Unbalanced Assignment Problems, Solved Assignment Problem

Unbalanced Assignment Problems

 If the number of columns and rows are not equivalent then such type of problems are known as unbalanced assignment problems.

Example 1

A company has 4 machines on which they need to perform 3 jobs. Each job can be allotted to one and only one machine. The cost of each job on each machine is provided in the following table

 

Machines

Jobs

 

W

X

Y

Z

A

18

24

28

32

B

8

13

17

19

C

10

15

19

22

Answer

18

24

28

32

8

13

17

19

10

15

19

22

0

0

0

0

 

Row Reduced matrix

0

6

10

14

0

5

9

11

0

5

9

12

0

0

0

0

 

I Modified Matrix

2034_Unbalanced_Assignment_Problems_1.png

 

N < n i.e. 2 < 4

 

II Modified Matrix

487_Unbalanced_Assignment_Problems_2.png

 

N < n i.e. 3 < 4

 

III Modified Matrix

406_Unbalanced_Assignment_Problems_3.png

 

N = n

 

Zero assignment

Multiple assignments presents

 

Solution Table -I

1544_Unbalanced_Assignment_Problems_4.png

Minimum cost = 18 + 13 + 19 = Rs 50

 

Solution Table -II

1724_Unbalanced_Assignment_Problems_5.png

Minimum cost = 18 + 17 + 15 = Rs 50