The Critical Path Method (CPM) - Construction Project Scheduling and Control - page 62

The CPM with Computer Software Programs

If we plot the previous CPM network by using one of the commercially available
computer software programs, such as Oracle Primavera P6 or Microsoft (MS) Project,
Figure 4.5c will be the result. The only difference between the network shown in
Figure 4.5b and that shown in Figure 4.5c is the start dates because, as mentioned
previously, these computer programs use the start of the day when calculating start
dates and the end of the day when calculating finish dates. This approach affects the
forward-pass and backward-pass calculations. Equations 4.1 through 4.4 are, thus,
rewritten as follows:

ES j = max( EF i )+1 (4.1)'

EF j = ES j + Dur j − 1 (4.2)'

LF j = min( LS k )−1 (4.3)'

and

LS j = LF j − Dur j + 1 (4.4)'

The Critical Path

If we think about the situation in the project we have just scheduled, we will notice
that activities A, B, D, and G are “driving” the schedule. These activities are critical
because any delay in their start or finish will delay the entire project. For example, if
activity B takes 9 days instead of 8 days, it will finish on day 14. Activity D can then
start and will finish on day 23. Finally, activity G can start on day 23 and will finish
on day 24, which is 1 day past the originally scheduled date. This delay in the project
completion date may not occur with a delay (within certain limits) in other activities,
such as C, E, or F. Project managers usually focus on the critical path because of
its criticality and direct impact on the project finish date. Knowing not only which
activities are critical and which are not but also the impact of the delay of one activity
on other activities and on the entire project is the crux of understanding scheduling.
Following are five observations about the critical path:

1. In every network, there must exist at least one critical path.
2. More than one critical path may exist. Multiple paths may share some activities.
3. Any critical path must be continuous from the start of the project until its end.
There is one exception: when a constraint is imposed (which is discussed later),
a path may become critical as a result of the constraint, from the start until the
constrained activity, or from the constrained activity until the end. In general,
the entire path must be either critical or noncritical.