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 | |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 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 periods

2. Given the following data:

|Job |M1 |M2 |M3 |M4 | |A |16 |14 |5 |3 | |B |12 |13 |13 |10 | |C |21 |10 |7 |4 | |D |10 |17 |12 |10 | |E |23 |6 |3 |5 |

By following the Johnson’s rule in CDS Heuristic, we can find the smallest processing time in the machine 1 and 4. If we follow Johnson’s rule to make the sequence, then the sequence would be-

1. SEQUENCE: D B E C A

In order to find the makespan for the sequence we need to draw a GANTT chart:

M1: DDDD DDDD DD BBBB BBBB BBBB EEEE EEEE EEEE EEEE EEEE EEE CCCC CCCC CCCC CCCC CCCC C AAAA AAAA AAAA AAAA

M2: _ _ _ _ _ _ _ _ _ _ DDDD DDDD DDDD DDDD D BBBB BBBB BBBB B _ _ _ _ _ EEEE EE _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ CCCC CCCC CC _ _ _ _ _ _ AAAA AAAA AAAA AA

M3: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ DDDD DDDD DDDD _ BBBB BBBB BBBB B EEE _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ CCCC CCC _ _ _ _ _ _ _ _ _ _ _ _ _ AAAA A

M4: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ DDDD DDDD DD _ _ _ _ BBBB BBBB BB EEEE E _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ CCCC _...