Maharashtra State BoardHSC Commerce 12th Board Exam
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Solve the Following Assignment Problem to Minimize the Cost: - Mathematics and Statistics

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Sum

Solve the following assignment problem to minimize the cost: 

Persons Jobs
I II III
A 7 3 5
B 2 7 4
C 6 5 3
D 3 4 7
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Solution

Number of columns ≠  Number of rows 

∴  Given problem is unbalanced 

Step 1:  For making it balanced, we add dummy job(iv) with cost zero

Step 2: Minimum elements of each row is subtracted from every element of that row. Resultant matrix is same.

Step 3: Minimum element in each column is subtracted from every element in that column.

Subordinates Jobs 

I II III IV
A 5 0 2 0
B 0 4 1 0
C 4 2 0 0
D 0 1 4 0

Zero element are covered with minimum number of straight lines: 

Subordinates Jobs 

I II III IV
A 5 0 2 0
B 0 4 1 0
C 4 2 0 0
D 0 1 4 0

Number of lines covering all zero is equal to number of rows/columns. The optimal solution has been reached. · Optimal assignment can be made as follows: 

Subordinates Jobs 

I II III IV
A 5 0 2 0
B 0 4 1 0
C 4 2 0 0
D 1 1 4 0

∴ Optimal assignment is obtained.

Subordinates Jobs Effectiveness
A II 3
B I 2
C III 3
D IV 0

The total (minimum) effectlveness = 3 + 2 + 3 + 0 = 8. 

Concept: Maxima and Minima
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