# Example

The following example will illustrate the relationships between activities and how can you create them through the precedence diagram.

The example in the following table shows the activities for a cast concrete foundation under machine package and connects the machine with piping to the facilities, which is a simple example of knowing how to arrange activities, account for the overall time of the project, and identify the critical path.

Table 4.2 Example for foundation

 Item Activity Time (Days) Precedence Activity 100 Mobilization 3 – 200 Excavation 8 too 300 (Pouring concrete foundation and piping support) 10 200,100 400 Install the piping 4 300,100 500 Install the mechanical package 1 300 600 Put the grouting 1 300,500 700 Connect the piping 5 400,500 800 Commissioning and start-up 2 700

In the above table, the first column contains the item number or the code for that item according to the project and its activities and the sub activities. Also, the main activity code may be 100 and the sub activity may be 110 and so on, but the above example is a simple case.

The second column is the name of the activity, which describes the activity, and the third column is the time period for each activity in days.

The fourth column specifies the relationships between activities.

Figure (4.7) shows the precedence diagram, and in each diagram there is a number with its time duration. Figure (4.8) shows the early start and finish for each activity by using the following equation:

EF = ES + D,

where EF = early finish, EF = early start, and D = duration.

Start with activity number 100. The early finish (EF) of this activ­ity is 3 days. So transfer this value to activities 200 and 400 in the early start (ES) rectangle zone.

Item number 800 depends on 600 and 700. So it will take the higher value in the early finish (EF), which is 23 days. Put this number as the early start (ES) for activity 800.

For the last activity, which has an early finish at 25 days, transfer this value to the latest finish (LF) rectangular zone.

 3 400 7 Install piping 4
 3 400 7 install piping 14 4 18

Figure (4.9) shows the latest start and finish for each activity by applying the following equation:

LS = LF-D.

In Figure (4.9), we can subtract latest start (LS), from latest finish (LF) and subtract early start (ES) from early finish (EF). We get the value of zero, so it means that this activity is on the critical path. But if the difference has a value, it means that this activity can be delayed by this time period without affecting the total project time.

When we calculated the early and late schedule dates for our proj­ect, we found that sometimes the early and late schedule dates were the same, and in other activities the dates were different. In these activities there was a difference between the earliest day that we could start an activity and the latest day we could start the activity. The difference between these two dates is called "float," or some­times "slack." These terms mean exactly the same thing and can be used interchangeably. The float of an activity is the amount of time that the activity can be delayed without causing a delay in the project.

Table 4.3 Float time calculation

 No. Activity D Earliest Latest Float Critical ES EF LS LF TF FF 100 Mobilization 3 0 3 0 3 0 0 * 200 Excavation 8 3 11 3 11 0 0 * 300 Pouring concrete foundation and piping support 10 11 21 11 21 0 0 * 400 Install piping 4 3 7 14 18 11 0 500 Install the mechanical package 1 21 22 21 22 0 0 * 600 Put the grouting 1 22 23 22 23 0 0 * 700 Connect the piping 5 7 12 18 23 11 11 800 Commissioning and start up 2 23 25 23 25 0 0 *

Using computerized project management scheduling software, we can modify the list of activities on the critical path to include activities that are nearly on the critical path. This is important since the critical path method is a management method for managing project schedules. The activities that have zero float are the activi­ties that cannot be delayed without delaying the completion of the project. These are the activities that must be monitored closely if we want our project to finish on time. Conversely, the activities that are not on the critical path, those activities that have something other than zero float, need not be managed quite as closely. In addition, it is important to know which activities in the project may be delayed without delaying the project completion.

Resources from activities having float could be made available to do a "workaround" if the need should arise.

By performing a simple calculation, we can find 11 days as a total float (TF) for installing piping. But installing piping has zero free float (FF), as any delay will affect the connection of the piping. The piping connecting activity has an 11-day FF, as there is no activity after that to delay.