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प्रश्न
Solve the following problem :
A foreman wants to process 4 different jobs on three machines: a shaping machine, a drilling machine and a tapping machine, the sequence of operations being shaping-drilling-tapping. Decide the optimal sequence for the four jobs to minimize the total elapsed time. Also find the total elapsed time and the idle time for every machine.
| Job | Shaping (Minutes) | Drilling (Minutes) | Trapping (Minutes) |
| 1 | 13 | 3 | 18 |
| 2 | 18 | 8 | 4 |
| 3 | 8 | 6 | 13 |
| 4 | 23 | 6 | 8 |
उत्तर
| job | 1 | 2 | 3 | 4 |
| Shaping (Minutes) | 13 | 18 | 8 | 23 |
| Drilling (Minutes) | 3 | 8 | 6 | 6 |
| Trapping (Minute) | 18 | 4 | 13 | 8 |
Here, Min Shaping = 8, Max Drilling = 8, Min Trapping = 4.
Since Min Shaping ≥ Max Drilling is satisfied, the problem can be converted into a two machine problem.
Let G and H be two fictitious machines such that G = Shaping + Drilling and H = Drilling + Trapping
Then the problem can be written as
| Job | 1 | 2 | 3 | 4 |
| Machine G | 16 | 26 | 14 | 29 |
| Machine H | 21 | 12 | 19 | 14 |
Observe that Min (G, H) = 12, corresponds to Job 2 on machine H.
∴ Job 2 is placed last in sequence.
| 2 |
Then the problem reduces to
| Job | 1 | 3 | 4 |
| Machine G | 16 | 14 | 29 |
| Machine H | 21 | 19 | 14 |
Now, Min (G, H) = 14, corresponds to Job 3 on machine G and Job 4 on machine H.
∴ Job 3 is placed first in the sequence, Job 4 is placed second last in the sequence and remaining Job 1 is placed second in the sequence.
∴ Optimal sequence is
| 3 | 1 | 4 | 2 |
Total elapsed time
| Job | Shaping | Drilling | Trapping | |||
| In | Out | In | Out | In | Out | |
| 3 (8, 6, 13) | 0 | 8 | 8 | 14 | 14 | 27 |
| 1(13, 3, 18) | 8 | 21 | 21 | 24 | 27 | 45 |
| 4 (23, 6, 8) | 21 | 44 | 44 | 50 | 50 | 58 |
| 2 (18, 8, 4) | 44 | 62 | 62 | 70 | 70 | 74 |
∴ Total elapsed time = 74 mins
Idle time for Shaping = 74 – 62 = 12 mins
Idle time for Drilling = (74 – 70) + 8 + 7 + 20 + 12 = 51 mins
Idle time for Trapping = 14 + 5 +12 = 31 mins.
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संबंधित प्रश्न
Find the optimal sequence that minimizes total time required to complete the following jobs in the order ABC. The processing times are given in hours.
| Jobs | I | II | III | IV | V | VI | VII |
| Machine A | 6 | 7 | 5 | 11 | 6 | 7 | 12 |
| Machine B | 4 | 3 | 2 | 5 | 1 | 5 | 3 |
| Machine C | 3 | 8 | 7 | 4 | 9 | 8 | 7 |
Choose the correct alternative :
The objective of sequencing problem is
If there are n jobs and m machines, then there will be_______ sequences of doing the jobs.
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 _______.
Fill in the blank :
The time required for printing of four books A, B, C and D is 5, 8, 10 and 7 hours while its data entry requires 7, 4, 3 and 6 hrs respectively. The sequence that minimizes total elapsed time is _______
State whether the following is True or False :
If there are two least processing times for machine A and machine B, priority is given for the processing time which has lowest time of the adjacent machine.
State whether the following is True or False :
In a sequencing problem, a machine can process more than one job at a time.
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 :
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 |
Choose the correct alternative:
If there are 3 machines A, B and C, conditions for reducing a 3 machine problem to a 2 machine problem with respect to minimum processing time is ______
If there are n jobs and m machines, then there will be _______ sequence of doing jobs.
Choose the correct alternative:
In solving 2 machine and n jobs sequencing problem, the following assumption is wrong
In sequencing problem the time required to transfer a job from one machine to another is ______
State whether the following statement is True or False:
One of the assumptions is made while sequencing n jobs on 2 machines is: two jobs must be loaded at a time on any machine
State whether the following statement is True or False:
In sequencing problem each machine is of different type
The processing times required for four jobs A, B, C and D on machine M1 are 5, 8, 10 and 7 hours and on machine M2 it requires 7, 4, 3 and 6 hours respectively. The jobs are processed in the order Ml, M2. The sequence that minimises total elapsed time is ______
A publisher produces 5 books on Mathematics. The books have to go through composing, printing and binding done by 3 machines A, B, C. The time schedule for the entire task in proper unit is as follows :
| 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 |
Determine the optimum time required to finish the entire task. Also, find idle time for machines A, B, C.
