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प्रश्न
There are five jobs, each of which must go through two machines in the order XY. Processing times (in hours) are given below. Determine the sequence for the jobs that will minimize the total elapsed time. Also find the total elapsed time and idle time for each machine.
| Job | 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 the 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 the 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 machine operator has to perform two operations, turning and threading on 6 different jobs. The time required to perform these operations (in minutes) for each job is known. Determine the order in which the jobs should be processed in order to minimize the total time required to complete all the jobs. Also find the total processing time and idle times for turning and threading operations.
| Job | 1 | 2 | 3 | 4 | 5 | 6 |
| Time of turning | 3 | 12 | 5 | 2 | 9 | 11 |
| Time for threading | 8 | 10 | 9 | 6 | 3 | 1 |
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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 |
Find the sequence in which the three jobs should be processed so as to take minimum time to finish all the three jobs. Also find idle time for both the departments.
An insurance company receives three types of policy application bundles daily from its head office for data entry and tiling. The time (in minutes) required for each type for these two operations is given in the following table:
| Policy | 1 | 2 | 3 |
| Data Entry | 90 | 120 | 180 |
| Filing | 140 | 110 | 100 |
Find the sequence that minimizes the total time required to complete the entire task.
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| Job | I | II | III | IV | V | VI | VII |
| Machine A | 7 | 16 | 19 | 10 | 14 | 15 | 5 |
| Machine B | 12 | 14 | 14 | 10 | 16 | 5 | 7 |
Fill in the blank :
The time for which a machine j does not have a job to process to the start of job is called _______.
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State whether the following is True or False :
The time involved in moving a job from one machine to another is negligibly small.
Solve the following problem :
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| Items | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| Time for Cutting | 5 | 7 | 3 | 4 | 6 | 7 | 12 |
| Time for Sewing | 2 | 6 | 7 | 5 | 9 | 5 | 8 |
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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. 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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| 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 |
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Solve the following problem :
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| 1 | 13 | 3 | 18 |
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Choose the correct alternative:
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State whether the following statement is True or False:
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The Total Elapsed is the time required to complete all the jobs i.e. entire task
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| Machine X | 10 | 2 | 18 | 6 | 20 |
| Machine Y | 4 | 12 | 14 | 16 | 8 |
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