activityonarrow

Activity-on-Arrow (AOA), also known as the arrow diagram method, is a classic technique for representing and analyzing project schedules using a network diagram. In AOA, each project activity is depicted as a directed arrow; the duration of the activity is associated with the arrow. The tail of the arrow marks the activity's start event, and the head marks its finish event. Nodes represent events, such as milestones or the completion of prerequisites. Arrows are connected through shared nodes to encode precedence constraints, so an activity cannot begin until the tail event is reached by all preceding activities.

Because multiple arrows may share the same tail or head, it is often necessary to introduce dummy activities — zero-duration arrows used solely to preserve logic without affecting timing — to prevent unintended dependencies from altering the network.

AOA is one of the traditional CPM network forms, the other being Activity-on-Node (AON). It originated with the early CPM work at DuPont in the 1950s and was popularized by James Kelley and Morgan Walker. While AOA remains taught and used in some industries, its networks can become visually complex for large projects, and many practitioners prefer AON for its simplicity and direct mapping of activities to nodes.

Calculations in AOA proceed via forward and backward passes to determine earliest and latest event times. From these, activity slack is derived, and the critical path is identified as the path of activities with zero slack. In practice, AOA emphasizes precedence logic and timing on the arrows, with event times at the nodes.