M1 Week 3

3. Given the following data:

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?
Answer:
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 |
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 EEEE EE FFFF FFFF FFFF FFFF FFFF FF GGGG GGGG GGGG G BBBB BBBB B DDDD DDD

So, the minimum makespan is the processing time of M2, which is 109 periods. Minimum Makespan = 109