1. Arrow Diagram

2. Activity Network diagram, CPM, CPS, PERT
Description
The arrow diagram is used to plan and show the required order of
tasks in a project or process, the best schedule for the entire
project, and potential scheduling and resource problems and their
solutions.
The arrow diagram, lets you calculate the critical path of the
project. This is the flow of critical steps where delays will affect the
timing of the entire project, and where addition of resources can
speed up the project.

3. When to use
• When planning a complex project or process with interrelated tasks and
resources.
• When analyzing the timing of a project; this analysis can happen before, during
or after the project.
• When allocating resources (such as people, money and time) to a project.
• When monitoring the progress of a project.
• When replanning a project in progress, due to changes in conditions or
resources.
• Only when you know the steps of the project or process, their sequence, and
how long each steps takes.

4. Procedure
Planning
1. List all the necessary tasks in the project or process. One convenient method
is to write each task on the top half of a card or Post It note. Across the middle of
the card, draw a horizontal arrow pointing right.
2. Determine the correct sequence of the tasks. Do this by asking three
questions for each task.
• Which tasks must happen before this one can begin?
• Which tasks can be done at the same time as this one?
• Which tasks should happen immediately after this one?
It can be useful to create a table with four columns - prior tasks, this task,
simultaneous tasks, following tasks.

5. Procedure...
3. Diagram the network of tasks. If you are using notes or cards,
arrange them in sequence on a large piece of paper. Time should flow
from left to right and concurrent tasks should be vertically aligned.
Leave space between the cards.
4. Between each two tasks, draw circles for events. An event marks the
beginning or end of a task, a milestone for the project. Thus, events are
nodes that separate tasks.

6. Procedure...
5. Look for three common problem situations and redraw them using
dummies or extra events. A dummy is an arrow drawn with dotted line
to separate tasks that would otherwise start and stop with the same
events, or to show logical sequence of tasks. Dummies are not real
tasks.
6. When the network is correct, label all events in sequence with event
numbers in the circle. It can be useful to label all tasks in sequence,
using letters.

7. Scheduling
7. Determine the take times. The task time is the best estimate of the
time that each task should require. Use one consistent measuring unit
(hours, days, weeks). Write the time on each task’s arrow.
8. Determine the critical path. The critical path is the longest path from
the beginning to the end of the project. Mark the critical path with a
heavy line or color. Calculate the length of the critical path: the sum of
all the task times on the path.

8. Scheduling...
9. Calculate the earliest times each task can start and finish, based on
how long preceding tasks take. Start with the first task, where the
earliest start is zero, and work forward.
Earliest start (ES) = the largest earliest finish of the tasks leading into
this one.
Earliest finish (EF) = earliest start + task time

9. Scheduling...
10. Calculate the latest times each task can start and finish without
upsetting the project schedule, based on how long later tasks will take.
Start from the last task, where the latest finish is the project deadline
and work backwards.
Latest finish (LF) = the smallest latest start of all the tasks leading out
this one.
Latest start (LS) = latest finish - task time

10. Scheduling...
11. Write all four times - ES. EF, LS, LF - beside the task arrow.
One common way to show them is in four boxes arranged as
follows:( Example of the arrow diagram on the next two slides )
Earliest Earliest
start finish
Latest Latest
start finish

11. Earliest start Earliest finish
Number of days 1
0 5 Latest finish
5 Develop broad plan 3 8
Latest start
2
5 7
2 Get approval 8 10
3
7 17
10 Identify team
10 20
4
17 19
2 Train team
20 22
19 21 Develop detailed plan
24 26 5
2
19 23
6 4 Conduct research
22 26
0
7
23 26
3 Identify key practices
28 31

12. 8
23 38 Identify partners
27 42 15 23 33
10 Collect data
26 36
Critical path
2 0
Identify current
Develop
11 state
questions
26 28 26 37
10 40 42 31 42 9
Critical path
0 6
33 39
Analyze data
39 45 36 42
Visit partners 6 11
48 54
39 51
12 Develop new process
12 42 54
0
13
2 51 53
Finalize new process Critical path
54 56
14
53 57
4 Get approval for implementation
56 60
15