion Cj and aij is the performance value of alternative Ai when
it is evaluated in terms of criterion Cj. Then, if one wishes to compare the two alternatives AK and AL (where m ≥ K, L ≥ 1)
then, the following product has to be calculated:[
Reference : Bridgman, P.W. (1922). Dimensional Analysis. New Haven, CT, U.S.A.: Yale University Press.

3. How it
Works ?

4. Example of
ANP
Decision Goal : To buy a car
Criteria : Cost and Speed
Alternatives : Mercedes Benz(M),
Jaguar(J), Toyota(T)
Aggregation Methods to be used :
Weighted Product Method

5. Example
Contd.
• If importance of Cost is more compared to the importance of Speed with respect to the
goal of the decision making, i.e., buying a car. The value of alternatives with respect to cost
and speed was normalized(value/sum of all values).Here Cost is a non-preferred criteria as
more the cost of the alternative less will it be preferred choice of selection
Goal :
Buy a
car
Cost
(Relative
Weight :
0.667)
Speed
(Relative
Weight :
0.333)
Sum of the product
function of Relative
Weight of Criteria and
the value of the
alternative for that
criteria
A (WSM
Score)
Rank based on
importance
M 0.500 0.200
(0.5/0.3)^0.667x(0.2/0.5)
^0.333 1.036 2
J 0.300 0.500
(0.3/0.2)^0.667x(0.5/0.3)
^0.333 1.554 1
T 0.200 0.300
(0.2/0.5)^0.667x(0.3/0.2)
^0.333 0.621 3