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 A D E C F Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 9-2

Project Scheduling Terms

• • • • • Merge activities Burst activities Node Path Critical Path B A D C Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall E F 9-3

Network Diagrams

Show interdependence Help schedule resources Facilitate communication Show start & finish dates Determine project completion 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… D E B F C B D …and activities on node.

E F C Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 9-5

Node Labels

Early Start Activity Float Late Start ID Number Activity Duration Early Finish Activity Descriptor Late Finish Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall 9-6

Duration Estimation Methods

• Past experience • Expert opinion • Mathematical derivation – Beta distribution – Most likely (m) – Most pessimistic (b) – Most optimistic (a) =

s

2     6    2 = TE 

a

 4 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 X Z Z a 7 13 14 b 8 16 18 W V Y, X W 12 1 14 4 T W 6 10 S T, V 11 14 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall c 15 19 22 16 13 14 19 9-8

Constructing the Critical Path

• Forward pass – an

additive move

through the network from

start to finish

• Backward pass – a

subtractive move

the network from

finish to start

through • 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 B - A 4 9 C D E F G H K A B B C D, F E, G H 11 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) B(6) C(9) ABC=18 days A 1 (1) A 2 (1) A 3 (1) B 1 (2) B 2 (2) Laddered ABC=12 days 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 0 5 5 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 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