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Weighted Sum Method – Multi Criteria Decision Making

  • Difficulty Level : Expert
  • Last Updated : 24 Dec, 2021

Weighted Sum Method is a multi-criterion decision-making method in which there will be multiple alternatives and we have to determine the best alternative based on multiple criteria. There are other methods available including Weighted Product Method (WPM), Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), VIKOR, MOORA, GTMA etc. Let’s understand the Weighted Sum Method works with an example. 

Consider a case where we have to select the best candidate among 5 candidates who are appearing for an interview. Table 1 consists of the details of 5 students which includes their CGPA, the salary that they are expecting per month, their scores in the technical exam and the grades achieved by them in the aptitude test. 

Table 1: Sample Data Set
 

AttributeCGPAExpected StipendTechnical Exam ScoreAptitude Test Grade
Student 191200072B1
Student 27.6850068B1
Student 38.2950063B2
Student 48.51000070A2
Student 59.31400072A2

Consider the weights assumed by the interviewing panel as follows : 
CGPA = 30%, Expected Stipend = 20%, Technical Exam Score = 25%, Aptitude Test Grade = 25% 

Table 2: The weights of each attribute 
 



AttributeCGPAExpected StipendTechnical Exam ScoreAptitude Test Grade
Weight0.30.20.250.25
Student 191200072B1
Student 27.6850068B1
Student 38.2950063B2
Student 48.51000070A2
Student 59.31400072A2

Beneficial attribute is one in which person desires maximum values. Here, CGPA, the technical exam score and aptitude test scores are beneficial attributes as company expects the students to have more of these attributes. 
Non-beneficial attribute is one in which minimum values are desired. In this case the expected stipend is a non-beneficial attribute. Company hikes people who are willing to work more with low stipend. 

Now let’s see which student is to be selected by the company by using Weighted Sum Method. 
For this, we must normalize the values in Table 2. 
 

  1. For beneficial attributes, X=x/xmax
  2. For non-beneficial attributes, X=xmin/x

Table 3: Deciding the maximum value for a beneficial attribute and minimum value for non- beneficial attribute 
 

AttributeCGPAExpected StipendTechnical Exam ScoreAptitude Test Grade
Weight0.30.20.250.25
Student 191200072(max)B1
Student 27.68500(min)68B1
Student 38.2950063B2
Student 48.51000070A2(max)
Student 59.3(max)1400072A2

We will consider the following points for the grade system 
A1 – 5 
A2 – 4 
B1 – 3 
B2 – 2 
C1 – 1 
Table 4: Updating the aptitude test grades 

AttributeCGPAExpected StipendTechnical Exam ScoreAptitude Test Grade
Weight0.30.20.250.25
Student 191200072(max)3
Student 27.68500(min)683
Student 38.29500632
Student 48.510000704(max)
Student 59.3(max)14000724

Normalize the values for the respective attribute depending on the beneficial and non-beneficial attribute. 
Table 5: Normalization 

AttributeCGPAExpected StipendTechnical Exam ScoreAptitude Test Grade
Weight0.30.20.250.25
Student 19/9.38500/1200072/723/4
Student 27.6/9.38500/850068/723/4
Student 38.2/9.38500/950063/722/4
Student 48.5/9.38500/1000070/724/4
Student 59.3/9.38500/1400072/724/4

Table 6: The Weight- Normalized decision matrix

AttributeCGPAExpected StipendTechnical Exam ScoreAptitude Test Grade
Weight0.30.20.250.25
Student 10.96770.708310.75
Student 20.817210.94440.75
Student 30.88170.89470.8750.5
Student 40.91340.850.97221
Student 510.607111

Table 7: Multiplying each parameter with the respective weights 

AttributeCGPAExpected StipendTechnical Exam ScoreAptitude Test Grade
Weight0.30.20.250.25
Student 10.9677 × 0.30.7083 × 0.21 × 0.250.75 × 0.25
Student 20.8172 × 0.31 × 0.20.9444 × 0.250.75 × 0.25
Student 30.8817 × 0.30.8947 × 0.20.875 × 0.250.5 × 0.25
Student 40.9134 × 0.30.85 × 0.20.9722 × 0.251 × 0.25
Student 51 × 0.30.6071 × 0.21 × 0.251 × 0.25

The above table is simplified as follows 
Table 8: Simplified version of table 7 

AttributeCGPAExpected StipendTechnical Exam ScoreAptitude Test Grade
Weight0.30.20.250.25
Student 10.290310.141660.250.1875
Student 20.245160.20.23610.1875
Student 30.264510.178940.218750.125
Student 40.274020.170.243050.25
Student 50.30.121420.250.25

We must add the components in each row and calculate the weighted sum which is the performance score and give the priorities to the students 
Table 9: Calculation of rank of ranks of student by performance score 

AttributeCGPAExpected StipendTechnical Exam ScoreAptitude Test GradePerformance ScoreRank
Weight0.30.20.250.25  
Student 10.290310.141660.250.18750.869473
Student 20.245160.20.23610.18750.868764
Student 30.264510.178940.218750.1250.78725
Student 40.274020.170.243050.250.937071
Student 50.30.121420.250.250.921422

Conclusion : From the Weighted Sum Method, it is decided that Student 4 is the best choice among others.




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