Project Scheduling: Networks, Duration estimation, and Critical Path

Project Scheduling Terms Successors Predecessors Network diagram Serial activities Concurrent activities E D C B A F

Project Scheduling Terms Merge activities Burst activities Node Path Critical Path E D C B A F Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Network Diagrams Help schedule resources Show interdependence Show start & finish dates Facilitate communication Determine project completion Identify critical activities Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

AOA vs. AON The same mini-project is shown with activities on arrow… D B F …and activities on node. C E D B F

Node and activity labels in AoA diagrams (NOT following the textbook) Deadline Activity identifier Duration 1 2 EET LET Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Node Labels in AoN diagrams (NOT completely following the textbook) Free float Early Start Total Float Early Finish Activity Descriptor Late Start Activity Duration Late Finish

Duration Estimation Methods Past experience Expert opinion Mathematical derivation – Beta distribution Most likely (m) Most pessimistic (b) Most optimistic (a)

Beta distribution Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Sketch the network described in the table. Determine the expected duration and variance of each activity. Task Predecessor a m b A -- 7 8 15 B 13 16 19 C 14 18 22 D B, C 12 E 1 4 F 6 10 G F, E 11 TE s2 9 1.8 16 1.0 18 14 0.4 5 4.0 10 14.3 1.4 Task a b c Mean Variance Z 7 8 15 9.00 1.78 Y 13 16 19 16.00 1.00 X 14 18 22 18.00 1.78 W 12 14 16 14.00 0.44 V 1 4 13 5.00 4.00 T 6 8 14 8.67 1.78 S 11 14 19 14.33 1.78 Task Early Start Early Finish Late Start Late Finish Slack Z 0 9 0 9 0 Y 9 25 11 27 2 X 9 27 9 27 0 W 27 41 27 41 0 V 41 46 44.67 49.67 3.67 T 41 49.67 41 49.67 0 S 49.67 64 49.67 64 0 Project Length 64 Project Variance 7.555556 Project Std.dev 2.748737

Solution with AoN diagram 2 2 b 9 25 2 11 27 16 e 41 46 5 51 a 9 d 27 41 14 g 51 65 14 c 9 27 18 f 41 51 10 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Constructing the Critical Path Forward pass – an additive move through the network from start to finish Backward pass – a subtractive move through the network from finish to start Critical path – the longest path from end to end which determines the shortest project length Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Rules for Forward/Backward Pass Forward Pass Rules (ES & EF) ES + Duration = EF EF of predecessor = ES of successor Largest preceding EF at a merge point becomes EF for successor Backward Pass Rules (LS & LF) LF – Duration = LS LS of successor = LF of predecessor Smallest succeeding LS at a burst point becomes LF for predecessor

Sketch the network described in the table. Task Predecessor Time A -- 4 B 9 C 11 D 5 E 3 F 7 G D, F H E, G 2 K 1 Sketch the network described in the table. Determine the ES, LS, EF, LF, and total float of each activity Task ES EF LS LF Slack A 0 4 0 4 0 B 4 13 8 17 4 C 4 15 4 15 0 D 13 18 17 22 4 E 13 16 22 25 9 F 15 22 15 22 0 G 22 25 22 25 0 H 25 27 25 27 0 K 27 28 27 28 0

Laddering Activities Project ABC can be completed more efficiently if subtasks are used ABC=18 days A(3) B(6) C(9) A1(1) A2(1) A3(1) B1(2) B2(2) B3(2) C1(3) C2(3) C3(3) Laddered ABC=12 days

Useful with a complex project or one that has a shared budget Hammock Activities Used as summaries for subsets of activities 0 A 5 0 5 5 B 15 5 10 15 15 C 18 15 3 18 0 Hammock 18 0 18 18 Useful with a complex project or one that has a shared budget

Reducing the Critical Path Eliminate tasks on the CP Convert serial paths to parallel when possible Overlap sequential tasks Shorten the duration on critical path tasks Shorten early tasks longest tasks easiest tasks tasks that cost the least to speed up Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Optional HW Create the AoA & AoN networks of your project using the symbols of this class. Prize: 15% Task list with cost estimation: +5% Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall

Thanks for your attention