# Intorduction to Project Management

PROJECT MANAGEMENT Time Management* Dr. L. K. Gaafar The American University in Cairo * This Presentation is Based on information from the PMBOK Guide 2000 L. K. Gaafar 01/26/20 Critical Path Method (CPM) CPM is a project network analysis technique used to predict total project duration A critical path for a project is the series of activities that determines the earliest time by which the project can be completed The critical path is the longest path through the network diagram and has the least amount of float L. K. Gaafar 01/26/20 Finding the Critical Path

Develop a network diagram Add the durations of all activities to the project network diagram Calculate the total duration of every possible path from the beginning to the end of the project The longest path is the critical path Activities on the critical path have zero float L. K. Gaafar 01/26/20 Simple Example Consider the following project network diagram. Assume all times are in days. Activity A B C D E F L. K. Gaafar IPA --A B B C D Duration (days) 2 5 2 7 1

2 01/26/20 Simple Example start 1 A=2 2 B=5 C=2 4 E=1 3 6 D=7 5 finish F=2 Activity-on-arrow network a. 2 paths on this network: A-B-C-E, A-B-D-F. b. Paths have lengths of 10, 16 c. The critical path is A-B-D-F d. The shortest duration needed to complete this project is 16 days L. K. Gaafar

01/26/20 Key ES EF Time Management 7 Slack Act Dur. LS LF 0 0 0 6 2 A 13 2 2 0 2 2 C 9

9 2 6 15 15 10 E 1 16 7 B Activity-on-node network Dummy 5 7 7 0 7 L. K. Gaafar D 14 14 7

0 14 14 16 F 2 16 01/26/20 Activity A B C D E F Days 2 5 2 7 1 2 Cost (\$) 200 500 200 500 100 100 L. K. Gaafar Cost/day

100 100 100 71.4 100 50 Cash Flow 01/26/20 Cash Flow Daily Expenses 180 Days 2 5 2 7 1 2 Cost (\$) 200 500 200 500 100 100 Cost/day 100 100 100 71.4 100 50

160 140 120 Cost (\$) Activity A B C D E F 100 80 60 40 Activity Cost of day Total cost A 100 100 A 100 200 B 100 300 B 100 400 B 100 500 B 100 600 B

100 700 C,D 171.4 871 C,D 171.4 1043 D,E 171.4 1214 D 71.4 1286 D 71.4 1357 D 71.4 1428 D 71.4 1500 F 50 1550 F 50 1600 L. K. Gaafar 20 0 1 2 3

4 5 6 7 8 9 10 11 12 11 12 13 14 15 16 13 14 15 01/26/20 16 Day Cumulative Expenses

1800 1600 1400 1200 Cost (\$) Day 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1000 800 600 400 200 0 1

2 3 4 5 6 7 8 9 10 Determining the Critical Path for Project X a. How many paths are on this network diagram? b. How long is each path? c. Which is the critical path? d. What is the shortest duration needed to complete this project? L. K. Gaafar 01/26/20 Stochastic (non-deterministic) Activity Durations Project Evaluation and Review Technique (PERT) 01/26/20 Stochastic Times Uniform

Triangular Beta 01/26/20 Important Distributions L. K. Gaafar 01/26/20 Stochastic Times The Central Limit Theorem The sum of n mutually independent random variables is well-approximated by a normal distribution if n is large enough. 01/26/20 PERT: Finding the Critical Path (Stochastic Times) Develop a network diagram Calculate the mean duration and variance of each activity Calculate the total mean duration and the variance of every possible path from the beginning to the end of the project by summing the mean duration and variances of all activities on the path. The path with the longest mean duration is the critical path If more than one path have the longest mean duration, the

critical path is the one with the largest variance. Calculate possible project durations using the normal distribution L. K. Gaafar 01/26/20 Example I Activity IPA A B C D E F G --A -A,C B,D A,C -- Duration (wks) a m b 4 6 14 3 4 8 4 5

6 7 7 7 3 3 6 6 8 14 13 18 20 Assuming that all activities are beta distributed, what is the probability that the project duration will exceed 19 weeks? 01/26/20 L. K. Gaafar Activity IPA A B C D E F G A 7, 2.8 --A -A,C B,D A,C -- 7

Duration a m b 4 6 14 3 4 8 4 5 6 7 7 7 3 3 6 6 8 14 13 18 20 7.00 4.50 5.00 7.00 3.50 8.67 17.50 2.78 0.69 0.11 0.00

0.25 1.78 1.36 B 4.5, 0.7 E 3.5, 0.25 14 C 5,0.1 D 7, 0 17.5 F8.7, 1.8 7 G 17.5, 1.36 L. K. Gaafar 01/26/20 A 7, 2.8 7 B 4.5, 0.7 E 3.5, 0.25 14 C 5,0.1 D 7, 0 17.5

F8.7, 1.8 7 G 17.5, 1.36 L. K. Gaafar Path ADE ABE AF CDE CF G 17.50 15.00 15.67 15.50 13.67 17.50 3.03 3.72 4.56 0.36 1.89 1.36 01/26/20 Example II Duration Activity IPA Distribution a

m A --- Uniform 4 NA B --- Triangular 3 4 C --- Beta 4 5 D C Beta 5 7 E A Triangular 3 3 F A, B Triangular 5 8 G E, D Uniform 9 NA b 8 5 6 12 6 8 9 Construct an activity-on-arrow network for the project above.

Provide a 95% confidence interval on the completion time of the project. L. K. Gaafar 01/26/20 Example II Activity A B C D E F G IPA ------C A A, B E, D Distribution Uniform Triangular Beta Beta Triangular Triangular Uniform Duration a m 4 NA 3 4 4 5

5 7 3 3 5 8 9 NA b 8 5 6 12 6 8 9 F B A Start Finish E C G D L. K. Gaafar 01/26/20 Example II B (4, 0.17)

Start F (7, 0.5) A (6, 1.33) C (5, 0.11) Finish E (4, 0.5) G (9, 0.0) D (7.5, 1.36) Path BF AF AEG CDG 11 13 19 21.5 0.67 1.83 1.83 1.47 L. K. Gaafar 01/26/20

Time Management: Crashing Consider the following project network diagram. Assume all times are in days. Activity A B C D E F IPA --A B B C D L. K. Gaafar Duration (days) Normal Crash 2 2 5 3 2 1 7 4 1 1 2 1 Total cost (\$) Normal Crash 200

200 500 700 200 250 500 650 100 100 100 350 01/26/20 Time Management C(2,1,50) A(2,2,0) E(1,1,0) B(5,3,100) D(7,4,50) Action No Crashing Crash D by 1 Crash D by 1 Crash D by 1 Crash B by 1 Crash B by 1 Crash F by 1 L. K. Gaafar F(2,1,250) Critical Path Duration (days) Total Cost (\$)

A-B-D-F A-B-D-F A-B-D-F A-B-D-F A-B-D-F A-B-D-F A-B-D-F 16 15 14 13 12 11 10 1600 1650 1700 1750 1850 1950 2200 01/26/20 Duration/Cost Decision Support Curve 2300 2200 2100 Total Cost (\$) 2000 1900

1800 1700 1600 1500 10 11 L. K. Gaafar 12 13 Duration (days) 14 15 16 01/26/20 Time Management C(2,1,50) A(2,2,0) E(1,1,0) B(3,3,100) D(4,4,50) F(1,1,250) Shortest Possible duration with crashing is 10 days. Critical path is not changed.

L. K. Gaafar 01/26/20 Example Problem Activity A B C D E F G IPA --A -A,C B,D A,C -- L. K. Gaafar Duration (days) Normal Crash 6 4 4 3 5 4 7 7 4 2 8 6 18

13 Total cost (\$) Normal Crash 100 120 80 93 95 110 115 115 64 106 75 99 228 318 01/26/20 Project Network A6 B4 E4 C5 D7 F8 G 18 Path A-B-E A-D-E A-F C-D-E C-F

G Duration 14 17 14 16 13 18 L. K. Gaafar Shortest possible normal duration is 18 at a cost of \$757 01/26/20 Time Management 0 1 A 1 6 6 6 4 7 10 10 B 4

14 13 1 0 Dummy 5 6 5 1 2 7 7 14 0 18 6 14 0 G 18 4 0

18 2 C L. K. Gaafar 10 13 D F 17 E 14 4 18 7 8 Dummy 18 01/26/20 Crashing A(4,4,10) B(4,3,13) E(2,2,21) D(7,7,0) C(4,4,15)

F(8,6,12) G(13,13,18) Action No Crashing Crash G Crash G&A Crash G&E Crash G&E Crash G,A&C ABE 14 14 13 12 11 10 L. K. Gaafar ADE 17 17 16 15 14 13 Duration AF CDE 14 16 14 16 13 16 13

15 13 14 12 13 CF 13 13 13 13 13 12 G 18 17 16 15 14 13 Extra Cost -18 28 39 39 43 Total Cost 757 775 803 842 881 924 01/26/20

Final Crashed Network A(4,4,10) B(4,3,13) E(2,2,21) D(7,7,0) C(4,4,15) F(8,6,12) G(13,13,18) The shortest crashed project duration is 13 days at a minimum total cost of \$924. Further crashing of B or F is useless L. K. Gaafar 01/26/20 Using Critical Path Analysis to Make Schedule Trade-offs Knowing the critical path helps you make schedule trade-offs Free slack or free float is the amount of time an activity can be delayed without delaying the early start of any immediately following activities Total slack or total float is the amount of time an activity may be delayed from its early start without delaying the planned project finish date This part is from a presentation by Kathy Schwalbe, [email protected] L. K. Gaafar http://www.augsburg.edu/depts/infotech/

01/26/20 Techniques for Shortening a Project Schedule Shortening durations of critical tasks by adding more resources or changing their scope Crashing tasks by obtaining the greatest amount of schedule compression for the least incremental cost Fast tracking tasks by doing them in parallel or overlapping them This part is from a presentation by Kathy Schwalbe, [email protected] L. K. Gaafar http://www.augsburg.edu/depts/infotech/ 01/26/20 Shortening Project Schedules Original schedule Shortened duration Overlapped tasks This part is from a presentation by Kathy Schwalbe, [email protected] L. K. Gaafar http://www.augsburg.edu/depts/infotech/ 01/26/20

L. K. Gaafar 01/26/20 Activity Definition L. K. Gaafar Activity Sequencing 01/26/20 Duration Estimation L. K. Gaafar Schedule Development 01/26/20 Schedule Control L. K. Gaafar 01/26/20

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