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Weighted Product Method – Multi Criteria Decision Making

  • Difficulty Level : Medium
  • Last Updated : 03 Jun, 2020
Geek Week

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

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%, Aptitute 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

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,  X=x/xmax
  • 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

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

AttributeCGPAExpected StipendTechnical Exam ScoreAptitude Test Grade
Weight0.30.20.250.25
Student 10.96770.30.70830.210.250.750.25
Student 20.81720.310.20.94440.250.750.25
Student 30.88170.30.89470.20.8750.250.50.25
Student 40.91340.30.850.20.97220.2510.25
Student 510.30.60710.210.2510.25

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

AttributeCGPAExpected StipendTechnical Exam ScoreAptitude Test GradePerformance ScoreRank
Weight0.30.20.250.25
Student 10.96770.30.70830.210.250.750.250.8600644
Student 20.81720.310.20.94440.250.750.250.8634813
Student 30.88170.30.89470.20.8750.250.50.250.7659075
Student 40.91340.30.850.20.97220.2510.250.9354511
Student 510.30.60710.210.2510.250.9050072

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

Attention reader! Don’t stop learning now. Get hold of all the important Machine Learning Concepts with the Machine Learning Foundation Course at a student-friendly price and become industry ready.




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