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प्रश्न
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.
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उत्तर
| 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 |
Observe that Min (A, B) = 3, corresponds to job VII on machine B.
∴ Job VII is placed last in sequence.
| VII |
Then the problem reduces to
| Machines | Jobs (Processing times in minutes) | |||||
| I | II | III | IV | V | VI | |
| Machine A | 12 | 6 | 5 | 11 | 5 | 7 |
| Machine B | 7 | 8 | 9 | 4 | 7 | 8 |
Now, Min (A, B) = 4, corresponds to job IV on machine B
∴ Job IV is placed before VII in sequence.
| IV | VII |
Then the problem reduces to
| Machines | Jobs (Processing times in minutes) | ||||
| I | II | III | V | VI | |
| Machine A | 12 | 6 | 5 | 5 | 7 |
| Machine B | 7 | 8 | 9 | 7 | 8 |
Now, Min (A, B) = 5, corresponds to job III and V on machine A.
∴ Job III and V is placed either first or second in sequence.
| III | V | IV | VII |
| OR |
| V | III | IV | VII |
Then the problem reduces to
| Machines | Jobs (Processing times in minutes) | ||
| I | II | VI | |
| Machine A | 12 | 6 | 7 |
| Machine B | 7 | 8 | 8 |
Now, Min (A, B) = 6, corresponds to job II on machine A
∴ Job II is placed on third place in sequence.
| III | V | II | IV | VII |
| OR |
| V | III | II | IV | VII |
Then the problem reduces to
| Machines | Jobs (Processing times in minutes) | |
| I | VI | |
| Machine A | 12 | 7 |
| Machine B | 7 | 8 |
Now, Min (A, B) = 7, corresponds to job I on machine B and VI on machine A.
∴ Job I is placed before IV and job VI on remaining in sequence.
| III | V | II | VI | I | IV | VII |
| OR |
| V | III | II | VI | I | IV | VII |
We take the optimal sequence as,
| III | V | II | VI | I | IV | VII |
Total elapsed time
| Job | Machine A | Machine B | ||
| In | Out | In | Out | |
| III (5, 9) | 0 | 5 | 5 | 14 |
| V (5, 7) | 5 | 10 | 14 | 21 |
| II (6, 8) | 10 | 16 | 21 | 29 |
| VI (7, 8) | 16 | 23 | 29 | 37 |
| I (12, 7) | 23 | 35 | 37 | 44 |
| IV (11, 4) | 35 | 46 | 46 | 50 |
| VII (6, 3) | 46 | 52 | 52 | 55 |
∴ Total elapsed time = 55 mins
Idle time for machine A = 55 – 52 = 3 mins
Idle time for machine B = 5 + 2 + 2 = 9 mins.
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संबंधित प्रश्न
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
Choose the correct alternative :
In a 3 machine and 5 jobs problem, the least of processing times on machine A, B and C are 5, 1 and 3 hours and the highest processing times are 9, 5 and 7 respectively, then it can be converted to a 2 machine problem if order of the machines is:
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 ______.
One machine - one job is not an assumption in solving sequencing problems.
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 :
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 :
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 :
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 |
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
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:
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 machine is of different type
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 |
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.
