9-1 Project Scheduling: Networks, Duration Estimation, and Critical Path Chapter 9 © 2007 Pearson Education

9-2 Project Scheduling Terms Successors Predecessors Network diagram Serial activities Concurrent activities E D C B A F Merge activities Burst activities Node Path Critical Path

9-3 Network Diagrams Show interdependence Facilitate communication Help schedule resources Identify critical activities Determine project completion Show start & finish dates

9-4 AOA Vs. AON The same mini-project is shown with activities on arc… C E D B F E C D B F …and activities on node.

9-5 Node Labels Early Start Activity Float Activity Descriptor Late Start ID Number Activity Duration Late Finish Early Finish

9-6 Duration Estimation Methods Past experience Expert opinion Mathematical derivation – Beta distribution –Most likely (m) –Most pessimistic (b) –Most optimistic (a)

9-7 TaskPredecessorabc Z YZ XZ WY, X VW1413 TW61014 ST, V Sketch the network described in the table. 2.Determine the expected duration and variance of each activity.

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

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

9-10 TaskPredecessorTime A--4 BA9 CA11 DB5 EB3 FC7 GD, F3 HE, G2 KH1 1.Sketch the network described in the table. 2.Determine the ES, LS, EF, LF, and slack of each activity

9-11 Laddering Activities Project ABC can be completed more efficiently if subtasks are used A(3)B(6)C(9) ABC=18 days Laddered ABC=12 days A 1 (1)A 2 (1)A 3 (1) B 1 (2)B 2 (2)B 3 (2) C 1 (3)C 2 (3)C 3 (3)

9-12 Hammock Activities Used as summaries for subsets of activities 0 A B C Hammock Useful with a complex project or one that has a shared budget

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