2/28: More CPM: Crashing

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2/28 More CPM Crashing

• Roll call / return exams / return homework
• Review Critical Path Management
• Creating the CPM diagram
• Calculating the critical path
• Calculating the ES EF, the LS LF
• Calculating the slack
• Crashing When youre willing to spend money to
  get the project done sooner.
• Small Group Exercise
• Homework for the week

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Exam Scores

• Maximum 100 (four people)
• Minimum 63
• Mean Median 88
• Correct exams are available athttp//www.adbook.
  net/teach022/305/m.htm

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CPM Creating the Diagram
Act. Dur. Follows
A 4 -
B 5 -
C 2 A
D 4 C
E 7 C
F 5 D
G 1 B
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CPM Calculating the Critical Path
Possible paths from start to finish A-C-D-F
A-C-E B-G
4245 15 427 13 51 6
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CPM Calculating the ES EF
Early start how soon it can start Early finish
ES Duration
D 6 10 4
F 10 15 5
A 0 4 4
C 4 6 2
start
finish
E 6 13 7
B 0 5 5
G 5 6 1
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CPM Calculating the LS LF
Late finish the last possible time it must be
done to not affect the overall project
time. Late start LF - Duration
D 6 10 4 6 10
F 10 15 5 10 15
A 0 4 4 0 4
C 4 6 2 4 6
start
finish
E 6 13 7 8 15
B 0 5 5 9 14
G 5 6 1 14 15
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CPM Calculating the slack
Slack how much wiggle room you have for an
activity Slack LS ES LF - EF
S0
S0
D 6 10 4 6 10
S0
S0
F 10 15 5 10 15
A 0 4 4 0 4
C 4 6 2 4 6
start
finish
S2
E 6 13 7 8 15
S9
S9
B 0 5 5 9 14
G 5 6 1 14 15
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Crashing Buying Time

• Sometimes you can buy a quicker time for an
  activity
• Paying overtime
• Paying for another worker to help
• Paying for guaranteed quicker delivery (EX
  FedEx)
• But is it worth it?

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Crashing Activity Times

• Things to consider
• Is the activity on the critical path?
• How much will it cost to crash the activity?
• Are there other activities that are more
  cost-effective to crash?
• How much do you need to crash the project time?

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Crashing Activity Times Example

• Shorten project by 2 days while minimizing costs.

Activity Duration Follows Normal Cost () Crashed Cost () Max. Time Reduction
A 4 - 600 800 2
B 5 - 1300 2000 2
C 2 A 400 700 1
D 4 C 1000 1200 3
E 7 C 1200 1500 4
F 5 D 300 200 2
G 1 B 400 - -
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Crashing Activity Times Example

• Shorten project by 2 days while minimizing costs.
• First, calculate the cost/day to crash each
  activity.

Act Dur Foll Norm Cost Crash Cost Max Red. Cost / day to crash
A 4 - 600 800 2 (800-600)/2
B 5 - 1300 2000 2
C 2 A 400 700 1
D 4 C 1000 1200 3
E 7 C 1200 1500 4
F 5 D 300 200 2
G 1 B 400 - -
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Crashing Activity Times Example

• Shorten project by 2 days while minimizing costs.
• Next, see whats on the critical path.

Act Dur Foll Norm Cost Crash Cost Max Red. Cost / day to crash CP?
A 4 - 600 800 2 100 Yes
B 5 - 1300 2000 2 450 No
C 2 A 400 700 1 300 Yes
D 4 C 1000 1200 3 66.66 Yes
E 7 C 1200 1500 4 75 No
F 5 D 300 200 2 50 Yes
G 1 B 400 - - - (irrelevant)
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Crashing Activity Times Example

• Shorten project by 2 days while minimizing costs.
• Finally, see what the cheapest way to reduce is.

Act Dur Foll Norm Cost Crash Cost Max Red. Cost / day to crash CP?
A 4 - 600 800 2 100 Yes
B 5 - 1300 2000 2 450 No
C 2 A 400 700 1 300 Yes
D 4 C 1000 1200 3 66.66 Yes
E 7 C 1200 1500 4 75 No
F 5 D 300 200 2 50 Yes
G 1 B 400 - - - (irrelevant)
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Crashing Activities Watch Out

• If we had to crash the project by more than two
  days, we would have had to look again the
  critical path may change.

A-C-D-F A-C-E B-G
4245 15 427 13 51 6
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Small Group Exercise

• Crash the project by 3 days while minimizing
  costs.

Act Dur Foll Norm Cost Crash Cost Max Red. Cost / day to crash CP?
A 6 - 600 900 2
B 4 A 500 700 2
C 5 A 1000 1200 1
D 6 B 1300 1600 4
E 7 C 800 1000 3
F 5 E 400 550 2
G 3 B 500 800 2
H 2 F 1100 1500 3
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Homework Do it on PAPER

• Ch. 10 21 a b
• Ch. 10 22 b c
• Ch. 10 24 a, c, d (use 26 weeks), f