What is an Arrow Diagram?

Quality Glossary Definition: Arrow diagram

Also called: activity on arrow diagram, activity network diagram, network diagram, activity chart, node diagram, CPM (critical path method) chart

Variation: PERT (program evaluation and review technique) chart

An arrow diagram is defined as a process diagramming tool used to determine optimal sequence of events, and their interconnectivity. It is used for scheduling and to determine the critical path through nodes. The arrow diagramming method shows 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—the flow of critical steps where delays can affect the timing of the entire project and where addition of resources can speed up the project.

When to Use an Arrow Diagram

• When scheduling and monitoring tasks within a complex project or process with interrelated tasks and resources
• When you know the steps of the project or process, their sequence, and how long each step takes
• When project schedule is critical, with serious consequences for completing the project late or significant advantage to completing the project early

Arrow Diagram Procedure

Materials needed: Sticky notes or cards, marking pens, and large writing surface (newsprint or flipchart pages).

Drawing the Network

1. List all the necessary tasks in the project or process. One method is to write each task on the top half of a card or sticky 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?
     Tip: Create a table with four columns: prior tasks, this task, simultaneous tasks, following tasks for ease of use.
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

   and can help visually separate tasks

   .

5. Look for the three common problem situations below and redraw them using “dummies” (not real tasks) or extra events. A dummy is an arrow drawn with dotted lines used to separate tasks that would otherwise start and stop with the same events or to show logical sequence.
   • Two simultaneous tasks start and end at the same events.
     • Solution: Use a dummy and an extra event to separate them. In Figure 1, event 2 and the dummy between 2 and 3 have been added to separate tasks A and B.
   • Task C cannot start until both tasks A and B are complete; a fourth task, D, cannot start until A is complete, but need not wait for B. (See Figure 2.)
     • Solution: Use a dummy between the end of task A and the beginning of task C.
   • A second task can be started before part of a first task is done.
     • Solution: Add an extra event where the second task can begin and use multiple arrows to break the first task into two subtasks. In Figure 3, event 2 was added, splitting task A.

       Figure 1: Dummy separating simultaneous tasks
       

       Figure 2: Dummy keeping sequence correct
       

       Figure 3: Using an extra event
       

6. When the network is correct, label all events in sequence with event numbers in the circles. It may be helpful to label all tasks in sequence, using letters.

Scheduling: Critical Path Method (CPM)

1. Determine task times—the best estimate of the time that each task should require. Use one measuring unit (hours, days, or weeks) throughout, for consistency. Write the time on each task’s arrow.
2. Determine the “critical path,” 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).
3. Calculate the earliest times each task can start and finish, based on how long preceding tasks take. These are called earliest start (ES) and earliest finish (EF). Start with the first task, where ES = 0, and work forward. Draw a square divided into four quadrants, as in Figure 4. Write the ES in the top left box and the EF in the top right.

   For each task:

   • Earliest start (ES): the largest EF of the tasks leading into this one
   • Earliest finish (EF): ES + task time for this task

   Figure 4: Arrow diagram time box

   ES Earliest
   start

   EF Earliest
   finish

   LS Latest
   start

   LF Latest finish

4. Calculate the latest times each task can start and finish without upsetting the project schedule, based on how long later tasks will take. These are called latest start (LS) and latest finish (LF). Start from the last task, where the latest finish is the project deadline, and work backwards. Write the LS in the lower left box and the LF in the lower right box.
   • Latest finish (LF): the smallest LS of all tasks immediately following this one
   • Latest start (LS): LF – task time for this task
5. Calculate slack times for each task and for the entire project.

   Total slack is the time a job could be postponed without delaying the project schedule.

   Total slack: LS -ES = LF -EF

   Free slack is the time a task could be postponed without affecting the early start of any job following it.

   Free slack: the earliest ES of all tasks immediately following this one – EF

Figure 5: Completed Arrow Diagram Example

Adapted from The Quality Toolbox, Second Edition, ASQ Quality Press.