The document describes three problems involving determining the optimal sequence of jobs through multiple machines to minimize the total elapsed time. For the first problem involving two machines, the optimal sequence is job 2, 1, 6, 5, 4, 3 with a total elapsed time of 85 hours. The second problem involving three machines is converted to two virtual machines, and the optimal sequence is job 3, 4, 2, 1, 5 with a total elapsed time of 51 hours. The third problem involving four machines is also converted to two virtual machines, and the optimal sequence is job C, A, B, D with a total elapsed time of 82 hours.

1. Sequencing Pavan Karva Rashmi Navaghane

2. 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

3. 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 1 6 5 4 3

4. 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

5. 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.

6. 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

7. Solution Given Step 1- 1 st 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

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

9. 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 4 2 1 5

10. Other Possible Sequences Job 5 4 1 2 3 Job 5 4 1 3 2

11. Continue… Total Elapsed time Machine 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

12. 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

13. 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

14. Continue… Given Step 1- 1 st 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

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

16. 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 C A B D JOB

17. 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

18. 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.

19. Thank You