The arrow diagramming method is one of those scheduling techniques that most project managers learn for the PMP exam and then rarely use in practice. I learned it properly for the exam, promptly forgot the details once I passed, and then had to relearn it properly a few years later when a client’s legacy scheduling system was built on AOA notation and I had to make sense of a network diagram that looked nothing like what modern software produces. That experience made me appreciate what ADM actually teaches — the forward pass, backward pass, and float logic underneath it are identical to what PDM does, just with different notation. If you understand ADM, PDM becomes almost obvious. This article covers the arrow diagramming method with a complete worked example, including the parts of the calculations that most tutorials leave half-explained.
Table of Contents
What is an Arrow Diagram?
Before you begin, watch the video that illustrates an example. See how this tool visually represents the sequence of project tasks and their dependencies, aiding project teams in identifying the critical path and enhancing project planning.
An arrow diagram (also known as activity on arrow diagram, node diagram) is a vplanning and scheduling tool that determines the optimal sequence of activities. With the help of nodes, it provides a clear picture of the project duration through the Critical Path Method. In simple terms, an arrow diagram demonstrates the sequence of tasks and their durations required to complete the project. By following the forward pass and backward pass steps, you can easily calculate the critical path.
ADM goes back to the late 1950s — it came out of the same era as PERT and CPM, developed separately by the US Navy and DuPont for large engineering programs. For decades it was the standard. Then software happened. Once scheduling tools started defaulting to Precedence Diagramming Method in the 1980s and 90s, ADM use dropped sharply, partly because PDM handles more dependency types and partly because dummy activities — which I’ll get to — are genuinely fiddly to manage. Most schedulers working today have never built an ADM network outside an exam context. But the math underneath it is the same as PDM, which is why working through it properly still pays off.
WHEN TO USE AN ARROW DIAGRAM?
- Creating a work schedule to plan and monitor project activities with resources.
- Understanding task sequences and each step to complete each task.
- Calculating the earliest and latest completion dates of the project and each task.
Honestly, for most people reading this, the realistic answer to “when to use ADM” is: when preparing for the PMP exam, or when you inherit a schedule that someone else built in AOA notation and you need to read it. There are still industries — construction, some government programs — where ADM-based systems survive because they were built before PDM became standard and nobody has replaced them. If you’re starting a new project from scratch in Primavera P6 or Microsoft Project, you’ll be in PDM territory automatically. The reason to understand ADM anyway is that the critical path logic is identical — once you can do it by hand in ADM, the software’s output stops being a black box.
Arrows, Nodes and Dummy task
There are two main elements of the Arrow Diagramming Method (ADM) which are arrows and nodes. One arrow represents one activity to be performed. The tail of the arrow is the start of the activity, the head of the arrow is the end of the activity and the length of the arrow is the duration of the activity. (Figure 1)
A dummy activity is not a real activity that is added to represent dependency between tasks. It can be used to separate tasks or to keep the sequence correct. The duration of a dummy task is often zero.
Figure 2: Dummy Activity
In the forward pass, we calculate the Start Dates of all the nodes. In the backward pass, the end node’s Start Date will be its Finish Date and the backward pass proceeds by subtracting the duration of the activities leading to the end node from the end node’s Finish Date to arrive at the Finish Dates for the preceding nodes.
Dummy activities are where most people get tripped up the first time they try to build an ADM network. They’re not real work — duration zero, no resources — but they affect the network logic, and they’re easy to either forget when you need one or add one when you don’t. The rule: if two separate activities both start and end at the same two nodes, the diagram can’t tell them apart. Say Activity A runs from Node 1 to Node 3, and Activity B also runs from Node 1 to Node 3. Both get identifier “1-3,” which breaks everything downstream. A dummy resolves it by routing one activity through an intermediate node, giving it a unique identifier. I’ve seen students spend 20 minutes wondering why their critical path calculation is wrong, only to find a missing dummy. It’s worth checking the node numbering carefully before you start calculating.
Arrow Diagramming Method vs Precedence Diagramming Method
This comparison comes up constantly in PMP prep and I’ve found it’s also genuinely useful for anyone who has to switch between legacy ADM-based systems and modern tools. Same logic, different notation — but the notation differences have real practical consequences.
| Arrow Diagramming Method (ADM) | Precedence Diagramming Method (PDM) | |
|---|---|---|
| Also known as | Activity-on-Arrow (AOA) | Activity-on-Node (AON) |
| Activities shown on | Arrows | Nodes (boxes) |
| Dependencies shown on | Nodes (circles) | Arrows |
| Dependency types | Finish-to-Start only (natively) | All four types (FS, FF, SS, SF) |
| Dummy activities | Required for some dependencies | Not needed |
| Software support | Limited (legacy systems) | Standard in most PM software |
| PMP exam relevance | Tested — know the concept | Tested — dominant method |
The critical path logic — forward pass, backward pass, float calculation — works identically in both methods. The difference is purely notational. If you can do the calculations in ADM, you can do them in PDM. The PMBOK Guide covers both but notes that PDM is “the most commonly used method for constructing a project schedule network diagram” because of its flexibility and software compatibility.
How to create an activity on arrow diagram?
At first, create the activity network diagram and perform the critical path calculations.
1. Define Activities and Dependencies of Activity Network Diagram
Begin with defining all the activities involved in your project. After that identify the dependencies between activities by determining which tasks must be completed before others can begin.
2. Define Nodes And Arrows
Draw the network diagram by representing each activity wih a node and link the nodes with arrows. The first node is the beginning of the project and the last node is the end milestone. From the beginning to the end, arrows demonstrade the workflow.
3. Estimate Activity Duration
Estimate durations for each activity by considering resources and project requirements. There are 6 tools for activity duration estimates. You can select the one that fits your project’s requirements best.
1. Expert Judgment
2. Analogous Estimating
4. Three-Point Estimates
5. Reserve analysis
6. Group Decision Making Techniques
Note that estimating activity durations is an important process for critical path calculations. There are many project scheduling tools available for this purpose.
4. Determine the Critical Path
After creating the activity network diagram, the next step is to determine the critical path of the project. For better understanding, let’s review the example below.
Arrow Diagramming Method Example
The following example shows a simple Activity on Arrow Diagram.
In this example A,B,C,D,E,F,G rows are representing the activities. Numbers above the rows are activity durations. As shown in the schema above only F-S Relationship is used to link activities.
Before running the calculations, note the structure: each circle (node) represents an event — either the start or end of one or more activities. Each arrow represents an activity with its duration. The network flows left to right. To find the critical path, you need to complete a forward pass (earliest dates), a backward pass (latest dates), and then calculate the float for each activity. Activities with zero float are on the critical path.
Step 1: Forward Pass Calculation
Starting from the 0 point (Start Milestone) perform the forward pass calculation to determine the earliest dates of the project. In the figure 4, earliest completion duration is 24 days.
Step 2: Backward Pass Calculation
Now you will turn back from the finish milestone and calculate the latest completion date for each activity.
Step 3: Float Calculation for Each Activity
Float can be calculated by subtracting the Start Date of an activity from its Finish Date.
Total Float = LS – ES (or LF – EF)
Step 4: Identifying the critical path
The critical path is the longest path in the network diagram and the total float of critical path is zero. As shown in the schema above, the critical path is marked red.
Reading the Arrow Diagramming Method Results Correctly
Once you’ve completed the four steps, the numbers tell you more than just which path is critical. A few things that come up in practice:
Total float vs free float. Total float is how much an activity can slip without delaying the project end. Free float is how much it can slip without delaying the next activity’s early start. An activity can have significant total float but zero free float — meaning it has flexibility in the project timeline but would immediately push the next activity if delayed. In the arrow diagramming method, free float is calculated as: Early Start of successor node − Early Finish of the activity.
Near-critical activities matter. Activities with small but non-zero float — a day or two on a six-month project — deserve the same attention as critical path activities. They’re not on the critical path today, but a small delay or resource conflict could put them there. I’ve seen projects where the “official” critical path stayed stable on paper while a near-critical parallel path quietly deteriorated and then became the actual constraint two months before completion. Tracking float trends across reporting periods catches this earlier than waiting for something to hit zero.
Multiple critical paths are possible. A network can have more than one path with zero float. When this happens, the project has multiple critical paths, which means more activities that can’t slip without delaying completion. This increases schedule risk and typically requires more intensive monitoring.
The critical path can shift. If a critical path activity finishes ahead of schedule, or a near-critical activity experiences a delay, the critical path through the network can change. Re-running the calculations periodically during execution — not just at planning — is what keeps the schedule analysis useful rather than decorative.
Limitations of the Arrow Diagramming Method
Knowing why ADM lost ground to PDM makes the limitations concrete rather than abstract. Three things in particular:
Only finish-to-start dependencies. ADM natively handles only one type of dependency: an activity must finish before the next can start. Real projects frequently involve other relationships — two activities overlapping (start-to-start with lag), an activity that can’t finish until another finishes (finish-to-finish). In ADM, these require workarounds or can’t be modeled accurately. PDM handles all four dependency types directly.
Dummy activities create complexity and errors. Every dummy activity in an ADM network is a potential source of error. They’re easy to forget when they’re needed, and easy to add incorrectly. A network with many parallel activities can require a significant number of dummies, making the diagram harder to read and validate. PDM eliminates the need for them entirely.
Harder to modify. When a project changes — activities added, removed, or resequenced — an ADM network often requires more extensive rework than a PDM network. Renumbering nodes and adjusting dummies throughout a complex diagram is time-consuming and error-prone.
None of this means ADM isn’t worth learning. The math — forward pass, backward pass, float, critical path — is the same in both methods. Working through it in ADM first, before relying on software to do the calculation, is how you build the kind of intuition that lets you spot when a scheduler’s output doesn’t look right. See also our article on the Critical Path Method for how this logic applies in modern scheduling contexts, and our PERT method guide for the related technique that adds probabilistic duration estimates to the same network approach.
Summary
The Arrow Diagramming Method (ADM) and The Precedence Diagramming Method (PDM) are two network scheduling techniques. The first one is the traditional one used widely in the past. The second one is the current method that we are using widely now. In this simple arrow diagramming method example we show how to make forward, backward, total float and critical path calculation. Nowadays this method lost its popularity because of the introduction of software solutions but in order to use this software successfully, it is important to understand both scheduling techniques.
See Also
External References
[1] CPM in Construction – A Manual for General Contractors (Copyright 1965 by the Associated General Contractors of America)
Irma Gilda is chief executive of Sonic Training and Consultancy Co., the training platform offers project planning and scheduling More than 60 k learners have used the platform to attain professional success. Irma is a professional Primavera P6 Trainer.
