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For the following problem, find the sequence that minimizes total elapsed time (in hours) required to complete jobs on two machines M1 and M2 in the order M1-M2 Also find the minimum elapsed time T. - Mathematics and Statistics

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For the following problem, find the sequence that minimizes total elapsed time (in hours) required to complete jobs on two machines M1 and M2 in the order M1-M2 Also find the minimum elapsed time T.

Jobs

A

B

C

D

E

Machine M1

5

1

9

3

10

Machine M2

2

6

7

8

4

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Solution

 

Given :

Jobs

A

B

C

D

E

Machine M1

5

1

9

3

10

Machine M2

2

6

7

8

4

finding the optimal sequence :

The minimum processing time on two machines is 1 which correspond to task B on machine M1. This shows that task B will be preceding first. After assigning task B, we are left with 4 tasks on two machines

 

Jobs

A

C

D

E

Machine M1

5

9

3

10

Machine M2

2

7

8

4

 

B        

Minimum processing time in this reduced problem is 2 which correspond to job A on machine M2 therefore task A will be processed in the last.

B       A

The problem now reduces to following 3 tasks on two machines with processing time as follows:

Jobs

C

D

E

Machine M1

9

3

10

Machine M2

7

8

4

Minimum processing time in this reduced problem is 3 which correspond to job D on machine M1 therefore task D will be processed in the next to B.

B D     A

The problem now reduces to following 2 tasks on two machines with processing time as follows:

Jobs

C

E

Machine M1

9

10

Machine M2

7

4

Minimum processing time in this reduced problem is 4 which correspond to job E on machine Mtherefore task E will be processed in the next to last.

B D C E A

Further, it is also possible to calculate the minimum elapsed time corresponding to the optimal sequencing B→D→C→E→A

Job Sequence

Machine M1

Machine M2

 

Time In

Time Out

Time In

Time Out

B

0

1

1

7

D

1

4

7

15

C 4 13 15 22
E 13 23 23 27
A 23 28 28 30

 

Hence the total elapsed time for this proposed sequence  staring from job B to completion of job A is 30 hours .During this time machine M1 remains idle for 2 hours and the machine M2 remains idle for 3 hours

Minimum time elapse : 30 Hours

 

Concept: Sequencing in Management Mathematics
  Is there an error in this question or solution?

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