Problem 3.2, HR7E WBS R. Saltzman

Level Level ID No. Activity1 1.0 Develop political campaign2 1.1 Fund-raising plan3 1.11 Set initial goals for fund-raising3 1.12 Set strategy, including identifying sources3 1.13 Raise the funds2 1.2 Develop position on major issues3 1.21 Identify voters' concerns3 1.22 Analyzer competitor's voting record3 1.23 Establish position on major issues2 1.3 Staffing for campaign3 1.31 Email old college classmates & friends3 1.32 Solicit resumes from local law school students3 1.33 Review resumes & call prospectives3 1.34 Interview & select key aides2 1.4 Paperwork compliance for candidacy3 1.41 File papers with Florida Election Commission3 1.42 Make tax records publicly available2 1.5 Ethical plan/issues3 1.51 Put investments into blind trust

Problem 3.3, HR7E AON & Critical Path R. Saltzman

Immediate TimeActivity Predecessors (Days)

A - 3B A 4C A 6D B 6E B 4F C 4G D 6H E, F 8

Draw the activity-on-node (AON) project network.ES EF

D, 6 G, 6 LS LF

B, 47 13 13 199 15 15 21

A, 3 3 7 E, 45 9

H, 80 3 7 110 3 C, 6 9 13

F, 4 13 2113 21

3 93 9 9 13

9 13

Project should take 21 days.Critical activities are shown in red.

Key

Problem 3.4, HR7E AOA/AON & Critical Path R. Saltzman

Immediate TimeActivity Predecessors (Days)

A - 5B A 2C A 4D B 5E B 5F C 5G E, F 2H D 3I G, H 5

The activity-on-arc (AOA) network is given in the back of the book.

Below is an activity-on-node (AON) representation of the project network.ES EF

D, 5 H, 3 LS LF

B, 27 12 12 158 13 13 16 I, 5

A, 5 5 7 E, 56 8

G, 2 16 210 5 7 12 16 210 5 C, 4 9 14

F, 5 14 1614 16

5 95 9 9 14

9 14

Project should take 21 days.Critical activities are shown in red.

Key

Problem 3.5, HR7E AOA & Critical Path R. Saltzman

TimeActivity Nodes (Days)

J 1-2 10K 1-3 8L 2-4 6M 2-3 3N 3-4 2O 4-5 7P 3-5 5

Draw the activity-on-arc (AOA) network.ES EF

0 10 LS LF0 10 10 16

J, 10 10 16start L, 6 16 23

16 2310 13 O, 711 14

M, 3 13 15 doneK, 8 N, 2 14 16

0 86 14 P, 5

13 1818 23

Project should take 23 days.Critical path is shown in red.

Key

1 2

4

5

3

Problem 3.7, HR7E AON & Critical Path R. Saltzman

Immed. TimeActivity Predec. (Hours)

A - 6.0B - 7.2C A 5.0D B, C 6.0E B, C 4.5F D 7.7G E, F 4.0

a) Draw the activity-on-node (AON) project network.ES EFLS LF

A, 6 C, 5 slack

0.0 6.0 6.0 11.0 D, 6 F, 7.70.0 6.0 6.0 11.00.0 0.0

B, 7.2 11.0 17.0 17.0 24.7 G, 411.0 17.0 17.0 24.7

0.0 0.00.0 7.2 E, 4.5 24.7 28.73.8 11.0 24.7 28.73.8 0.0

11.0 15.520.2 24.7

9.2

b) Critical path is shown in red.c) Total project completion time is 28.7 hours.d) Draw a Gantt chart for the project (uses the EF and ES times):

ActivityABCDEFG

0 4 8 12 16 20 24 28 Hours

Key

Problem 3.9, HR7E AON & Critical Path R. Saltzman

Immediate TimeActivity Predecessors (Hours)

A - 20B A 60C A 100D B 30E C, D 20F E 10

Draw the activity-on-node (AON) project network.ES EF

D, 30 LS LF

B, 6080 11090 120 E, 20 F, 10

A, 20 20 8030 90

120 140 140 1500 20 120 140 140 1500 20 C, 100

20 12020 120

Project should take 150 hours.Critical activities are shown in red.

Key

Problem 3.11, HR7E AON & Critical Path R. Saltzman

Immed. TimeActivity Predec. (Weeks)

A - 6B - 7C A 3D A 2E B 4F B 6G C, E 10H D, F 7

a) Draw the activity-on-node (AON) project network.ES EF

C, 3 LS LFslack

6 9 G, 10A, 6 8 11

2D, 2 11 21

0 6 11 212 8 6 8 02 12 14

6 H, 7E, 4

B, 77 11 13 207 11 14 21

0 7 0 10 7 F, 60

7 138 141

b) Critical path is shown in red.c) Total project completion time is 21 weeks.

Key

Problem 3.14, HR7E Probabilistic Times R. Saltzman

Immed. Mean VarianceActivity Predec. a m b t σ2

A - 3 6 8 5.83 0.69B - 2 4 4 3.67 0.11C - 1 2 3 2.00 0.11D C 6 7 8 7.00 0.11E B, D 2 4 6 4.00 0.44F A, E 6 10 14 10.00 1.78G A, E 1 2 4 2.17 0.25H F 3 6 9 6.00 1.00I G 10 11 12 11.00 0.11 ES EFJ C 14 16 20 16.33 1.00 LS LFK H, I 2 8 10 7.33 1.78 slack

Draw the activity-on-node (AON) project network.

13.00 15.17 15.17 26.1715.83 18.00 18.00 29.00

0 5.83 13.00 23.00 2.83 2.837.17 13.00 13.00 23.007.17 0.00

23.00 29.000 3.67 9.00 13.00 23.00 29.00

5.33 9.00 9.00 13.00 0.00 29.00 36.335.33 0.00 29.00 36.33

0.00

0 2.00 2.00 9.000.00 2.00 2.00 9.000.00 0.00

2.00 18.3320.00 36.3318.00

Problem 3.15, HR7E Total project completion time is 36.33 days

Problem 3.16, HR7E Probability that project completion time is 40 days or less

Variance along critical path 5.22Std. Dev. along critical path 2.29Prob{Normal(36.33, 2.29) <= 40} = Prob{Z <= 1.60 } = .9452 (Appendix I)

Time (Days)

Key

I

K

A F

H

G

C

J

B

D

E

Problem 3.17, HR7E Probabilistic Times R. Saltzman

Immed. Mean VarianceActivity Predec. a m b t σ2

A - 4 8 10 7.67 1.00B A 2 8 24 9.67 13.44C A 8 12 16 12.00 1.78D A 4 6 10 6.33 1.00E B 1 2 3 2.00 0.11F C, E 6 8 20 9.67 5.44G C, E 2 3 4 3.00 0.11H F 2 2 2 2.00 0.00I F 6 6 6 6.00 0.00 ES EFJ D,G,H 4 6 12 6.67 1.78 LS LFK I, J 2 2 3 2.17 0.03 slack

Draw the activity-on-node (AON) project network.

7.67 17.33 17.33 19.338.00 17.67 17.67 19.67 29.33 31.330.33 0.33 29.33 31.33

19.67 29.33 0.0019.67 29.33

0.000.00 7.67 7.67 19.67 29.33 35.330.00 7.67 7.67 19.67 32.00 38.000.00 0.00 2.67 38.00 40.17

19.67 22.67 38.00 40.1728.33 31.33 0.00

8.677.67 14.00 31.33 38.00

25.00 31.33 31.33 38.0017.33 0.00

a) Expected time for activity C is 12.00b) Variance for activity C is 1.78c) What is the critical path? See red nodes and arcs.d) Estimated time of critical path? 40.17e) Variance along the critical path? 10.03 Std. Dev. along the critical path? 3.17f) Prob{completion before week 36} = Prob{Z < -1.32 } = 9.342%

Time (Days)

Key

A

B

C

D

E

F

G

I

H

J

K

Problem 3.19, HR7E Crashing Critical Path R. Saltzman

Immed. Normal Normal Crash CrashActivity Predec. Time Cost Time Cost

A - 7 6,000$ 6 6,600$ B A 4 1,200$ 2 3,000$ C B 11 4,000$ 9 6,000$

a) What action would you take to reduce the critical path by one day?

Crash Cost Max. Activity per day Crash time

A 600$ 1B 900$ 2C 1,000$ 2

Since A is the critical activity with the lowest crash cost per day, crash A first.

b) To crash the critical path a second day, crash B since it has the second lowest cost.

c) What is the total cost of the 2-day reduction? 1,500$

Problem 3.20, HR7E Crashing Critical Path R. Saltzman

Immed. Normal Normal Crash CrashActivity Predec. Time Cost Time Cost

A - 4 2,000$ 3 2,600$ B - 2 2,200$ 1 2,800$ C - 3 500$ 3 500$ D A 8 2,300$ 4 2,600$ E B 6 900$ 3 1,200$ F C 3 3,000$ 2 4,200$ G D, E 4 1,400$ 2 2,000$

ES EFLS LF

slack0 4 4 120 4 4 120 0

12 1612 16

0 2 2 8 04 6 6 124 4

0 3 3 610 13 13 1610 10

a) Project completion date is 16 weeks.b) Total cost required to complete project in normal time is 12,300$ c) Which activity should be crashed first? Critical activity D, for 75$

Crash Cost Max. Activity per week Crash time

A 600$ 1B 600$ 1C #DIV/0! 0D 75$ 4E 100$ 3F 1,200$ 1G 300$ 2

d) What is the maximum time that can be crashed?Crash D for 4 weeks. Cost = $300 After which B & E become critical.Crash G by 2 weeks. Cost = 600$ Crash A & E by 1 week. Cost = 700$

Total 7 weeks $1,600

Key

A

B

C

D

E

F

G