Page 165 - DCOM303_DMGT504_OPERATION_RESEARCH

Operations Research

Notes Step 4: Hungarian approach is used.
Machines W X Y Z
Jobs A 0 6 10 14
B 0 5 9 10
C 0 5 9 12
D 0 0 0 0
L 1 L 2
Step 5:

Machines W X Y Z
Jobs A 0 1 5 9
B 0 0 4 5
C 0 0 4 7
D 5 0 0 0

Step 6: Trial assignment.
Machines W X Y Z
Jobs A 0 1 1 5
B 0 0 0 1
C 0 0 0 3
D 9 4 0 0

Step 7: Calculation of total minimum cost.
Jobs Machines Total cost (`)
A W 18
B X/Y 13/17
C Y/X 19/15
D Z 0
Minimum Time required
50

Inference
Therefore, the minimum cost associated with the assignment of 3 jobs to 4 machines is ` 50.

Example: Find the assignment of machines to jobs that will result in a maximum profit
and which is the job that should be declined from the following. The owner of a small machine
shop has 4 machines available to assign 2 jobs for the day, 5 jobs are offered with the expected
profit (`) per machinist on each job being as follows.

Job A B C D E
Machinist 1 6.20 7.80 5 10.10 8.20
2 7.10 8.40 6.10 7.30 5.90
3 8.70 9.20 11.10 7.10 8.10
4 4.80 6.40 8.70 7.70 8.00

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