# 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

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

#### 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
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2014-2015 (March)

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