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## Unbalanced Assignment Problems, Solved Assignment Problem

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

N < n i.e. 2 < 4

II Modified Matrix

N < n i.e. 3 < 4

III Modified Matrix

N = n

Zero assignment

Multiple assignments presents

Solution Table -I

Minimum cost = 18 + 13 + 19 = Rs 50

Solution Table -II

Minimum cost = 18 + 17 + 15 = Rs 50