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374 CHAPTER 9 PROJECT SCHEDULING: PERT/CPM

Figure 9.2 Souk al Bustan Shopping Centre Project Network with Activity Times

E F
1 4

A D G
5 3 14

C H I
Start Finish
4 12 2

B
6

Problem 3 provides the To determine the project completion time, we have to analyze the network and
immediate predecessor identify what is called the critical path for the network. The critical path is the
information for a project
with seven activities and longest path through the network and shows the minimum time in which the
asks you to develop the project can be completed. A path is a sequence of connected nodes that leads
project network. from the Start node to the Finish node. For instance, one path for the network in
Figure 9.2 is defined by the sequence of nodes A-E-F-G-I. By inspection, we see
For convenience, we use
the convention of that other paths are possible, such as A-D-G-I, A-C-H-I and B-H-I. All paths in
referencing activities with the network must be traversed in order to complete the project, so we will look for
letters. Generally, we the path that requires the most time. Because all other paths are shorter in
assign the letters in duration, this longest path determines the total time required to complete the
approximate order as we
move from left to right project. If activities on the longest path are delayed, the entire project will be
through the project delayed. So, the longest path is the critical path. Activities on the critical path are
network. referred to as the critical activities for the project. The following discussion
presents a step-by-step algorithm for finding the critical path in a project network.

Determining the Critical Path
We begin by finding the earliest start time and a latest start time for all activities in
the network. The earliest start time is the earliest time that activity can start (it may
be dependent on other activities being completed first). Let:

ES ¼ earliest start time for an activity
EF ¼ earliest finish time for an activity
t ¼ activity time

The earliest finish time for any activity is:

EF ¼ ES þ t (9:1)

Activity A can start as soon as the project starts, so we set the earliest start time for
activity A equal to 0. With an activity time of five weeks, the earliest finish time for
activity A is EF ¼ ES + t ¼ 0+5 ¼ 5.

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