Project Management OPER 576
Project Networks
Greg Magnan, Ph.D.
April 29, 2004
Project Life Cycle Stages
Definition Planning Execution/Impl./Control Closeout
Leve
l of E
ffort
Selection Charter Goals Specs Tasks Responsi
bilities
Estimates Schedules Sequencing Budgets Resources Risks Staffing
Status Reports Changes Quality Forecasts
Training Transfer
Documents Release
Resources Lessons
Learned
II. Project Planning7. Sequence Deliverables
• To help schedule work efficiently
• Consider all WBS elements
• Estimate calendar duration for each
• List precedence for each task
• May construct network diagram
• CRITICAL PATH: longest path through the network showing minimum time needed
• Delays to elements on the critical path delay the entire project!
• Mascitelli: Critical Core
Activity Time Estimates
• PERT-based• Assumptions:
– “normal” operations– independent estimates for activities
• Optimistic / Most-likely / Pessimistic• Formula
(O + 4M + P)/6
• Example(10 + 4*15 + 26)/6 = 16
Project Networks• Developed from WBS
– WBS must be deliverables-oriented!– Activity Labeling: use WBS outline as basis
• Used for Planning, scheduling, controlling• Activities, sequences, precedence rel’ps
• Critical Path / “Crashing” network
• Basis for Resource Scheduling
• Communication to stakeholders
• Estimate of project duration
EarlyStart
Duration
EarlyFinish
LateStart
SlackLate
Finish
Task Name
EarlyStart
Duration
EarlyFinish
LateStart
SlackLate
Finish
Task Name
EarlyStart
Duration
EarlyFinish
LateStart
SlackLate
Finish
Task Name
EarlyStart
Duration
EarlyFinish
LateStart
SlackLate
Finish
Task Name
EarlyStart
Duration
EarlyFinish
LateStart
SlackLate
Finish
Task Name
EarlyStart
Duration
EarlyFinish
LateStart
SlackLate
Finish
Task Name
EarlyStart
Duration
EarlyFinish
LateStart
SlackLate
Finish
Task Name
Network Terms• Activity
– An element in the project that consumes time, but doesn’t necessarily require resources (e.g., approvals, contract signing)
• “Events” do not consume time– Can include one or more Work Packages
• Verb/noun format
• Critical path– Path: a sequence of connected, dependent activities– CP: Longest path through the network
• Activity-on-Node (AON) vs. Activity-on-Arc (AOA)– AON is most commonly used (software packages)– Nodes reflect activities
AON Network Development Rules• Arrows indicate precedence and flow
– Flow from left to right– Precedence determined after WBS complete
• Predecessor and Successor activities
– Preceding activities must be complete before beginning successor activities
• Activities need labels– Larger numbers than preceding activities
• No Looping!– No conditional (if/then) statements
• Single Start and End nodes
Project Scheduling: Node Elements
Early Start Duration Early Finish
Late Start Slack Late Finish
Task Name
PERT Diagram(Activity on Node)
EarlyStart
Duration
EarlyFinish
LateStart
SlackLate
Finish
Task Name
EarlyStart
Duration
EarlyFinish
LateStart
SlackLate
Finish
Task Name
EarlyStart
Duration
EarlyFinish
LateStart
SlackLate
Finish
Task Name
EarlyStart
Duration
EarlyFinish
LateStart
SlackLate
Finish
Task Name
EarlyStart
Duration
EarlyFinish
LateStart
SlackLate
Finish
Task Name
EarlyStart
Duration
EarlyFinish
LateStart
SlackLate
Finish
Task Name
EarlyStart
Duration
EarlyFinish
LateStart
SlackLate
Finish
Task Name
Sample Problem
Activity Duration PredecessorA 5 noneB 10 noneC 15 AD 10 AE 5 BF 20 CG 20 EH 5 D, F, GI 15 H
Forward & Backward Pass• Determine:
– Early Start (ES) and Early Finish (EF)
– Late Start (LS) and Late Finish (LF)…and then Slack
• Forward Pass (EF and ES)– For each path in the network, add activity times (duration)
to each ES to get EF (ES + Dur = EF)
– EF of preceding activity becomes ES of successor, unless• Succeeding activity is a merge activity (>1 predecessor)
• Then select LARGEST EF time from all predecessor EF times to become ES for successor activity
Forward & Backward Pass• Backward Pass (LF and LS)
– Must have already completed Forward Pass
– Start with the latest EF of last activity in the network
– For each path in the network, subtract activity times (duration) from each LF to get LS (LF - Dur = LS)
– LS of successor activity becomes LF of preceding, unless
• The next preceding activity is a burst activity (>1 successor)
• Then select SMALLEST LS time from all immediate successor activities to determine LF time
Conclusion…
• Projects are everywhere
• Can be actively managed
• Science AND art
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