Question

Draw the AON network for the following project and answer the questions that follow. Determine ES, EF, LS, LF, and slack for each activity and then determine the total project completion time and the critical path for the project.

Activity Immediate predecessors Time (days)
A - 5
B - 3
C A, B 2
D B 4
E C, D 5
f E 2

Answer 1

To determine the AON network and critical path, one must calculate the ES, EF, LS, LF, and slack for each activity. In the given scenario, activity A, B, C, D, E, and F need to be analyzed for predecessors and durations to determine the overall timeline. The critical path, with a duration of 14 days, consists of activities A-C-E-F.

Step-by-step explanation:

Activity-on-Node (AON) Network and Critical Path Method

The Activity-on-Node (AON) network is a project management tool used to visualize the order of activities and determine the critical path and overall project duration. The steps to calculate the Early Start (ES), Early Finish (EF), Late Start (LS), Late Finish (LF), and slack for each activity along with determining the critical path are as follows:

1. Draw the network diagram with nodes representing the activities and arrows showing dependencies.
2. Identify all possible paths from start to end and calculate the duration of each path.
3. Calculate ES and EF for each activity, starting from the beginning of the project.
4. Calculate LS and LF for each activity, starting from the end of the project.
5. Determine the slack for each activity by subtracting ES from LS or EF from LF.
6. The path with zero slack is the critical path.

For the given project:

• Activity A and B have no predecessors and can start at day 0. ES️=0, EF=A.duration=5 for A and EF=B.duration=3 for B.
• Activity C can start after A and B are finished, so ES=C is max(EF️=A, EF️=B)=5, EF=ES+C.duration=7.
• Activity D follows B, thus ES️=D=EF️=B=3, EF=ES+D.duration=7.
• Activity E can start after C and D are completed, so ES️=E=max(EF️=C, EF️=D)=7, EF=ES+E.duration=12.
• Finally, activity F follows E, therefore ES️=F=EF️=E=12 and EF=ES+F.duration=14, indicating the project completion time is 14 days.

Backtracking from the project end time, you set LF️=F to project duration, thus LS️=F=LF-F.duration=12. Continuing this process for each activity gives the LS and LF values. The critical path is the sequence of activities with zero slack; here, it is A-C-E-F with a duration of 14 days.