1. 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

2. Exam Scores Maximum: 100% (four people) Minimum: 63% Mean & Median: 88% Correct exams are available at: http://www.adbook.net/teach022/305/m.htm http://www.adbook.net/teach022/305/m.htm

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

4. 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 4+2+4+5 = 15 4+2+7 = 13 5+1 = 6

5. CPM: Calculating the ES & EF start A | 0 4 4 | B | 0 5 5 | C | 4 6 2 | E | 6 13 7 | D | 6 10 4 | F | 10 15 5 | G | 5 6 1 | finish Early start: how soon it can start Early finish: ES + Duration

6. CPM: Calculating the LS & LF start A | 0 4 4 | 0 4 B | 0 5 5 | 9 14 C | 4 6 2 | 4 6 E | 6 13 7 | 8 15 D | 6 10 4 | 6 10 F | 10 15 5 | 10 15 G | 5 6 1 | 14 15 finish Late finish: the last possible time it must be done to not affect the overall project time. Late start: LF - Duration

7. CPM: Calculating the slack start A | 0 4 4 | 0 4 B | 0 5 5 | 9 14 C | 4 6 2 | 4 6 E | 6 13 7 | 8 15 D | 6 10 4 | 6 10 F | 10 15 5 | 10 15 G | 5 6 1 | 14 15 finish Slack: how much “wiggle room” you have for an activity Slack = LS – ES = LF - EF S=0 S=9 S=2 S=9

8. 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?

9. 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?

10. 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--

11. 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 A4-6008002(800-600)/2 B5-130020002 C2A4007001 D4C100012003 E7C 15004 F5D3002002 G1B400--

12. 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? A4-6008002100Yes B5-130020002450No C2A4007001300Yes D4C10001200366.66Yes E7C12001500475No F5D300200250Yes G1B400---(irrelevant)

13. 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? A4-6008002100Yes B5-130020002450No C2A4007001300Yes D4C10001200366.66Yes E7C12001500475No F5D300200250Yes G1B400---(irrelevant)

14. 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 4+2+4+5 = 15 4+2+7 = 13 5+1 = 6

15. Small Group Exercise Crash the project by 3 days while minimizing costs. ActDurFollNorm Cost Crash Cost Max Red. Cost / day to crash CP? A6-6009002 B4A5007002 C5A100012001 D6B130016004 E7C80010003 F5E4005502 G3B5008002 H2F110015003

16. 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