A project has been defined to contain the following list of activities along with their required times for completion.
|Activity No.||Activity||Time (weeks)||Immediate Predecessors|
|9||Test and document||7||7|
a. Draw a network diagram for the activities.
b. Calculate the earliest expected completion time.
c. Show the critical path.
d. What would happen if activity 6 were revised to take six weeks instead of two weeks?
a. Network diagram of the Project activities
• The project activities includescollection of requirements, analyzing processes, analyzing data, designing processes, designing data, designing screens, program, test and documentation, install.
• Image displaying network diagram of various activities is as shown:
b. Calculating Expected Time
Expected time is theamount of time that is needed to complete each task in the project. By using program evaluation review technique, user can calculate expected time for an activity.
Formula for calculating Expected Time:
In the above formula “o” represents optimistic completion time for task, “r” represents realistic completion time for task, and “p” represents pessimistic completion time for task respectively. But here, the values of Estimated times are already given.
Earliest Expected Time: Earliest expected time is also called as early finish defined as the amount that can be required to complete the task of the project.
Here ES is the Early Start of the task. It is the Early Finish of the preceding task or it can be Zero if it is the first task in the project.
For the task A, (Early Start is 0 and the duration is 3)
For the task B, (ES = EF of Preceding task + duration) and similarly, it is calculated for the entire task.
For the task J,
For the task I, and similarly it is calculated for the entire task.
Table displaying Earliest Expected Time in tabular format:
|S.No||Task||Duration (in Weeks)||Precedence events||Earliest Expected Time (TE)|
|I||Test & Documentation||7||7||22|
The diagram below shows the T E as Earliest Expected Completion Time.
c. Critical path
critical path is the amount of time to take completion of the project.
- Critical path deals with time constraints.
- Whenever there are a need and urgency in developing the project time constraint will play a major role.
- The developer has to put maximum effort in developing the project within the time-bound.
- The TL is constructed to compute the critical path.
Diagram below shows the T L for e very path:
Consider the following paths to reach the destination in this project:
ABDGIJ = 168days
ABCEGIJ = 161days
ABCFHJ = 112days
ABCEGHJ = 147days
ABDFHJ = 140days
Hence, the path ABDGIJ is critical path because this is the longest path among four paths.
Critical path is shown in following diagram:
d. Changes Made in Duration for Task
After changes done for the task 6, user will get two critical paths having same length.
ABDFHJ = 168days
ABDGIJ = 168days
Due to this Network diagram will be modified according to changes.
Screenshot displaying Network diagram is shown below: