Question

Three jobs are to be assigned to three machines. Cost for each job-machine combination appears in...

Three jobs are to be assigned to three machines. Cost for each job-machine combination appears in the table below. Perform the assignment method. What is the optimal assignment?

Machine A

Machine B

Machine C

Job 1

11

14

6

Job 2

8

10

11

Job 3

9

12

7
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Answer #1

Machine A

Machine B

Machine C

Job 1

11

14

6

Job 2

8

10

11

Job 3

9

12

7

Column reduction=

Machine A

Machine B

Machine C

Job 1

11-8

14-10

6-6

Job 2

8-8

10-10

11-11

Job 3

9-8

12-112

7-7

Machine A

Machine B

Machine C

Job 1

3

4

0

Job 2

0

0

5

Job 3

1

2

1

Row Reduction=

Machine A

Machine B

Machine C

Job 1

3-0

4-0

0-0

Job 2

0-0

0-0

5-0

Job 3

1-1

2-1

1-1

Machine A

Machine B

Machine C

Job 1

3

4

0

Job 2

0

0

5

Job 3

0

1

0

Job 1 will get assigned to Machine C

Job 3 will be assigned to Machine A

Job 2 will be assigned to Machine B

Total cost =6+10+9=25

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