Weighted Sum Method: An Introduction
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The weighted sum method (WSM) is a multi-criteria decision-making technique used to evaluate alternatives based on various criteria, requiring all data to be in the same unit. This method assigns relative weights to each criterion and calculates a score for each alternative by aggregating these weighted values. An example illustrates its application in choosing a car, demonstrating how to prioritize cost and speed with normalized values.
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