Job M1 M2 (processing times at machine 1 and 2)
A 9 12
B 13 9
C 8 20
D 11 7
E 16 18
F 18 22
G 14 13
What is the minimum makespan?
In order to find the minimum makespan for the two macines we can apply Johnson’sRule:
Step 1: Look at the processing times for all jobs on both machines.
Step 2: Find the smallest processing time.
Here the smallest processing time are shown in the shaded boxes.
|Jobs |M1 |M2 |
|A |9 |12 |
|B |13 |9 |
|C |8 |20 |
|D |11 |7 |
|E |16 |18 |
|F |18 |22 |
|G |14 |13 |
Step 3: If the smallest processing time is on the first machine, assign that job at the beginning of the sequence and eliminate the job.
Step 4: If the smallest processing time is on the second machine, assign that job at the end of the sequence and eliminate the job.
SEQUENCE: C A E F G B D
In order to find the makespan for the sequence we need to draw a GANTT chart:
M1: CCCC CCCC AAAA AAAA A EEEE EEEE EEEE EEEE FFFF FFFF FFFF FFFF FF GGGG GGGG GGGG GG BBBB BBBB BBBB B DDDD DDDD DDD
M2 : _ _ _ _ _ _ _ _ CCCC CCCC CCCC CCCC CCCC AAAA AAAA AAAA EEEE EEEE EEEE