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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 |
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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
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 |
Find the sequence that minimizes the total elapsed time to complete the following jobs in the order AB. Find the total elapsed time and idle times for both the machines.
| 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 |
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 :
In solving 2 machine and n jobs sequencing problem, the following assumption is wrong
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 _______.
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, the processing times are dependent of order of processing the jobs on machines.
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 :
A readymade garments manufacturer has to process 7 items through two stages of production, namely cutting and sewing. The time taken in hours for each of these items in different stages are given below:
| 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 |
Find the sequence in which these items are to be processed through these stages so as to minimize the total processing time. Also find the idle time of each machine.
Solve the following problem :
Find the sequence that minimizes the total elapsed time to complete the following jobs. Each job is processed in order AB.
| 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 |
Determine the sequence for the jobs so as to minimize the processing time. Find the total elapsed time and the idle times for both the machines.
Choose the correct alternative:
| Machine | Job | |||
| A | B | C | D | |
| I | 5 | 6 | 8 | 4 |
| II | 4 | 7 | 9 | 10 |
The optimal sequence for above data 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 assignment problem each worker or machine is ______ capable of handling any job
State whether the following statement is True or False:
The Total Elapsed is the time required to complete all the jobs i.e. entire task
State whether the following statement is True or False:
The idle time for a machine is the when machine is available but is not waiting for any job to be processed
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.
