2/28: More CPM: Crashing Roll call / return exams / return homework Review: Critical Path Management –Creating the CPM diagram –Calculating the critical.

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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:

CPM: Creating the Diagram Act.Dur.Follows A4- B5- C2A D4C E7C F5D G1B start A4A4 B5B5 C2C2 E7E7 D4D4 F5F5 G1G1 finish

CPM: Calculating the Critical Path start A4A4 B5B5 C2C2 E7E7 D4D4 F5F5 G1G1 finish Possible paths from start to finish: A-C-D-F A-C-E B-G = = = 6

CPM: Calculating the ES & EF start A | | B | | C | | E | | D | | F | | G | | finish Early start: how soon it can start Early finish: ES + Duration

CPM: Calculating the LS & LF start A | | 0 4 B | | 9 14 C | | 4 6 E | | 8 15 D | | 6 10 F | | G | | 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 B | | 9 14 C | | 4 6 E | | 8 15 D | | 6 10 F | | G | | finish Slack: how much “wiggle room” you have for an activity Slack = LS – ES = LF - EF S=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: Example Shorten project by 2 days while minimizing costs. ActivityDurationFollowsNormal Cost ($) Crashed Cost ($) Max. Time Reduction A4-$600$8002 B5-$1300$20002 C2A$400$7001 D4C$1000$12003 E7C $15004 F5D$300$2002 G1B$400--

Crashing Activity Times: Example Shorten project by 2 days while minimizing costs. First, calculate the cost/day to crash each activity. ActDurFollNorm Cost Crash Cost Max Red. Cost / day to crash A ( )/2 B C2A D4C E7C F5D G1B400--

Crashing Activity Times: Example Shorten project by 2 days while minimizing costs. Next, see what’s on the critical path. ActDurFollNorm Cost Crash Cost Max Red. Cost / day to crash CP? A Yes B No C2A Yes D4C Yes E7C No F5D Yes G1B400---(irrelevant)

Crashing Activity Times: Example Shorten project by 2 days while minimizing costs. Finally, see what the cheapest way to reduce is. ActDurFollNorm Cost Crash Cost Max Red. Cost / day to crash CP? A Yes B No C2A Yes D4C Yes E7C No F5D Yes G1B400---(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 A4A4 B5B5 C2C2 E7E7 D4D4 F5F5 G1G1 finish A-C-D-F A-C-E B-G = = = 6

Small Group Exercise Crash the project by 3 days while minimizing costs. ActDurFollNorm Cost Crash Cost Max Red. Cost / day to crash CP? A B4A C5A D6B E7C F5E G3B H2F

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