The document discusses sequencing problems and provides an example problem. A sequencing problem aims to determine the optimal order of jobs to minimize costs. The example problem involves 6 jobs that must pass through 2 machines (A then B) with processing times provided. The optimal sequence was determined to be jobs 2, 3, 4, 5, 6, 1 with a total elapsed time of 85 hours and idle times of 8 hours for machine A and 17 hours for machine B.

1. DEPARTMENTOFMATHEMATICS
OPERATIONS RESEARCH – II
D.K.MCOLLEGEFORWOMEN(AUTONOMOUS), VELLORE-1
Dr. M. KASTHURI,
Assistant Professor of Mathematics,
Department of Mathematics,
D.K.M College for Women (Autonomous),
Vellore-1

2. SEQUENCING PROBLEM
A problem in which it is necessary to determine the
orders or sequences of jobs in which they should be
performed so as to minimize the total effectiveness on
the sum of the pertinent costs is known as sequencing
problems.

3. TermsusedinSequencingProblem
Jobs - Jobs / items / customers are the primary stimulus for sequencing.
Number of Machines - a machine is characterized by a certain processing
capability or facilities through which a job must pass
before it is completer in job.
Processing Time – It means the time each job requires at each machine.
Total Elapsed Time – It is the time between starting the first job and completing
the last one.

4. Idle Time – It is the time the machine remains idle during the
total elapsed time.
Technological Order – It refers to the order in which various
machines are required for completing the jobs.
It is also known as Processing Order.
No Passing Rule – It implies that passing is not allowed. That is the same order
of the jobs is maintained over each machine. If each of n-jobs
are to be processed n 2 machines A and B in the order AB
then this rule will mean that each job will go to A first and
then to B.

5. Problem: There are six jobs which must go through two machine A and B in
the order A-B. Processing time (in hours) is given here:
Job 1 2 3 4 5 6
Machine A 8 10 11 12 16 20
Machine B 7 15 10 14 13 9
Determine the optimum sequence and the total elapsed time?
Solution:
From the given data, the job sequence is,
Job 2 3 4 5 6 1
Machine A Machine B

6. Job 1 2 3 4 5 6
Machine A 8 10 11 12 16 20
Machine B 7 15 10 14 13 9
Total Elapsed Time:
Job
Sequence
Machine A Machine B
In Time Add Time
Taken
Out
Time
In Time Add Time
Taken
Out Time
2 0 + 10 10 10 + 15 25
3 10 + 11 21 25 + 10 35
4 21 + 12 33 35 + 14 49
5 33 + 16 49 49 + 13 62
6 49 + 20 69 69 + 9 78
1 69 + 8 77 78 + 7 85

7. Total Elapsed Time = 85 hrs
Idle Time for Machine A = Total Elapsed Time – Total Processing Time on Machine A
= 85 – 77
= 8 hrs.
Idle Time for Machine B = Total Elapsed Time – Total Processing Time on Machine B
= 85 – 68
= 17 hrs.