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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 - PowerPoint PPT Presentation
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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 you’re willing to spend money to get the project done sooner.
• Small Group Exercise
• Homework for the week
Exam Scores• Maximum: 100% (four people)
• Minimum: 63%
• Mean & Median: 88%
• Correct exams are available at:http://www.adbook.net/teach022/305/m.htm
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
start
A4
B5
C2
E7
D4 F
5
G1
finish
CPM: Calculating the Critical Path
start
A4
B5
C2
E7
D4 F
5
G1
finish
Possible paths from start to finish:A-C-D-F A-C-EB-G
4+2+4+5 = 154+2+7 = 135+1 = 6
CPM: Calculating the ES & EF
start
A | 0 4 4 |
B | 0 55 |
C | 4 62 |
E | 6 137 |
D | 6 104 | F | 10 15
5 |
G | 5 61 |
finish
Early start: how soon it can startEarly finish: ES + Duration
CPM: Calculating the LS & LF
start
A | 0 4 4 | 0 4
B | 0 55 | 9 14
C | 4 62 | 4 6
E | 6 137 | 8 15
D | 6 104 | 6 10 F | 10 15
5 | 10 15
G | 5 61 | 14 15
finish
Late finish: the last possible time it must be done to not affect the overall project time.Late start: LF - Duration
CPM: Calculating the slack
start
A | 0 4 4 | 0 4
B | 0 55 | 9 14
C | 4 62 | 4 6
E | 6 137 | 8 15
D | 6 104 | 6 10 F | 10 15
5 | 10 15
G | 5 61 | 14 15
finish
Slack: how much “wiggle room” you have for an activitySlack = LS – ES = LF - EF
S=0 S=0
S=0S=0
S=9
S=2
S=9
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?
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?
Crashing Activity Times: ExampleShorten 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 - -
Crashing Activity Times: ExampleShorten 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 - -
Crashing Activity Times: ExampleShorten project by 2 days while minimizing costs.
Next, see what’s 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)
Crashing Activity Times: ExampleShorten 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)
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.
start
A4
B5
C2
E7
D4 F
5
G1
finish
A-C-D-F A-C-EB-G
4+2+4+5 = 154+2+7 = 135+1 = 6
Small Group ExerciseCrash 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
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