# Mgt 314

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