Page 202 - DCOM303_DMGT504_OPERATION_RESEARCH

Unit 10: Sequencing Problems and Replacement Theory

 Total Elapsed Time T: It is the time interval between starting the first job and completing Notes
the last job including the idle time (if any) in a particular order by the given set of
machines.
 Idle Time I : It is the time for which a machine j does not have a job to process, i.e., idle time
ij
from the end of job (i-1) to the start of job i.
 Processing Order: It refers to the order or sequence in which machines are required for
completing the job.
 Number of Machines: It refers to the service facilities available through which a job must
pass before it is assumed to be completed.
 No Passing Rule: It refers to the condition to be satisfied in which the order of jobs are to
be processed on given machines.
Assumptions

There are some assumptions made while solving sequencing problems.
1. The processing times on different machines are exactly known and are independent of the
order of the jobs in which they are to be processed.

2. The time taken by the jobs in moving from one machine to another is negligible.
3. Once a job has begun in a machine, it must be completed before another job can begin on
the same machine.

4. A job starts on a machine as soon as the previous job is over, and the machine is free to
work.
5. No machine can process more than one job simultaneously.

6. Machines to be used are of different types.
7. The order of completion of jobs are independent, i.e., no job is given priority.
As discussed earlier, the objective of sequencing is to determine the sequence of jobs so that all
the jobs are performed in a minimum completion time from the beginning of the first job till the
completion of the last job.
The advantages of sequencing are:

1. We get the information like which machines are idle and period of idle time.
2. Completion time needed for all the jobs to be completed.

Notes There are also some other objectives of scheduling (or sequencing) such as
minimizing customers wait time, meeting promised delivery dates, keeping stock level
low, giving preferred working pattern, minimizing waiting time of patients in a hospital
for different types of tests and so on.

Give three different examples of sequencing problems from your daily life.
Task

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