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प्रश्न
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.
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 |
Find the total elapsed time and also find idle time for machine B.
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उत्तर
| 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 |
Here min A = 12, max B = 12, min C = 8.
Since min A ≥ max B is satisfied, the problem can be converted into a two-machine problem.
Let G and H be two fictitious machines such that G = A + B and H = B + C
Then the problem can be written as
| Type | 1 | 2 | 3 | 4 | 5 |
| Machine G | 26 | 32 | 16 | 20 | 30 |
| Machine H | 18 | 30 | 20 | 18 | 18 |
Using the optimal sequence algorithm, any one is an optimal sequence that can be obtained.
| 3 | 2 | 5 | 4 | 1 | |
| or | 3 | 2 | 5 | 1 | 4 |
| or | 3 | 2 | 4 | 5 | 1 |
| or | 3 | 2 | 4 | 1 | 5 |
| or | 3 | 2 | 1 | 4 | 5 |
| or | 3 | 2 | 1 | 5 | 4 |
| Type | Machine A | Machine B | Machine C | |||
| In | Out | In | Out | In | Out | |
| 3 | 0 | 12 | 12 | 16 | 16 | 32 |
| 2 | 12 | 32 | 32 | 44 | 44 | 62 |
| 5 | 32 | 54 | 54 | 62 | 62 | 72 |
| 4 | 54 | 68 | 68 | 74 | 74 | 86 |
| 1 | 68 | 84 | 84 | 94 | 94 | 102 |
∴ Total elapsed time = 102 hrs.
Idle time for machine A = 102 – 84 = 18 hrs
Idle time for machine B = (102 – 94) + 54 = 62 hrs
Idle time for machine C = 16 + 12 + 2 + 8 = 38 hrs.
Notes
Students can refer to the provided solution According to their question.
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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 |
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.
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 _______.
One machine - one job is not an assumption in solving sequencing problems.
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 :
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.
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
______ time is the time when the machine is available but is waiting for a job to be processed
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:
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
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.
