Project Scheduling Networks Duration Estimation and Critical Path

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) 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 W V T S Y, X W W T, V a 7 13 14 b 8 16 18 c 15 19 22 12 1 6 11 14 4 10 14 16 13 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 G H K B B C D, F E, G H 5 3 7 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) A 1(1) B(6) A 2(1) B 1(2) Laddered ABC=12 days C(9) ABC=18 days A 3(1) B 2(2) C 1(3) Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall B 3(2) C 2(3) C 3(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 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