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Sequencing

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Sequencing

  1. 1. Sequencing Pavan Karva Rashmi Navaghane
  2. 2. PROBLEM 1 <ul><li>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: </li></ul><ul><li>Determine the optimum sequence and the total elapsed time? </li></ul>Job 1 2 3 4 5 6 Machine A 8 10 11 12 16 20 Machine B 7 15 10 14 13 9
  3. 3. Solution <ul><li>Given </li></ul><ul><li>Sequence </li></ul><ul><li>MACHINE A MACHINE B </li></ul>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. 4. Continue… <ul><li>Total Elapsed time </li></ul><ul><li>Total Elapsed time=85hrs </li></ul>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. 5. Continue… <ul><li>Idle Time for M/c A= </li></ul><ul><li>Total Elapsed Time- Total time of M/c A </li></ul><ul><li>85-77=8 hrs. </li></ul><ul><li>Idle Time for M/c B= </li></ul><ul><li>Total Elapsed Time- Total time of M/c B </li></ul><ul><li>85-68=17 hrs. </li></ul>
  6. 6. PROBLEM 2 <ul><li>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: </li></ul><ul><li>Determine the optimal processing sequence and total elapsed time? </li></ul>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. 7. Solution <ul><li>Given </li></ul><ul><li>Step 1- 1 st we have to convert this problem into two machine problem. For that we have to check following condition: </li></ul><ul><li>Min A or Min C >= Max B </li></ul><ul><li>here Min A=6, Min C=4, Max B=6. </li></ul><ul><li>therefore 6=6 </li></ul><ul><li>Min A=Max B </li></ul>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. 8. Continue…. <ul><li>Consolidation or Conversion Table </li></ul><ul><li>New job timing According to Consolidation Table </li></ul>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. 9. Continue….. <ul><li>Sequencing According to consolidation Table: </li></ul><ul><li>Consolidated table: </li></ul><ul><li>Job sequence: </li></ul>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. 10. Other Possible Sequences Job 5 4 1 2 3 Job 5 4 1 3 2
  11. 11. Continue… <ul><li>Total Elapsed time </li></ul>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. 12. Continue… <ul><li>Idle Time for M/c A= </li></ul><ul><li>Total Elapsed Time- Total time of M/c A </li></ul><ul><li>51-42=9 hrs. </li></ul><ul><li>Idle Time for M/c B= </li></ul><ul><li>Total Elapsed Time- Total time of M/c B </li></ul><ul><li>51-20=31hrs. </li></ul><ul><li>Idle Time for M/c C= </li></ul><ul><li>Total Elapsed Time- Total time of M/c B </li></ul><ul><li>51-29=22hrs. </li></ul><ul><li>Total Elapsed time=51 hrs </li></ul>
  13. 13. PROBLEM 3 <ul><li>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. </li></ul>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. 14. Continue… <ul><li>Given </li></ul><ul><li>Step 1- 1 st we have to convert this problem into two machine problem. For that we have to check following condition: </li></ul><ul><li>Min M1 or Min M4 >= Max M2 or Max M3 </li></ul><ul><li>here Min M1=8, Min M4=14, Max M2=7, Max M3=8. </li></ul><ul><li>therefore 8=8 </li></ul><ul><li>Min M1=Max M3 </li></ul>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. 15. Continue… <ul><li>Consolidation or Conversion Table </li></ul><ul><li>New job timing According to Consolidation Table </li></ul>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. 16. Continue… <ul><li>Sequencing According to consolidation Table: </li></ul><ul><li>Consolidated table: </li></ul><ul><li>Job sequence: </li></ul>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. 17. Elapsed time calculation <ul><li>START TIME – ST,TIME TAKEN –TT,END TIME -ET </li></ul>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. 18. Continue… <ul><li>Total Elapsed time= 82 hrs </li></ul><ul><li>Idle Time for M/c 1= </li></ul><ul><li>Total Elapsed Time- Total time of M/c 1 </li></ul><ul><li>82-42= 40hrs. </li></ul><ul><li>Idle Time for M/c 2= </li></ul><ul><li>Total Elapsed Time- Total time of M/c 2 </li></ul><ul><li>82-26= 56hrs. </li></ul><ul><li>Idle Time for M/c 3= </li></ul><ul><li>Total Elapsed Time- Total time of M/c 3 </li></ul><ul><li>82-26= 56hrs. </li></ul><ul><li>Idle Time for M/c 4= </li></ul><ul><li>Total Elapsed Time- Total time of M/c 4 </li></ul><ul><li>82-63=19hrs. </li></ul>
  19. 19. <ul><li>Thank You </li></ul>

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