(Dilworth 1992, p.567)
Using the precedence diagram and activity schedule given, the following bar chart was made showing earliest and latest dates for activities A through K. To work out the early start and early finish of our network one has to start at the beginning activity, that is the activity/ activities with no predecessor. The early start of a job in a network is the earliest that a job can begin. In the case of a job with predecessors, the early start of a job is the largest of the early finish times of its predecessors. The early finish of a job is its early finish plus its own duration. This procedure of starting at the beginning and working out the early start and early finish of the activities in a network is often referred to as "forward pass".
without extending the total time of the project. Late finish of an activity is the late start of the activity that succeeds. If an activity has more than one successor, then the smaller of the late starts is to be taken. In the case of activities that do not have a successor, the late finish is taken as the total time of the project. The late start of such activities is their late finish less their duration.
Working out the late start of activities will help answer the questions: can the start of some activities be delayed, and if so by how much It must be mentioned at this juncture that this is a luxury that does not apply to activities on the critical path. By definition a critical path is "the longest path or sequence of connected activities, through the network" (Wiest & Levy 1977, p.26).
Table 1 below gives the early start (ES), early finish (EF), late start (LS) and late finish (LF) for the activities under normal duration.
Activity ES EF LS LF Slack
A 0 6 5 11 5
B 0 10 4 14 4
C 0 14 0 14 0
D 6 10 11 15 5
E 14 16 14 16 0
F 16 17 16 17 0
G 14 19 15 20 1
H 17 25 17 25 0
J 19 23 21 25 2
K 19 24 20 25 1
Bar chart showing earliest and latest dates for each activity, using normal cost durations
Critical Path under Normal Cost Duration
An analysis of the network in fig 1 shows that the An analysis of the data given under normal cost duration shows that the path CEFH is the longest sequence of connected activities and it is therefore the critical path. The duration of the critical path is 25 weeks. In other words this is the total duration of the project.
Although by definition a critical path in a network is of the longest duration, it does not mean that there cannot be more than one critical path. Besides by lengthening or shortening the duration of one or more activities, the critical path in a network could change. (Wagner 1972, p. 186).
The total normal cost of all the activities is 96000 pounds. To this add the weekly setup cost @ 4500 pounds per week and the total cost of the project is 208500 pounds.
Activities rescheduled after 16 weeks
In a review of project status 16 weeks from its start it was observed that activities A, B, C, and E were all completed on time. However activity F has been delayed by a
week and the duration of activity D is now 12 weeks. An extension of a week has been granted. The assumption here