Miomir Arandelovic, DBA
Most of the projects, especially in a domain of Artificial Intellegence, benefits from structuring the work to sub-tasks. Program Evaluation and Review Technique (PERT) is a well-known method used to create a network of tasks within Work Breakdown Structure (WBS). A network of project tasks can be represented either hierarchically or as a graph where activities are mapped to nodes or paths between nodes. Two of most frequently used conventions in associating tasks to the graph are Activity-On-Arrow (AOA) and Activity-On-Node (AON) (Perera, 2011).
The topic of this paper is to analyze a sample task, present it by AOA and AON graph and explain differences and various aspects of their use. A special focus would be paid to the notion of critical paths and their importance in the project.
Network Graphs of Yard Maintenance Work
To illustrate the application of AOA and AON methods a sample project specified by Kapur (2004) defines the maintenance yard work that is comprises of the following tasks:
● Pick up Trash
● Put Gas in Equipment
● Get Hedge Clippers
● Trim Hedge
● Mow Front Yard
● Mow Back Yard
● Edge Sidewalk
● Clean Sidewalk
● Bag Grass
In order to develop project schedule, it is necessary to define the related activities, sequence them in the right order, estimate the resources needed, and estimate the time it will take to complete the tasks (Kapur, 2004; Wait, 2010). In the case of yard maintenance project, the aforementioned project work or WBS could be structured into preparation, execution and cleanup. The set of resources allocated to the project would be comprised of hedge clippers, weed eater and one or two lawn movers, along with people handling the equipment. The parallel horizontal paths in the project planning graph would represent the activities that could be done in parallel. For instance, if four people are available to perform yard maintenance work, they can simultaneously trim the hedge using clippers, mow front yard, mow back yard and use the weed eater to edge the sidewalk. Figures 1 and 2 below present the AOA and AON network diagrams of these activities.
Figure 1. Yard Maintenance Project Presented by AOA Diagram
Kapur (2004) explains that AOA method to present network diagram tasks associated tasks to the arcs of the graph or connecting lines or arrows between events, which are shown as small circles. Task description or and ID is written above the line and the task effort and/or duration is written below the line. Network nodes represent the events that might be actual milestones or just stop points of consolidating the tasks. The nodes might be named or not, depending on semantics. This method also requires the use of dummy tasks (dashed lines) to link the tasks to the common transition points. This makes project tracking difficult. Because of the need to use dummy activities as well as the need of software that can effectively draw curved or angular lines, this method had been used mostly in manual drawings and it is rarely used in computer-aided project management.
Figure 2. Yard Maintenance Project Presented by AON Diagram
The AON method of drawing network diagram, each task is represented within a node, with its description or an ID within the square box that represents the node (as labeled boxes much more convenient to draw in most of the computer drawing apps than circles). The lines between boxes show the dependency between various tasks, in a similar way as in AOA diagrams. Four different types of dependencies are used in AON diagrams: Start-to-Finish (SF), Finish-to-Start (FS), Start-to-Start (SS) and Finish-to-Finish (FF). SF dependency is used most often and arrows denote the dependency direction, by pointing from the independent to the dependent task (Kapur, 2004).
According to Paramsoty (2012) explains that while AOA method is intuitive to the human perception, as lines can be intuitively designated to the tasks, another of its limitation is that it is not possible to show lead or lag time except by adding or subtracting time. On the other side, AON method depicts the time just as an attribute of the tasks, so its change doesn’t affect the dependency between tasks. According to Wait (2010) the intent of each activity in AOA and AON network diagrams is to track the fulfillment of the deliverables detailed in the WBS. These activities are not associated directly to deliverables themselves but to the units of work that have to be completed to fulfill the designated deliverables. In addition to node and ID or name of the activity, depicted on the AOA or AON diagrams, the detailed activity definition should be comprised of everything we know about the marching project task. When project manager works on the new domain, it is good practice to use the local field expert’s help to define tasks. For the activities that are not known at the beginning of the project, the good practice is to use placeholders for the unknown portions until the tasks are detailed.
Critical Paths in Task Network Diagrams
The Project Management Body of Knowledge (PMBOK) defines the critical path as the longest sequence of tasks in a project plan that must be completed on time in order for the project to meet its deadline. If there is a delay in any task on the critical path, then your whole project will be delayed. In a network diagram, the critical path can be identified by the longer sequence of activities (Wait, 2010).
In the aforementioned AOA diagram, the critical path is comprised of task sequence: Put Gas to Equipment - Edge Sidewalk – Clean Sidewalk – Bag Grass. The critical path comprises a sequence of tasks of the longest duration, so the whole job cannot be finished while it is done. If the team of multiple people is doing the described yard project, upon completion of their tasks, the other 3 designated to hedge, front yard and back yard would need to wait for the fourth member of the team that defines edges of the sidewalks. In the larger real-world business projects, the milestones would be determined based on critical paths, and it is important to parallelize the task sequences to reduce the difference between lengths of the different paths, to avoid wasting time and resources at the project points of synchronization, where all previous tasks would need to be completed in order for project to continue. In the aforementioned yard maintenance project, such points of synchronization would be bagging and hauling the grass.
An importance of the critical is easiest to demonstrate by the fact that any delay in the tasks associated to that path cause the delay of the whole project. In the aforementioned sample, moving of the front yard could be delayed up to 5 minutes and the whole project would still finish on schedule. However, if any of the tasks in the critical path slip even by a minute, that time would be directly influencing a delay of the overall plan.
According to Nayab (2010) it is common for large and complex projects have multiple critical paths. The activities associated to these paths are commonly categorized as such within a WBS. All the tasks on the multiple critical paths are critical which means that a delay in any one of those tasks will cause a delay to the completion of the project. One of the methods to minimize duration of the project is to use mathematical algorithms, so called Critical Path Method, to derive a logical and efficient order of activities and events by planning for task parallelization when possible. Project managers also try to complete projects faster by “crashing the critical path” by adding more resources which can help shorten the duration of critical path by working in parallel.
WBS of any project defines the groups of tasks within the project, which can be structured in a different manner. In project planning it is important to establish a viable sequence of the tasks within a network that depicts the logical execution order of tasks. Such networks depict the logical sequence and concurrence of various deliverables, tasks, and milestones in a project. The network is built by analyzing the order in which various tasks can be executed. The most common methods to visually construct such task network are AOA and AON diagrams, where the advantage of the first is the intuitive association of the graph lines to the activities, but the second is used much more often as it is easier to draw using computer software and it is more flexible when the specific parameters of the network need to change.
The construction of the activity network diagrams enables project managers and other project participants to visualize the ongoing flow and progress of the project. A particularly important element of the network diagrams is a definition of the one or more critical paths that defines the longest lasting sequences of activities, as each of the tasks associated to such activities directly affects possible delays of project as a whole.
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