Problem 3

Using the computing algorithm, determine the slack times for the following AOA diagram. Identify the activities on the critical path.

Steps (Problems 3)

Perform a forward pass: Calculate the earliest start time (EST) and earliest finish time (EFT) for each activity in the network.

Begin at the start node, with an EST of 0.

Move forward through the network, calculating the EST and EFT for each activity by adding its duration to the EFT of its immediate predecessor.

If an activity has multiple predecessors, choose the largest EFT among them as the EST for that activity.

Perform a backward pass: Calculate the latest start time (LST) and latest finish time (LFT) for each activity in the network.

Begin at the end node, with an LFT equal to the EFT of the project (i.e., the EFT of the last activity in the network).

Move backward through the network, calculating the LST and LFT for each activity by subtracting its duration from the LST of its immediate successor.

If an activity has multiple successors, choose the smallest LST among them as the LFT for that activity.

Calculate the slack times: For each activity, calculate the total float or slack time by subtracting its EST from its LST (or its EFT from its LFT). The total float represents the amount of time an activity can be delayed without affecting the project duration.

Identify the critical path: The critical path consists of activities with a total float of zero. These activities cannot be delayed without extending the project duration. Trace the sequence of activities with zero total float from the start node to the end node to determine the critical path.