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Project Scheduling: Networks, Duration Estimation, and Critical Path Chapter 9 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 9-1 • • • • • Project Scheduling Terms Successors Predecessors Network diagram Serial activities Concurrent activities B D A E F C Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 9-2 Project Scheduling Terms • • • • • Merge activities Burst activities Node Path Critical Path B D A E F C Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 9-3 Network Diagrams Show interdependence Help schedule resources Facilitate communication Determine project completion Show start & finish dates Identify critical activities Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 9-4 AOA Vs. AON The same mini-project is shown with activities on arc… B E D F C …and activities on node. E D B F C Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 9-5 Node Labels Early Start Activity Float Late Start ID Number Early Finish Activity Descriptor Activity Duration Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Late Finish 9-6 Duration Estimation Methods • Past experience • Expert opinion • Mathematical derivation – Beta distribution – Most likely (m) – Most pessimistic (b) – Most optimistic (a) ba Activity Variance = s 6 2 2 a 4m b Activity Duration = TE 6 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 9-7 1. Sketch the network described in the table. 2. Determine the expected duration and variance of each activity. Task Predecessor Z -Y Z X Z a 7 13 14 b 8 16 18 c 15 19 22 W V T Y, X W W 12 1 6 14 4 10 16 13 14 S T, V 11 14 19 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 9-8 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 9-9 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 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 9-10 Task Predecessor Time A -4 B A 9 C A 11 D E F B B C 5 3 7 G H K D, F E, G H 3 2 1 1. Sketch the network described in the table. 2. Determine the ES, LS, EF, LF, and slack of each activity Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 9-11 Laddering Activities Project ABC can be completed more efficiently if subtasks are used A(3) A1(1) B(6) A2(1) B1(2) Laddered ABC=12 days C(9) ABC=18 days A3(1) B2(2) C1(3) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall B3(2) C2(3) C3(3) 9-12 Hammock Activities Used as summaries for subsets of activities 0 A 5 5 B 15 15 C 18 0 5 5 10 15 15 3 18 5 0 Hammock 18 0 18 18 Useful with a complex project or one that has a shared budget Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 9-13 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 9-14 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 9-15