This section focuses on the sequencing problem of processing two jobs through
m machines. Problems under this category can be solved with the help
of graphical method. The graphical method below is explained with the help
of the following example.
Two jobs are to be performed on five machines A, B, C, D, and E. Processing
times are given in the following table.
On small screens, use horizontal scrollbar to view full calculation
Use graphical method to obtain the total minimum elapsed time.
- Mark the processing times of job 1 & job 2 on X-axis & Y-axis
- Draw the rectangular blocks by pairing the same machines as shown
in the following figure.
- Starting from origin O, move through the 450 line until
a point marked finish is obtained.
- The elapsed time can be calculated by adding the idle time for either
job to the processing time for that job. In this illustration, idle
time for job 1 is 5 (3+2) hours.
Elapsed time = Processing time of job 1 + Idle time of job 1
= (3 + 4 + 2 + 6 + 2) + 5 = 17 + 5 = 22 hours.
Likewise, idle time for job 2 is 2 hours.
Elapsed time = Processing time of job 2 + Idle time of job 2
= (5 + 4 + 3 + 2 + 6) + (2) = 20 + 2 = 22 hours.
In this chapter, you learned
how to determine an optimal sequence in which the jobs should be
performed on the machines so that the total elapsed time is minimum.
The chapter discussed the following cases:
- Processing n jobs through two machines.
- Processing n jobs through three machines.
- Processing 2 jobs through m machines.