A project involves eight activities with the precedence relationship and duration as shown in the table below. The slack for the activity D is __________ hours (answer in integer).
Show Hint
To calculate the slack of an activity, use the formula:
\[
{Slack} = {LS} - {ES}
\]
If the slack is positive, the activity has some flexibility in its scheduling.
Step 1: Understanding the precedence relationships.
From the table, the immediate predecessors and durations of activities are as follows:
A: No predecessors, duration = 4 hours
B: Predecessor A, duration = 8 hours
C: Predecessor A, duration = 5 hours
D: Predecessor B, duration = 2 hours
E: Predecessor B, duration = 7 hours
F: Predecessor C, duration = 6 hours
G: Predecessor D, duration = 3 hours
H: Predecessors E, F, G, duration = 9 hours
Step 2: Calculating the Early Start (ES) and Early Finish (EF) times.
We begin by calculating the Early Start and Early Finish for each activity by working forward from the start:
ES for Activity A = 0, EF for Activity A = 4 (0 + 4)
ES for Activity B = 4, EF for Activity B = 12 (4 + 8)
ES for Activity C = 4, EF for Activity C = 9 (4 + 5)
ES for Activity D = 12, EF for Activity D = 14 (12 + 2)
ES for Activity E = 12, EF for Activity E = 19 (12 + 7)
ES for Activity F = 9, EF for Activity F = 15 (9 + 6)
ES for Activity G = 14, EF for Activity G = 17 (14 + 3)
ES for Activity H = 19, EF for Activity H = 28 (19 + 9)
Step 3: Calculating the Late Start (LS) and Late Finish (LF) times.
Next, calculate the Late Finish (LF) and Late Start (LS) by working backward from the project completion:
LF for Activity H = 28, LS for Activity H = 19 (28 − 9)
LF for Activity G = 19, LS for Activity G = 16 (19 − 3)
LF for Activity F = 19, LS for Activity F = 13 (19 − 6)
LF for Activity E = 19, LS for Activity E = 12 (19 − 7)
LF for Activity D = 16, LS for Activity D = 14 (16 − 2)
LF for Activity C = 12, LS for Activity C = 7 (12 − 5)
LF for Activity B = 12, LS for Activity B = 4 (12 − 8)
LF for Activity A = 4, LS for Activity A = 0 (4 − 4)
Step 4: Calculating the Slack.
The slack for each activity is calculated as:
\[
\text{Slack} = \text{LS} - \text{ES}
\]
For Activity D:
\[
\text{Slack for D} = 14 - 12 = 2 \text{ hours}
\]
Step 5: Conclusion.
The slack for Activity D is 2 hours.
