Question: A Company wishes to assign 4 salesman to 4 districts. The volume of sales matrix is given below. Make the optimal assignment which results in maximum volume of sales.
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**Mumbai University > Mechanical Engineering > Sem 7 > Production planning and control

Marks: 10M

Year: May 2016**

 modified 2.7 years ago  • written 2.7 years ago by Juilee • 2.4k
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The above problem is of maximization type

To convert it into minimization

By applying Hungarian Method

1.

250 200 80 100
150 100 300 250
0 125 100 150
100 150 80 200

Applying row operation

2.

170 120 0 20
50 0 200 150
0 125 100 150
20 70 0 120

Applying Column operation and assignment

Priority from left to right and top to bottom

3.

170 120 0
50 0
0 125
20 70 100 130
100

No of assignment ≠ Size of Matrix

Therefore we change the priority of solutions taking Priority Right to Left and top to bottom

4.

170 120 0 0
50 0 300 130
0 125 100 130
20 70 100 130

Therefore Number of assignments = size of the Matrix

The given below solution is Optimal

3.

Salesman District Sales
1 D 400
2 B 400
3 A 500
4 C 420

Total Sales = 1720 Units