CHAPTER 7 | NETWORK MODEL: CPM
Group 3: Alioden, Bantilan, Mipantao, Samsodin Step 2. Compute the cost slope of each activity
using the time and cost data with the formula:
CPM is used to evaluate plans on
expediting project completion. Expediting Cost slope = (Crash Cost-Normal
projects require more resources resulting in Cost)/(Normal Time-Crash Time)
higher cost. However, there is a compelling
reason why there is a need to expedite project in
spite of the higher cost. Considerable savings or
profits may be achieved, from other sources
when projects are finished much ahead of
schedule.
Steps in the CPM Analysis
The CPM has four steps, they are as follows: Step 3. Draw all-normal time network and the
all-crash time network. In each network identify
Step 1 and list down the paths and determine critical
Determination of normal and crash times, and path.
the corresponding costs.
3.1. All-normal time network
Step 2
Computation of the cost slopes.
Step 3
Drawing of the all-normal and all-crash time
networks and determination of paths and the
critical paths.
3.2. Paths in the all normal time network
Step 4.a
Doing the expansion process.
Step 4.b
Conducting the compression process.
3.3. All-crash time network
Applying CPM Analysis on Mr. Go’s Case 3.4. Paths in the all crash time network
Step 1. Determine the normal and crash times,
and the corresponding normal and crash costs.
Step 4.a. Conduct an expansion process
4.a.1. Based on the all-crash time net-
work, list all the non-critical activities
from highest to lowest in terms of cost
slope, list also the maximum expansion
of each activity.
Non-critical Cost Slopes Maximum
Activities (P000) Expansion Activity g is expanded by 2 weeks.
(nt-ct) Activity g time duration is now 4+2 = 6 weeks
Cost savings is 2 x P60,000 = P120,000
f P80 11-7=4
4th Expansion: Activity b
e 70 5-2=3 Cost Slope = P50,000 with Maximum
Expansion = 2 weeks
g 60 6-4=2
b 50 9-7=2
c 30 7-4=3
4.a.2. Expand the non-critical activities
in the order of their cost slopes, from highest to Activity b is expanded by 1 week.
lowest and without going over the maximum Activity b time duration is now 7+1 = 8 weeks
expansion of each activity and the desired Cost savings is 1 x P50,000 = P50,000
project time duration. All paths must have time
duration equal or less than that of the desired 5th Expansion: Activity c
project time completion which in this case, is 17 Cost Slope = P30,000 with Maximum
weeks. Expansion = 3 weeks
1st Expansion: Activity f
Cost Slope = P80,000 with Maximum
Expansion = 4 weeks
4.a.3. Summarize the expanded non-
critical activities and the savings thereof. Also
check if the expansions are feasible.
Activity f is expanded by 2 weeks.
Activity f time duration is now 7+2 = 9 weeks
Cost savings is 2 x P80,000 = P160,000
2nd Expansion: Activity e
Cost Slope = P70,000 with Maximum
Expansion = 3 weeks
4.a.4. Adjust the network to reflect the
new time duration of the pants with expanded
activities.
Activity e is expanded by 1 week.
Activity e time duration is now 2+1 = 3 weeks
Cost savings is 1 x P70,000 = P70,000
3rd Expansion: Activity g
Cost Slope = P60,000 with Maximum
Expansion = 2 weeks
4.a.5 List the paths. Check that no path 4.b.4. Adjust the network to reflect the
has time duration over 17 weeks. compressed activities and to check that all paths
have time duration of 20 or less than 20 weeks.
Step 4.b. Conduct a compression process. This
process involves crashing of critical activities in
an all-normal time network until the desired
completion time duration is obtained.
4.b.5. Compute cost of the desired
4.b.1. List all critical activities in the all- completion duration (20 weeks).
normal time network with their respective cost
slopes (refer to Step 2) starting from the activity
with the lowest cost slope down to the activity
with the highest cost slope. List also the
maximum compression of each activity.
SUMMARY
✓ The all-normal time duration of the
government project is 25 weeks.
✓ The all-normal time profit is P940,000.
✓ The all-crash time duration of the
government project is 17 weeks.
4.b.2. Determine the needed time
reduction. a) If he will crash all activities to the
maximum and finish the project in
17 weeks, he will lose P60,000.
b) If he will expedite the project com-
pletion in 17 weeks but leave some
4.b.3. Compress critical activities activities not crashed, he will gain
starting with the activity with the lowest cost P340,000.
slope, without going over the maximum c) If he will expedite the project com-
compression of each activity and the needed pletion in 20 weeks, he will earn
reduction in time. Compute compression costs. bigger, P790,000.
❖ What is the all-normal time duration of
the government project? 25 weeks
❖ Will the all-normal time allow Mr. Go
to take the private project? No
❖ How much will Mr. Go gain if he will
complete the project following all-nor-
mal time? P940,000
❖ What is the shortest completion time of
the government project if Mr. Go will
expedite? 17 weeks
❖ Will this allow Mr. Go to take the pri-
vate project? Yes
❖ Will Mr. Go gain from the government
project if he will expedite it? Yes
