HSC Commerce 12th Board ExamMaharashtra State Board
Share
Notifications

View all notifications

# 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. - HSC Commerce 12th Board Exam - Mathematics and Statistics

Login
Create free account

Forgot password?

#### Question

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

Is there an error in this question or solution?

#### APPEARS IN

2014-2015 (March) (with solutions)
Question 5.1.1 | 3.00 marks
Solution 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. Concept: Sequencing in Management Mathematics.
S