A project has been defined to contain the following list of activities along with their…


A project has been defined to contain the following list of activities along with their required times for completion.

Activity No.ActivityTime (weeks)Immediate Predecessors
1Collect requirements3 
2Analyze processes21
3Analyze data22
4Design processes62
5Design data33
6Design screens23,4
7Design reports44,5
9Test and document77

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:

E:\Umar Malik\Old CF\submission 28-12-18\IMG_20181228_123249\IMG_20181228_125447.png

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.NoTaskDuration (in Weeks)Precedence eventsEarliest Expected Time (TE)
ACollecting Requirements303
BAnalyze Processes215
CAnalyze Data227
DDesign Processes6211
EDesign Data3310
FDesign Screens23,413
GDesign Reports44,515
ITest & Documentation7722

The diagram below shows the T E as Earliest Expected Completion Time.

E:\Umar Malik\Old CF\submission 28-12-18\IMG_20181228_123249\IMG_20181228_121007.png

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:

E:\Umar Malik\Old CF\submission 28-12-18\IMG_20181228_123249\IMG_20181228_122654.png

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:

E:\Umar Malik\Old CF\submission 28-12-18\IMG_20181228_123249\IMG_20181228_123249.png

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:

Network diagram:

E:\Umar Malik\Old CF\submission 28-12-18\IMG_20181228_123249\IMG_20181228_125447 (2).png

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