## Time Remaining

Latest Start, Latest Finish

Figure 15-9. AOA Activity Information Representation

Figure 15-9. AOA Activity Information Representation

An AOA network is illustrated in Figure 15-10, and two AON networks are represented irFigure 15-11. AOA representations are seldom used today. Whichever network representation is used, the principles remain the same. For our purposes of network analysis, we will use the AON representation. In an AON network, there is a start node, usually placed on the left, and anendnode, placed to the right. All the nodes in-between represent activities in the project WBS. There is a one-to-one correspondence of activities to network nodes. Although they could be represented as boxes, circles, or whatever shape is preferred for a node, we will represent nodes as shown in Figure 15-8.

Figure 15-10. Sample AON Network Diagrams

Figure 15-10. Sample AON Network Diagrams

Figure 15-11. Sample AOA Network Diagram

You'll notice that all of these network diagrams show precedence very well. This is their major strength. It is easy to follow a path of activities from left to right, and to see how various activity sequences relate to each other. These diagrams are widely used to construct project plans from scratch when no WBS template exists, that is, when you are inventing the project activities from a brainstorming session (as discussed in Chapter 14). The weakness of these diagrams is the same as for the Gantt and other graphical representations. For large projects with lots of activities, they get very messy and hard to follow. But they are a great way to get started with planning and to get a WBS under control.

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PERT and CPM Scheduling

These two methods of schedule analysis have been around since the 1950s, and form the foundation of what the profession knows about scheduling today. CPM (critical path method) was developed by DuPont in 1958-59, and uses fixed-time estimates for each activity. PERT (program evaluation and review technique) was developed for the U.S. Navy Special Projects Office Polaris missile submarine project by the consultants Booz, Allen, and Hamilton during the same years.

Both PERT and CPM use network-diagramming techniques to illustrate activity precedence. But most scheduling today is done using CPM. First we'll look at the major difference between the two methods (point estimate or weighted average), and then see how to use network diagramming for CPM analysis.

PERT

PERT's time estimates involve the beta probability distribution to capture three estimates (optimistic, most likely, and pessimistic) of the duration of an activity. The PERT beta distribution is shown in Figure 15-12.

Figure 15-12. PERT Beta Distribution