Chapter 14- Solved Problems
Problem 1
You have been assigned to a project team with the following tasks. Your assigned tasks are: (1) create a Gantt chart for the project, (2) calculate early and late start and finish times for all tasks, (3) designate the critical path, and (4) calculate slack.
Task / Estimate of Completion Time (days) / PredecessorsA / 3 / --
B / 2 / A
C / 5 / A
D / 8 / B,C
E / 3 / --
F / 4 / D,E
G / 1 / F
H / 9 / G
Answer Problem 1
TASK / DURATIONA / 3
B / 2
C / 5
D / 8
E / 3
F / 4
G / 1
H / 9
TASK / DURATION / ES / EF / LS / LF / SLACK
A / 3 / 0 / 3 / 0 / 3 / 0
B / 2 / 3 / 5 / 6 / 8 / 3
C / 5 / 3 / 8 / 3 / 8 / 0
D / 8 / 8 / 16 / 8 / 16 / 0
E / 3 / 0 / 3 / 13 / 16 / 13
F / 4 / 16 / 20 / 16 / 20 / 0
G / 1 / 20 / 21 / 20 / 21 / 0
H / 9 / 21 / 30 / 21 / 30 / 0
Tasks on the critical path are designated with a bold line in the above diagram and by shading in the above table.
Problem 2
You have been assigned to a project that is failing. You have been asked to evaluate the project to determine whether it is possible to decrease the time to completion in an effort to save it. The remaining task times are given below. Your task is to: (1) draw the network diagram, (2) calculate LS, LF, ES, EF for each task, (3) designate the critical path, (4) calculate slack, and (5) evaluate alternatives for reducing the project delivery schedule.
Task / Estimate of Completion Time (days) / PredecessorsP / 10 / --
Q / 12 / P
R / 7 / P
S / 21 / P
T / 34 / Q,R,S
U / 18 / --
V / 4 / T,U
W / 11 / --
X / 27 / W
Y / 15 / Y
Z / 8 / V,Y
Crashing Options:
Option A: Cost $5000, reduces the time for task X by 50%
Option B: Cost $1000, reduces time on task Q by 25%
Option C: Cost $10,000, reduces time for task V by 25%
Option D: Cost $25,000, reduces time for task P by 30%
Answer Problem 2
TASK / DURATION / ES / EF / LS / LF / SLACKP / 10 / 0 / 10 / 0 / 10 / 0
Q / 12 / 10 / 22 / 19 / 31 / 9
R / 7 / 10 / 17 / 14 / 31 / 4
S / 21 / 10 / 31 / 10 / 31 / 0
T / 34 / 31 / 65 / 31 / 65 / 0
U / 18 / 0 / 18 / 47 / 65 / 47
V / 4 / 65 / 69 / 65 / 69 / 0
W / 11 / 0 / 11 / 12 / 23 / 12
X / 27 / 11 / 38 / 23 / 50 / 12
Y / 15 / 38 / 53 / 50 / 65 / 12
Z / 8 / 69 / 77 / 69 / 77 / 0
Tasks on the critical path are designated with a bold line in the above diagram and by shading in the above table.
Options A and B are not on the critical path and therefore would be rejected. Options C and D are on the critical path. Cost benefit analysis would be conducted to determine whether reducing the completion time by 4 days is worth $35,000.
Problem 3
Inglefield Construction is currently in the planning phase for installation of the roof of a major stadium project. The planning team has identified 15 tasks that must be accomplished and key personnel have given estimates for completing each. As a member of the planning team you have been tasked with four deliverables: (1) draw the network diagram, (2) calculate the early and late start times for each task, (3) identify the critical path, (4) calculate slack times for all tasks.
Task / Estimate of Completion Time (days) / PredecessorsA / 4 / --
B / 7 / --
C / 9 / A,B
D / 3 / C
E / 10 / D
F / 22 / B
G / 3 / --
H / 8 / G
I / 14 / F
J / 30 / H
K / 3 / I, J
L / 8 / --
M / 10 / K,L
N / 1 / M
O / 28 / N
Answer Problem 3
Task / Duration / ES / EF / LS / LF / SlackA / 4 / 0 / 4 / 59 / 63 / 59
B / 7 / 0 / 7 / 0 / 7 / 0
C / 9 / 7 / 16 / 63 / 72 / 56
D / 3 / 16 / 19 / 72 / 75 / 56
E / 10 / 19 / 29 / 75 / 85 / 56
F / 22 / 7 / 29 / 7 / 29 / 0
G / 3 / 0 / 3 / 2 / 5 / 2
H / 8 / 3 / 11 / 5 / 13 / 2
I / 14 / 29 / 43 / 29 / 43 / 0
J / 30 / 11 / 41 / 13 / 43 / 2
K / 3 / 43 / 46 / 43 / 46 / 0
L / 8 / 0 / 8 / 38 / 46 / 38
M / 10 / 46 / 56 / 46 / 56 / 0
N / 1 / 56 / 57 / 56 / 57 / 0
O / 28 / 57 / 85 / 57 / 85 / 0
Tasks on the critical path are designated with a bold line in the above diagram and by shading in the above table.