Weighted Sum Method – Multi Criteria Decision Making

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

Attribute CGPA Expected Stipend Technical Exam Score Aptitude Test Grade
Student 1 9 12000 72 B1
Student 2 7.6 8500 68 B1
Student 3 8.2 9500 63 B2
Student 4 8.5 10000 70 A2
Student 5 9.3 14000 72 A2

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

Table 2: The weights of each attribute



Attribute CGPA Expected Stipend Technical Exam Score Aptitude Test Grade
Weight 0.3 0.2 0.25 0.25
Student 1 9 12000 72 B1
Student 2 7.6 8500 68 B1
Student 3 8.2 9500 63 B2
Student 4 8.5 10000 70 A2
Student 5 9.3 14000 72 A2

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

Attribute CGPA Expected Stipend Technical Exam Score Aptitude Test Grade
Weight 0.3 0.2 0.25 0.25
Student 1 9 12000 72(max) B1
Student 2 7.6 8500(min) 68 B1
Student 3 8.2 9500 63 B2
Student 4 8.5 10000 70 A2(max)
Student 5 9.3(max) 14000 72 A2

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

Attribute CGPA Expected Stipend Technical Exam Score Aptitude Test Grade
Weight 0.3 0.2 0.25 0.25
Student 1 9 12000 72(max) 3
Student 2 7.6 8500(min) 68 3
Student 3 8.2 9500 63 2
Student 4 8.5 10000 70 4(max)
Student 5 9.3(max) 14000 72 4

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

Attribute CGPA Expected Stipend Technical Exam Score Aptitude Test Grade
Weight 0.3 0.2 0.25 0.25
Student 1 9/9.3 8500/12000 72/72 3/4
Student 2 7.6/9.3 8500/8500 68/72 3/4
Student 3 8.2/9.3 8500/9500 63/72 2/4
Student 4 8.5/9.3 8500/10000 70/72 4/4
Student 5 9.3/9.3 8500/14000 72/72 4/4

Table 6: The Weight- Normalized decision matrix

Attribute CGPA Expected Stipend Technical Exam Score Aptitude Test Grade
Weight 0.3 0.2 0.25 0.25
Student 1 0.9677 0.7083 1 0.75
Student 2 0.8172 1 0.9444 0.75
Student 3 0.8817 0.8947 0.875 0.5
Student 4 0.9134 0.85 0.9722 1
Student 5 1 0.6071 1 1

Table 7: Multiplying each parameter with the respective weights

Attribute CGPA Expected Stipend Technical Exam Score Aptitude Test Grade
Weight 0.3 0.2 0.25 0.25
Student 1 0.9677 × 0.3 0.7083 × 0.2 1 × 0.25 0.75 × 0.25
Student 2 0.8172 × 0.3 1 × 0.2 0.9444 × 0.25 0.75 × 0.25
Student 3 0.8817 × 0.3 0.8947 × 0.2 0.875 × 0.25 0.5 × 0.25
Student 4 0.9134 × 0.3 0.85 × 0.2 0.9722 × 0.25 1 × 0.25
Student 5 1 × 0.3 0.6071 × 0.2 1 × 0.25 1 × 0.25

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

Attribute CGPA Expected Stipend Technical Exam Score Aptitude Test Grade
Weight 0.3 0.2 0.25 0.25
Student 1 0.29031 0.14166 0.25 0.1875
Student 2 0.24516 0.2 0.2361 0.1875
Student 3 0.26451 0.17894 0.21875 0.125
Student 4 0.27402 0.17 0.24305 0.25
Student 5 0.3 0.12142 0.25 0.25

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

Attribute CGPA Expected Stipend Technical Exam Score Aptitude Test Grade Performance Score Rank
Weight 0.3 0.2 0.25 0.25
Student 1 0.29031 0.14166 0.25 0.1875 0.86947 3
Student 2 0.24516 0.2 0.2361 0.1875 0.86876 4
Student 3 0.26451 0.17894 0.21875 0.125 0.7872 5
Student 4 0.27402 0.17 0.24305 0.25 0.93707 1
Student 5 0.3 0.12142 0.25 0.25 0.92142 2

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

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