The following CPM network has estimates of the normal time in weeks listed for t
ID: 435788 • Letter: T
Question
The following CPM network has estimates of the normal time in weeks listed for the activities:
a. Identify the critical path.
b. What is the length of time to complete the project?
Number of weeks
c. Which activities have slack, and how much?
Here is a table of normal and crash times and costs.
d-1. Which activities would you shorten to cut two weeks from the schedule in a rational fashion?
d-2. What would be the total incremental cost?
Total incremental cost $
d-3. Is the critical path changed?
Explanation / Answer
The possible parallel paths and their corresponding durations as follows :
A-B-D-F-G = 7 + 4 + 6 + 5 +2 = 24
A-B-D-E-G = 7 + 4 + 6 + 3 + 2 = 22
A-C-D-F-G = 7 + 2 + 6 + 5 + 2 = 22
A-C-D-E – G = 7 + 2 + 6 + 3 + 2 = 20
Out of the above, ABDBFG has the longest duration and hence forms the critical path .
CRITICAL PATH = A-B-D-F-G
Length of time to complete the project is same as duration of the critical path . Therefore, length of time to complete the project is 24 weeks
LENGTH OF TIME TO COMPLETE THE PROJECT = 24 WEEKS
It is to be noted that all activities lying on critical path have NO slack.
Therefore activities which do not have slack are : A/B/D/F/G
Slack for activity E = Duration A-B-D-F-G – Duration A-B-D-E-G = 24 – 22 = 2 weeks
Slack for activity C = Duration A-B-D-F-G – Duration A-C-D-F-G = 24 – 22 = 2 weeks
SLACK : C , 2 WEEKS AND E , 2 WEEKS
Activities which should be cut to shorten total duration by 2 weeks must be those activities lying on critical path. Therefore, combination of activities which should be crashed/cut must be from A-B-D-F-G
Cost of crashing activity A by 1 day ( 7 to 6 days ) = $9800 - $7500 = $2300
Cost of crashing activity B by 1 day ( 4 days to 3 days ) = $8500 - $6000 = $2500
Cost of crashing activity D by 2 days ( 6 days to 4 days ) = $4800 - $2500 = $2300
Cost of crashing activity F by 1 day ( 5 days to 4 days ) = $7000 - $5200 = $1800
Cost of crashing activity G by 1 day ( 2 days to 1 day ) = $7800 - $4250 = $3550
From the above data , it is thus evident that most ECONOMIC way to cut 2 weeks from the schedule is to crash activity D by 2 days since it is the LEAST COST option.
Th next best option is to choose activity A and F with incremental cost of $2300 + $1800 = $4100 , which is also not given as part of the options
The next best option is to choose activity B and F with incremental cost of $2500 + $1800 = $4300
ACTIVITIES SHOULD BE CHOSEN = B, F
TOTAL INCREMENTAL COST = $4300
WIL THE CRITICAL PATH CHANGE : NO
CRITICAL PATH = A-B-D-F-G