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.

- 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 |

**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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