Problem 17-5 For each of the problems listed, determine the following quantities
ID: 453495 • Letter: P
Question
Problem 17-5
For each of the problems listed, determine the following quantities for each activity: the earliest start time, latest start time, earliest finish time, latest finish time, and slack time. List the critical activities, and determine the expected duration of the project.
a.
b.
c.
For each of the problems listed, determine the following quantities for each activity: the earliest start time, latest start time, earliest finish time, latest finish time, and slack time. List the critical activities, and determine the expected duration of the project.
Explanation / Answer
EARLIEST TIMES
ES is the earliest time an activity can start.
ESij = Maximum (EFi)
EF is the earliest start time plus the activity time.
EFij = ESij + tij
LATEST TIMES
LS is the latest time an activity can start.
LSij = LFij – tij
LF is the latest start time plus the activity time.
LFij = Minimum (LSj)
Slack = LS-ES or LF-EF
Critical path is the one on which activities have zero slack.
Expected duration is sum of the duration of critical path activities
Using all this information:
1)
Critical Path = 1-3-6-9-11-12
Duration of the project = 10+6+4+5+6 = 31
2)
Critical Path = 1-2-5-7-8-9
Duration of the project = 5+18+10+11+9+2 = 55
3)
Critical Path = F-H-J-K
Duration of the project = 8+9+14+6 = 37 days
Activity Activity time ES EF LF LS Slack 1–2 4 0 4 10 6 6 2–4 9 4 13 19 10 6 4–7 5 13 18 24 19 6 7–10 2 18 20 26 24 6 10–12 3 21 24 31 28 7 2–5 8 4 12 19 11 7 5–8 7 12 19 26 19 7 8–10 2 19 21 28 26 7 1–3 10 0 10 10 0 0 3–6 6 10 16 16 10 0 6–9 4 16 20 20 16 0 9–11 5 20 25 25 20 0 11–12 6 25 31 31 25 0