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Solve the following problem : Five jobs must pass through a lathe and a surface grinder, in that order. The processing times in hours are shown below. Determine the optimal sequence of the jobs. Als - Mathematics and Statistics

Sum

Solve the following problem :

Five jobs must pass through a lathe and a surface grinder, in that order. The processing times in hours are shown below. Determine the optimal sequence of the jobs. Also find the idle time of each machine.

Job I II III IV V
Lathe 4 1 5 2 5
Surface grinder 3 2 4 3 6
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Solution

Job I II III IV V
Lathe 4 1 5 2 5
Surface grinder 3 2 4 3 6

Observe that Min (lathe, grinder) = 1, corresponds to job II on lathe.
∴ Job II is placed first in sequence.

II        

Then the problem reduces to

Job I III IV V
Lathe 4 5 2 5
Surface grinder 3 4 3 6

Now, Min (lathe, grinder) = 2, corresponds to job IV on lathe.
∴ Job IV is placed after II in sequence.

II IV      

Then the problem reduces to

Job I III V
Lathe 4 5 5
Surface grinder 3 4 6

Now, Min (lathe, grinder) = 3, corresponds to job I on grinder.
∴ Job I is placed last in sequence.

II IV     I

Then the problem reduces to

Job III V
Lathe 5 5
Surface grinder 4 6

Now, Min (lathe, grinder) = 4, corresponds to job III on grinder.
∴ Job III is placed before I and V on remaining in sequence.

∴ Optimal sequence is

II IV V III I

Total elapsed time

Job Lath Surface
Grinder
In Out In Out
II (1, 2) 0 1 1 3
IV (2, 3) 1 3 3 6
V (5, 6) 3 8 8 14
III (5, 4) 8 13 14 18
I (4, 3) 13 17 18 21

∴ Total elapsed time = 21 hrs
Idle time for lathe = 21 – 17 = 4 hrs
Idle time for surface grinder = 1 + 2 = 3 hrs.

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APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 7 Assignment Problem and Sequencing
Part II | Q 2 | Page 129
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