Weighted Product Method – Multi Criteria Decision Making

Weighted Product 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 the Weighted Sum Method (WSM), Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), VIKOR, MOORA, GTMA, etc. Let’s understand how the Weighted Product 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

Two types of attribute:

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

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

• For beneficial attributes,
• 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

To calculate the weighted product, we take the power of each component with the respective weights as follows Table 7: Calculation of powers of attributes

Attribute	CGPA	Expected Stipend	Technical Exam Score	Aptitude Test Grade
Weight	0.3	0.2	0.25	0.25
Student 1	0.96770.3	0.70830.2	10.25	0.750.25
Student 2	0.81720.3	10.2	0.94440.25	0.750.25
Student 3	0.88170.3	0.89470.2	0.8750.25	0.50.25
Student 4	0.91340.3	0.850.2	0.97220.25	10.25
Student 5	10.3	0.60710.2	10.25	10.25

To calculate the weighted product, we will multiply the value of each attribute in every column row-wise. The value with the highest weighted product is given the higher rank. Table 8: Calculating the weighted product and finding the rank

Attribute	CGPA	Expected Stipend	Technical Exam Score	Aptitude Test Grade	Performance Score	Rank
Weight	0.3	0.2	0.25	0.25
Student 1	0.96770.3	0.70830.2	10.25	0.750.25	0.860064	4
Student 2	0.81720.3	10.2	0.94440.25	0.750.25	0.863481	3
Student 3	0.88170.3	0.89470.2	0.8750.25	0.50.25	0.765907	5
Student 4	0.91340.3	0.850.2	0.97220.25	10.25	0.935451	1
Student 5	10.3	0.60710.2	10.25	10.25	0.905007	2

You can refer the link below to understand the Weighted Sum Method here.