Page 204 - DCOM303_DMGT504_OPERATION_RESEARCH

Unit 10: Sequencing Problems and Replacement Theory

Step 3: Delete the job which has been sequenced, and repeat step 2 until all the jobs are sequenced. Notes
Step 4: Establish a tabular column to determine the total elapsed time and also the idle time for
both the machines A and B.

1. Total Elapsed Time: Time when the last job in the sequence has finished on Machine B.
2. Idle Time for Machine A: (Total Elapsed Time) – (Time when the last job has finished on
machine B)

3. Idle Time for Machine B: Time at which the first job is finished on machine
th
    – (Time when the (j – 1) job finishes on

machine B)

Example: There are five jobs, each of which must go through the two machines A and B
in the order AB. Processing times (in hours) are given in the table 10.2 below:

Table 10.2: Sequence Problem

Job 1 2 3 4 5
Machine A 5 1 9 3 10
Machine B 2 6 7 8 4

Determine a sequence for the five jobs that will minimize the elapsed time.
Solution:

In the given problem, the jobs must be processed through the machines A and B in the order AB,
i.e., the first machine to be processed is A and then B. Establish a sequence table containing 5 job
cells to sequence the jobs. Now, select the least processing time considering both the machines.
The least time is taken by job 2 on machine A (i.e., 1). Place job 2 in the first cell from left to right
of the Table 10.3 (since it occurs in row 1).
Table 10.3: Job 2 has Least Processing Time

2
Machine A Machine B
Delete the allotted Job 2. Now select the least processing time available in the existing Table
10.4.

Table 10.4: Reduced Table Column for Job 2 Deleted
Job 1 3 4 5
Machine A 5 9 3 10
Machine B 2 7 8 4

The least processing time in the reduced Table 10.5 is 2 for Job l, on machine B. Place this job 1
from right to left in the last cell (since it occurs in row 2).

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