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


1

Colect requirements

2

-


2

Analyze processes

3

1


3

Analyze data

3

2


4

Design processes

7

2


5

Design data

6

2


6

Design screens

1

3, 4

7

Design reports

5

4, 5

8

Program

4

6, 7

9

Test and document

8

7


10

Install

2

8, 9

a. Draw a network diagram chart 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 one week?
e. Construct a Gantt chart for the project defined above.

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a. To draw a network diagram chart for the activities, we need to first list down the activities and their immediate predecessors:

Activity 1: Collect requirements (no immediate predecessor)
Activity 2: Analyze processes (predecessor: Activity 1)
Activity 3: Analyze data (predecessor: Activity 2)
Activity 4: Design processes (predecessor: Activity 2)
Activity 5: Design data (predecessor: Activity 2)
Activity 6: Design screens (predecessors: Activity 3, Activity 4)
Activity 7: Design reports (predecessors: Activity 4, Activity 5)
Activity 8: Program (predecessors: Activity 6, Activity 7)
Activity 9: Test and document (predecessor: Activity 7)
Activity 10: Install (predecessors: Activity 8, Activity 9)

Now, let's draw the network diagram chart:

----->Activity 1-------->Activity 2-------->Activity 4-------->Activity 7-------->Activity 8---------->
/ \
/ \
Start End
\ /
----->Activity 3-------->Activity 6----------------------------------------------------
\ /
----->Activity 5--------------------------------------------->Activity 9----->
\
\--->Activity 10--->

b. To calculate the earliest expected completion time, we use the forward pass method. We start with the start node and assign a time of 0 to it. Then, we move forward and calculate the earliest time for each activity, taking into account its predecessors.

Start node: 0
Activity 1: 0 + 2 = 2
Activity 2: 2 + 3 = 5
Activity 3: 5 + 3 = 8
Activity 4: 5 + 7 = 12
Activity 5: 5 + 6 = 11
Activity 6: max(8 + 1, 12 + 1) = 13
Activity 7: max(12 + 5, 11 + 5) = 17
Activity 8: 13 + 4 = 17
Activity 9: 17 + 4 = 21
Activity 10: max(17 + 2, 21 + 2) = 23
End node: 23

Therefore, the earliest expected completion time is 23 weeks.

c. The critical path is the longest path through the network diagram, which determines the minimum time required to complete the project. A delay in any activity on the critical path will result in a delay in the project completion. In this case, the critical path is:

Start --> Activity 2 --> Activity 4 --> Activity 7 --> Activity 8 --> Activity 9 --> Activity 10 --> End

d. If activity 6 is revised to take six weeks instead of one week, the earliest expected completion time and the critical path will be affected. Let's recalculate:

Start node: 0
Activity 1: 0 + 2 = 2
Activity 2: 2 + 3 = 5
Activity 3: 5 + 3 = 8
Activity 4: 5 + 7 = 12
Activity 5: 5 + 6 = 11
Activity 6: max(8 + 6, 12 + 6) = 18 (revised duration)
Activity 7: max(12 + 5, 11 + 5) = 17
Activity 8: 18 + 4 = 22 (updated duration)
Activity 9: 17 + 4 = 21
Activity 10: max(22 + 2, 21 + 2) = 24 (updated duration)
End node: 24

Therefore, the earliest expected completion time with the revised duration is 24 weeks. The critical path remains the same.

e. To construct a Gantt chart for the project, we need to list down the activities in chronological order and allocate the required time to each activity:

Activity 1: Collect requirements (2 weeks)
Activity 2: Analyze processes (3 weeks)
Activity 3: Analyze data (3 weeks)
Activity 4: Design processes (7 weeks)
Activity 5: Design data (6 weeks)
Activity 6: Design screens (1 week)
Activity 7: Design reports (5 weeks)
Activity 8: Program (4 weeks)
Activity 9: Test and document (4 weeks)
Activity 10: Install (2 weeks)

Now, we can visually represent the start and end dates for each activity in the Gantt chart.

a. To draw a network diagram chart for the activities, you will need to identify the activities and their immediate predecessors. Start by writing down the activities in a table format, including the activity number, activity name, time required, and immediate predecessors. Then, you can draw the network diagram by connecting the activities based on their dependencies.

Here is an example of a network diagram for the given activities:

1
/
2
/ | \
3 4 5
| | |
6 7 8
|
9
|
10

b. To calculate the earliest expected completion time, you need to determine the earliest start and finish times for each activity. Start by assigning an early start time of 0 to the first activity. Then, compute the early finish time for each activity by adding its duration to its early start time. Continue this process until you reach the last activity, and the early finish time for the last activity will be the earliest expected completion time.

Based on the given data, the earliest expected completion time is 24 weeks.

c. The critical path is the longest path through the network diagram and represents the activities that must be completed on time in order to avoid delaying the project. To determine the critical path, you need to calculate the total float for each activity. Total float is the amount of time an activity can be delayed without delaying the project completion time.

In this case, the critical path is as follows: 1 -> 2 -> 4 -> 7 -> 8 -> 9 -> 10

d. If activity 6 is revised to take six weeks instead of one week, it would delay the start of activity 7, activity 8, and subsequently activity 9. This delay would affect the total project completion time as it would increase the overall duration of the project.

e. To construct a Gantt chart for the project, you will need to plot the activities against the timeline. Start by creating a horizontal axis representing the timeline and a vertical axis representing the activities. Then, plot each activity as a horizontal bar on the Gantt chart, starting from its earliest start time and ending at its earliest finish time.

Here is an example of a Gantt chart for the given project:

Activity 1: |----2----|
Activity 2: |----3----|
Activity 3: |----3----|
Activity 4: |----7----|
Activity 5: |----6----|
Activity 6: |----1----|
Activity 7: |----5----|
Activity 8: |----4----|
Activity 9: |----8----|
Activity 10: |----2----|

The Gantt chart provides a visual representation of the project schedule and helps to identify the timeline for each activity.