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%, Aptitude 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, 
2. For non-beneficial attributes, 

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.