Weighted Product Method : A brief introduction

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A simple introduction about the Weight Product Method with an example.After going through this tutorial you can apply this method in simple decision making.

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Weighted Product Method
Dr. Mrinmoy Majumder
Course Name : Intro to Multi Criteria Decision Making Methods
Lecture No.08 out of 15
https://opticlasses.teachable.com
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http://www.energyinstyle.website

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.

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

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

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Weighted Product Method : A brief introduction

1. Weighted Product Method Dr. Mrinmoy Majumder Course Name : Intro to Multi Criteria Decision Making Methods Lecture No.08 out of 15 https://opticlasses.teachable.com Follow me on : RG : Mrinmoy Majumder Twitter : kuttu80 Founding Honorary Editor http://www.baipatra.ws http://www.energyinstyle.website

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

Weighted Product Method : A brief introduction

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