Advertisements
Advertisements
Question
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.
Advertisements
Solution
| 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 |
Observe that Min (cutting, sewing) = 2, corresponds to item 1 on sewing.
∴ Item 1 is placed last in sequence.
| 1 |
Then the problem reduces to
| Items | 2 | 3 | 4 | 5 | 6 | 7 |
| Time for Cutting | 7 | 3 | 4 | 6 | 7 | 12 |
| Time for Sewing | 6 | 7 | 5 | 9 | 5 | 8 |
Now, Min (cutting, sewing) = 3, corresponds to item 3 on cutting.
∴ Item 3 is placed first in sequence.
| 3 | 1 |
Then the problem reduces to
| Items | 2 | 4 | 5 | 6 | 7 |
| Time for Cutting | 7 | 4 | 6 | 7 | 12 |
| Time for Sewing | 6 | 5 | 9 | 5 | 8 |
Now, Min (cutting, sewing) = 4, corresponds to item 4 on cutting.
∴ Item 4 is placed after 3 in sequence.
| 3 | 4 | 1 |
Item 4 is placed after 3 in sequence.
| Items | 2 | 5 | 6 | 7 |
| Time for Cutting | 7 | 6 | 7 | 12 |
| Time for Sewing | 6 | 9 | 5 | 8 |
Now, Min (cutting, sewing) = 5, corresponds to item 6 on sewing
∴ Item 6 is placed before 1 in sequence.
| 3 | 4 | 6 | 1 |
Then the problem reduces to
| Items | 2 | 5 | 7 |
| Time for Cutting | 7 | 6 | 12 |
| Time for Sewing | 6 | 9 | 8 |
Now, Min (cutting, sewing) = 6, corresponds to item 2 on sewing and item 5 on cutting.
∴ Item 2 is placed before 6 and item 5 is placed after 4 and item 7 on remaining in sequence.
∴ Optimal sequence is
| 3 | 4 | 5 | 7 | 2 | 6 | 1 |
Total elapsed time
| Item | Cutting | Sewing | ||
| In | Out | In | Out | |
| 3 (3, 7) | 0 | 3 | 3 | 10 |
| 4 (4, 5) | 3 | 7 | 10 | 15 |
| 5 (6, 9) | 7 | 13 | 15 | 24 |
| 7 (12, 8) | 13 | 25 | 25 | 33 |
| 2 (7, 6) | 25 | 32 | 33 | 39 |
| 6 (7, 5) | 32 | 39 | 39 | 44 |
| 1 (5, 2) | 39 | 44 | 44 | 46 |
∴ Total elapsed time = 46 hrs
Idle time for cutting = 46 44 = 2 hrs
Idle time for sewing = 3 + 1 = 4 hrs.
APPEARS IN
RELATED QUESTIONS
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 :
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 _______.
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 :
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
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.
______ 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:
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:
In sequencing problem each job once started on any machine must be processed still its completion
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 |
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 ______
