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Weighted Sum Method
Dr. Mrinmoy Majumder
Course Name : Intro to Multi Criteria Decision Making Methods
Lecture No.09 out of 15
https://opticlasses.teachable.com
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Twitter : kuttu80
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What is Weighted Sum Method
• In decision making problems, the Weighted Sum Model or
Method(WSM) (Fishburn et.al.,1967) is the simplest known multi-
criteria decision making(MCDM) method for evaluating a number of
alternatives in terms of a number of decision criteria.
• Applicable only when all the data are in exactly the same unit.
Let wj describe the relative weight of significance of the criterion Cj and aij is the performance value or
normalized magnitude of alternative Ai when it is evaluated in terms of criterion Cj. Then, the total (i.e.,
when all the criteria are considered simultaneously) importance of alternative Ai, denoted as Ai
WSM-score
Reference : Fishburn, P.C. (1967). "Additive Utilities with Incomplete Product Set: Applications to Priorities
and Assignments". Operations Research Society of America (ORSA), Baltimore, MD, U.S.A.
How it
Works ?
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 Sum 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
(WSMScore)
Rank based on
importance
M 0.500 0.200 0.5x0.667+0.2x0.333 0.400 1
J 0.300 0.500 0.3x0.667+0.5x0.333
0.367 2
T 0.200 0.300 0.2x0.667+0.3x0.333
0.233 3

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Weighted Sum Method: An Introduction

  • 1. Weighted Sum Method Dr. Mrinmoy Majumder Course Name : Intro to Multi Criteria Decision Making Methods Lecture No.09 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 Sum Method • In decision making problems, the Weighted Sum Model or Method(WSM) (Fishburn et.al.,1967) is the simplest known multi- criteria decision making(MCDM) method for evaluating a number of alternatives in terms of a number of decision criteria. • Applicable only when all the data are in exactly the same unit. Let wj describe the relative weight of significance of the criterion Cj and aij is the performance value or normalized magnitude of alternative Ai when it is evaluated in terms of criterion Cj. Then, the total (i.e., when all the criteria are considered simultaneously) importance of alternative Ai, denoted as Ai WSM-score Reference : Fishburn, P.C. (1967). "Additive Utilities with Incomplete Product Set: Applications to Priorities and Assignments". Operations Research Society of America (ORSA), Baltimore, MD, U.S.A.
  • 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 Sum 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 (WSMScore) Rank based on importance M 0.500 0.200 0.5x0.667+0.2x0.333 0.400 1 J 0.300 0.500 0.3x0.667+0.5x0.333 0.367 2 T 0.200 0.300 0.2x0.667+0.3x0.333 0.233 3