sequencing
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TRANSCRIPT
Sequencing
Pavan KarvaRashmi Navaghane
PROBLEM 1
There are six job which must go through two machine A and B in the order A-B. Processing time (in hours) is given here:
Determine the optimum sequence and the total elapsed time?
Job
1 2 3 4 5 6
Machine A
8 10 11 12 16 20
Machine B
7
15 10 14 13 9
Solution
Given
Sequence
MACHINE A MACHINE B
Job
1 2 3 4 5 6
Machine A
8 10 11 12 16 20
Machine B
7
15 10 14 13 9
Job 2 16543
Continue…
Total Elapsed time
Total Elapsed time=85hrs
Machine A Machine B
Sequence
Start time
Add Time taken
End time
Start time
Add Time taken
End time
2 0 + 10 10 10 + 15 25
3 10 + 11 21 25 + 10 35
4 21 + 12 33 35 + 14 49
5 33 + 16 49 49 + 13 62
6 49 + 20 69 69 + 9 78
1 69 + 8 77 78 + 7 85
Total Time
77 68
Continue…
Idle Time for M/c A=
Total Elapsed Time- Total time of M/c A
85-77=8 hrs.
Idle Time for M/c B=
Total Elapsed Time- Total time of M/c B
85-68=17 hrs.
PROBLEM 2
There are five jobs, each of which must go through machines A, B and C in the order ABC. Processing time (in hours) are given below:
Determine the optimal processing sequence and total elapsed time?
Job 1 2 3 4 5
Machine A 10 11 8 7 6
Machine B 6 4 5 3 2
Machine C 9 5 4 6 8
Solution
Given
Step 1- 1st we have to convert this problem into two machine
problem. For that we have to check following condition: Min A or Min C >= Max B here Min A=6, Min C=4, Max B=6. therefore 6=6 Min A=Max B
Job 1 2 3 4 5
Machine A 10 11 8 7 6
Machine B 6 4 5 3 2
Machine C 9 5 4 6 8
Continue….
Consolidation or Conversion Table
New job timing According to Consolidation Table
Job New M/c 1 New M/c 2
P(A+B) New time P(B+C) New time
1 10+6= 16 6+9= 15
2 11+4= 15 4+5= 9
3 8+5= 13 5+4= 9
4 7+3= 10 3+6= 9
5 6+2= 8 2+8= 10
Job 1 2 3 4 5
New M/c 1 16 15 13 10 8
New M/c 2 15 9 9 9 10
Continue…..
Sequencing According to consolidation Table:
Consolidated table:
Job sequence:
Job 1 2 3 4 5
New M/c 1 16 15 13 10 8
New M/c 2 15 9 9 9 10
Job 3 4215
Other Possible Sequences
Job 5 4 1 2 3
Job 5 4 1 3 2
Continue…
Total Elapsed timeMachine A Machine B Machine C
Sequence
Start time
Total time
End time
Start time
Total time
End time
Start time
Total time
End Time
5 0 6 6 6 2 8 8 8 16
3 6 8 14 14 5 19 19 4 23
1 14 10 24 24 6 30 30 9 39
2 24 11 35 35 4 39 39 5 44
4 35 7 42 42 3 45 45 6 51
TOTAL TIME
42 20 29
Continue…
Idle Time for M/c A=
Total Elapsed Time- Total time of M/c A
51-42=9 hrs.
Idle Time for M/c B= Total Elapsed Time- Total time of M/c B
51-20=31hrs.
Idle Time for M/c C=
Total Elapsed Time- Total time of M/c B
51-29=22hrs.
Total Elapsed time=51 hrs
PROBLEM 3
There are 4 job ABCD are required to be processed on four machine M1, M2, M3, M4 in that order. Determine optimal sequence and total elapsed time.
Job M1 M2 M3 M4
A 13 8 7 14
B 12 6 8 19
C 9 7 5 15
D 8 5 6 15
MACHINES
Continue…
Given
Step 1- 1st we have to convert this problem into two machine problem. For that we have to check following condition:
Min M1 or Min M4 >= Max M2 or Max M3 here Min M1=8, Min M4=14, Max M2=7, Max M3=8. therefore 8=8 Min M1=Max M3
Job M1 M2 M3 M4
A 13 8 7 14
B 12 6 8 19
C 9 7 5 15
D 8 5 6 15
Continue…
Consolidation or Conversion Table
New job timing According to Consolidation Table
JOB MACHINES 5 MACHINES 6
P(M1+M2+M3) NEW TIME P(M2+M3+M4) NEW TIME
A 13+8+7 28 8+7+14 29
B 12+6+8 26 6+8+19 33
C 9+7+5 21 7+5+15 27
D 8+5+6 19 5+6+15 26
Job A B C D
New M/c 5 28 26 21 19
New M/c 6 29 33 27 26
Continue…
Sequencing According to consolidation Table:
Consolidated table:
Job sequence:
Job A B C D
New M/c 5 28 26 21 19
New M/c 6 29 33 27 26
CABDJOB
Elapsed time calculation
START TIME – ST,TIME TAKEN –TT,END TIME -ET
Machine 1 Machine 2 Machine 3 Machine 4
S.Q ST TT ET ST TT ET ST TT ET ST TT ET
D 0 8 8 8 5 13 13 6 19 19 15 34
B 8 12 20 20 6 26 26 8 34 34 19 53
A 20 13 33 33 8 41 41 7 48 53 14 67
C 33 9 42 42 7 49 49 5 54 67 15 82
T.T 49 26 26 63
Continue…
Total Elapsed time= 82 hrs
Idle Time for M/c 1=
Total Elapsed Time- Total time of M/c 1
82-42= 40hrs.
Idle Time for M/c 2=
Total Elapsed Time- Total time of M/c 2
82-26= 56hrs.
Idle Time for M/c 3=
Total Elapsed Time- Total time of M/c 3
82-26= 56hrs.
Idle Time for M/c 4=
Total Elapsed Time- Total time of M/c 4
82-63=19hrs.
Thank You