Home > Operation Research calculators > Sequencing Problems example

Sequencing Problems example ( Enter your problem)
  1. Example-1
  2. Example-2
  3. Example-3
  4. Example-4
Other related methods
  1. Processing n Jobs Through 2 Machines Problem
  2. Processing n Jobs Through 3 Machines Problem
  3. Processing n Jobs Through m Machines Problem
  4. Processing 2 Jobs Through m Machines Problem

2. Example-2
(Previous example)
4. Example-4
(Next example)

3. Example-3





Find solution of Processing 7 Jobs Through 3 Machines Problem
Job1234567
Machine-13874987
Machine-24325143
Machine-3675115612


Solution:
Job1234567
Machine M_13874987
Machine M_24325143
Machine M_3675115612


Since any of condition min{T_(1j)} >= max{T_(ij)} and/or min{T_(mj)} >= max{T_(ij)}, for j=2,3,...,m-1 is satisfied.

So given problem can be converted to 2-machine problem.

Machine-G
71199101210

Machine-H
101071661015


1. The smallest processing time is 6 hour for job 5 on Machine-H. So job 5 will be processed last.
5

2. The next smallest processing time is 7 hour for job 1 on Machine-G. So job 1 will be processed first.
15

3. The next smallest processing time is 7 hour for job 3 on Machine-H. So job 3 will be processed before job 5.
135

4. The next smallest processing time is 9 hour for job 4 on Machine-G. So job 4 will be processed after job 1.
1435

5. The next smallest processing time is 10 hour for job 2,6 on Machine-H and for this jobs 11 is smallest on Machine-G. So job 2 will be processed before job 3.
14235

6. The next smallest processing time is 10 hour for job 6 on Machine-H. So job 6 will be processed before job 2.
146235

7. The next smallest processing time is 10 hour for job 7 on Machine-G. So job 7 will be processed after job 4.
1476235


According to Johanson's algorithm, the optimal sequence is as below
1476235


JobM_1
In time
M_1
Out time
M_2
In time
M_2
Out time
M_3
In time
M_3
Out time
Idle time
M_2
Idle time
M_3
100 + 3 = 333 + 4 = 777 + 6 = 1337
433 + 4 = 777 + 5 = 121313 + 11 = 24--
777 + 7 = 141414 + 3 = 172424 + 12 = 362-
61414 + 8 = 222222 + 4 = 263636 + 6 = 425-
22222 + 8 = 303030 + 3 = 334242 + 7 = 494-
33030 + 7 = 373737 + 2 = 394949 + 5 = 544-
53737 + 9 = 464646 + 1 = 475454 + 5 = 597-


The total minimum elapsed time = 59

Idle time for Machine-1
=59 - 46

=13


Idle time for Machine-2
=(3)+(14-12)+(22-17)+(30-26)+(37-33)+(46-39)+(59-47)

=3+2+5+4+4+7+12

=37


Idle time for Machine-3
=(7)+(59-59)

=7+0

=7


This material is intended as a summary. Use your textbook for detail explanation.
Any bug, improvement, feedback then Submit Here



2. Example-2
(Previous example)
4. Example-4
(Next example)





Share this solution or page with your friends.
 
 
Copyright © 2025. All rights reserved. Terms, Privacy
 
 

.