# sol6 - Homework#6 solutions IEOR4405 1 1 Consider the...

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Homework #6 solutions / IEOR4405 1 1 Consider the following jobs ( a, b, c, d ) with the processing times (7 , 8 , 9 , 11). The algorithm to solve is LRPT-FM. Denote the machines with speeds 1,2,4 as M1, M2 and M3 respectively. Machine/Job present at each time instant M/T 0 1 2 3 4 M1 : B C B A B M2 : C B C B A M3 : D A D C D B The job with the shortest processing time is A, it is clear from the table that the job is processed in all the 3 machines. 2 Look at the algorithm in the lecture slides. 5.8 Applying LRPT we get t J 1 J 2 J 3 J 4 Assignment t = 0 36 24 16 12 J 1 - M 1 , J 2 - M 2 t = 4 28 20 16 12 J 1 - M 1 , J 2 - M 2 t = 8 20 16 16 12 J 1 - M 1 , J 2 - M 2 t = 12 12 12 16 12 J 3 - M 1 , J 2 - M 2 t = 16 12 8 8 12 J 1 - M 1 , J 4 - M 2 t = 20 4 8 8 8 J 2 - M 1 , J 4 - M 2 t = 24 4 0 8 4 J 3 - M 1 , J 4 - M 2 t = 28 4 0 0 0 J 1 - M 1 t = 32 0 0 0 0 Therefore, the schedule for M1 is 1,1,1,3,1,2,3,1 and for M2 is 2,2,2,2,4,4,4 with C max = 30 The table is, t J 1 J 2 J 3 J 4 Assignment t = 0 36 24 16 12 J 1 - M 1 , J 2 - M 2 t = 2 32 22 16 12 J 1 - M 1 , J 2 - M 2 t = 4 28 20 16 12 J 1 - M 1 , J 2 - M 2 t = 6 24 18 16 12 J 1 - M 1 , J 2 - M 2 t = 8 20 16 16 12 J 1 - M 1 , J 2 - M 2 t = 10 16 14 16 12 J 1 - M 1 , J 3 - M 2

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