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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 |
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.
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 :
The objective of sequencing problem is
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 _______.
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 :
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 :
One of the assumptions made while sequencing n jobs on 2 machines is: two jobs must be loaded at a time on any machine.
State whether the following is True or False :
In a sequencing problem, a machine can process more than one job at a time.
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 :
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 |
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.
A toy manufacturing company produces five types of toys. Each toy has to go through three machines A, B, C in the order ABC. The time required in hours for each process is given in the following table.
| 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 |
Solve the problem for minimizing the total elapsed time.
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
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 ______
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
______ time is the time when the machine is available but is waiting for a job to be processed
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
State whether the following statement is True or False:
In sequencing problem each job once started on any machine must be processed still its completion
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.
