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प्रश्न
Find the sequence that minimizes total elapsed time to complete the following jobs in the order XY. Find the total elasped time and idle times for each machine.
| Jobs | A | B | C | D | E |
| Machine X | 10 | 2 | 18 | 6 | 20 |
| Machine Y | 4 | 12 | 14 | 16 | 8 |
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उत्तर
| Job | A | B | C | D | E |
| Machine X | 10 | 2 | 18 | 6 | 20 |
| Machine Y | 4 | 12 | 14 | 16 | 8 |
Observe that Min(X, Y) = 2, corresponding to job B on machine X.
∴ Job B is placed first in sequence
| B |
Then the problem reduces to
| Job | A | C | D | E |
| Machine X | 10 | 18 | 6 | 20 |
| Machine Y | 4 | 14 | 16 | 8 |
Now, Min(X, Y) = 4, corresponds to job A on machine Y.
∴ Job A is placed last in sequence.
| B | A |
Then the problem reduces to
| Job | C | D | E |
| Machine X | 18 | 6 | 20 |
| Machine Y | 14 | 16 | 8 |
Now, Min(X, Y) = 6, corresponds to job D on machine X.
∴ Job D is placed second in sequence.
| B | D | A |
Then the problem reduces to
| Job | C | E |
| Machine X | 18 | 20 |
| Machine Y | 14 | 8 |
Now, Min(X, Y) = 8, corresponds to job E on machine Y.
∴ Job E is placed fourth and job C on remaining in sequence.
∴ The optimal sequence is
| B | D | C | E | A |
Total elapsed time,
| Job | Machine X | Machine Y | ||
| In | Out | In | Out | |
| B (2, 12) | 0 | 2 | 2 | 14 |
| D (6, 16) | 2 | 8 | 14 | 30 |
| C (18, 14) | 8 | 26 | 30 | 44 |
| E (20, 8) | 26 | 46 | 46 | 54 |
| A (10, 4) | 46 | 56 | 56 | 60 |
∴ Total elapsed time = 60 hrs.
Idle time for machine X = 60 – 56 = 4 hrs
Idle time for machine Y = 2 + 2 + 2 = 6 hrs
संबंधित प्रश्न
A company has three jobs on hand. Each of these must be processed through two departments, in the order AB where
Department A: Press shop and
Department B: Finishing
The table below gives the number of days required by each job in each department
| Job | I | II | III |
| Department A | 8 | 6 | 5 |
| Department B | 8 | 3 | 4 |
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| Machine A | 7 | 16 | 19 | 10 | 14 | 15 | 5 |
| Machine B | 12 | 14 | 14 | 10 | 16 | 5 | 7 |
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| Job | I | II | III | IV | V |
| Lathe | 4 | 1 | 5 | 2 | 5 |
| Surface grinder | 3 | 2 | 4 | 3 | 6 |
Solve the following problem :
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| Machines | Jobs (Processing times in minutes) | ||||||
| I | II | III | IV | V | VI | VII | |
| Machine A | 12 | 6 | 5 | 11 | 5 | 7 | 6 |
| Machine B | 7 | 8 | 9 | 4 | 7 | 8 | 3 |
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| Type | 1 | 2 | 3 | 4 | 5 |
| Machine A | 16 | 20 | 12 | 14 | 22 |
| Machine B | 10 | 12 | 4 | 6 | 8 |
| Machine C | 8 | 18 | 16 | 12 | 10 |
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| Job | Shaping (Minutes) | Drilling (Minutes) | Trapping (Minutes) |
| 1 | 13 | 3 | 18 |
| 2 | 18 | 8 | 4 |
| 3 | 8 | 6 | 13 |
| 4 | 23 | 6 | 8 |
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| Machine | Job | |||
| A | B | C | D | |
| I | 5 | 6 | 8 | 4 |
| II | 4 | 7 | 9 | 10 |
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| Book | I | II | III | IV | V |
| Machine A | 4 | 9 | 8 | 6 | 5 |
| Machine B | 5 | 6 | 2 | 3 | 4 |
| Machine C | 8 | 10 | 6 | 7 | 11 |
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