# Project Scheduling: Networks, Duration Estimation, and ...

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)

b a 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 a b c Z

-- 7 8 15 Y Z 13 16 19 X Z 14 18 22

W Y, X 12 14 16 V W 1 4 13 T W 6 10 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 B 5 E B 3 F C 7 G D, F 3 H

E, G 2 K H 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

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