# JohnsonRule (2)

```MSCI 306M
Dr. Abe Feinberg
Examples of Johnson’s Rule for Scheduling Jobs Through Two Work Centers
Johnson’s Rule is:
1. From the list of unscheduled jobs, select the one with the shortest processing time
in either work center.
2. If the shortest time is at the first work center, do the job first in the schedule
otherwise do the job last in the schedule.
3. Remove the job assigned in Step 2 from the list of unscheduled jobs.
4. Repeat steps 1,2 and 3 filling in the schedule from the front and the back until all
jobs have been scheduled.
Example 1
At the end of each month, a research and development team writes status reports for the projects at
work. The team leaders, Andrew and Julie, submit them to the R&D director on the first Monday of
each month. Unfortunately, they forgot to check their calendar one month until late Friday evening. To
their surprise, they discovered that the month ended on Sunday and the reports were due the following
Monday morning. As they had not started writing them, they decided to come to work early Saturday
morning, so they could finish the reports before Monday morning. They split the work as follows:
Andrew writes and edits the reports while Julie collates data and draws all the necessary graphs.
Assume that Julie starts her work on a report as soon as Andrew is finished with it and that Andrew
works continuously. Times for the reports (in hours) are as follows:
Projects
A
B
C
D
E
Andrew
4
3
5
7
8
Julie
2
5
1
3
6
What is the order of the tasks using Johnson's rule?
Andrew
CALCULATIONS
Julie
Order of jobs using Johnson's rule:
B -> E -> D -> A -> C
How many hours will it take them to finish all the reports?
CALCULATIONS
Andrew: B (3), E
(11),
D (18),
A (22),
C (27)
Julie:
B (8), E
(17),
D (21),
A (24),
(time in parentheses is cumulative hours to complete)
It will take 28 hours to complete all of the reports
How many hours is Andrew idle?
CALCULATIONS:
1
Andrew’s idle time: 28 - 27 = 1 hour
How many hours is Julie idle?
CALCULATIONS:
11
Julie’s idle time: 3 + 3 + 1 + 1 + 3 = 11 hours
C (28)
Johnson’s Rule is:
1. From the list of unscheduled jobs, select the one with the shortest processing time
in either work center.
2. If the shortest time is at the first work center, do the job first in the schedule
otherwise do the job last in the schedule.
3. Remove the job assigned in Step 2 from the list of unscheduled jobs.
4. Repeat steps 1,2 and 3 filling in the schedule from the front and the back until all
jobs have been scheduled.
Example 2
A company is faced with seven tasks that have to be processed through two work centers. Assume
work center I works continuously and that they are using Johnson's rule. Data appear below in hours:
Work center I
Work center II
A
B
C
D
E
F
G
2.58
1.66
2.71
5.52
3.38
5.22
2.89
3.47
5.84
2.41
1.99
7.62
1.73
1.11
What is the sequence of tasks?
Job order using Johnson's rule:
B -> A -> E -> C -> D -> F -> G
Work Center I
Work Center II
B-A-E-C-D-F-G
What is the time in hours to complete all the tasks in both work centers?
CALCULATIONS
Work center I: B (1.66); A (4.24); E (7.62);
C (10.33); D (15.85); F (21.07); G (23.96)
Work center II: B (7.50); A (10.97); E (18.59);
C (21.00); D (22.99); F (24.72); G (25.83)
(time in parentheses is cumulative hours to complete)
It will take 25.83 hours to complete all tasks
What is the total idle time in hours for work center I?
CALCULATIONS:
Work center I idle time: 25.83 - 23.96 = 1.87 hours
What is the total idle time in hours for work center II?
CALCULATIONS
Work center II idle time: 1.66 hours (wait for task B)