Project Scheduling

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Project Scheduling

• Dr. Dale Masel
• ISE 536
• January 31, 2004

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Project Scheduling

• Important component of project plan
• Client requirements
• Measure of success
• Resource requirements
• Tools
• Critical Path Method (CPM)
• Program Evaluation and Review Technique (PERT)
• Gantt Chart

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CPM/PERT Terminology

• Activity
• Task or set of tasks
• Use resources
• Event
• State at end of 1 activities
• No resources or time
• Milestone
• Significant Event

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CPM/PERT Terminology (cont.)

• Network
• Diagram of nodes and arcs
• Illustration of relationships
• Path
• Series of connected activities
• Options
• Activity-on-Arrow Network
• Activity-on-Node Network

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CPM/PERT Terminology (cont.)

• Critical Path
• Path from start to finish
• If delayed ? delay completion of project
• Critical Time
• Time to complete all activities on critical path

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Example Activities Precedence
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AON Network
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AOA Network
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AOA Network

• Dummy Task
• Used to enforce precedence
• All tasks from a node have same precedence
• May need to create different combinations
• No time required

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Example Activities Precedence
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AON Network
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Important Values for AON

• First Pass Calculate EST then EFT
• Start to Finish
• Second Pass Calculate LFT then LST
• Finish to Start

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Activity Slack

• Time available for delay
• Calculating
• Slack LST EST
• Slack LFT - EFT
• Activities on Critical Path
• Slack 0

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PERT Distribution of Activity Times

• ET (a 4m b)/6
• s2 (b-a)2/36

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Completion Probability

• In Excel
• NORMDIST(D, ?, ??, TRUE)
• µ S(a 4m b)/6
• s2µ S(b-a)2/36
• Sum for all activities on critical path
• D Desired project completion time

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Determining Completion Date

• In Excel
• NORMINV(probability, ?, ??, TRUE)
• Select probability that you want to be right when
  determining Z
• Typical 0.90, 0.95

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PERT Example
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PERT AON Network
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Probability for Completion Date
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Simulation

• Generate event time for each activity
• Based on distribution of a, m, b
• Identify critical path based on simulated times
• Perform multiple replications to obtain an
  estimate of the completion time

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Statistics vs. Simulation

• Similarities
• Must list alternate paths
• Differences
• Simulation does not require assumption of path
  independence

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Gantt Chart

• Graphical representation of schedule
• Shows all activities
• Early Start Time
• Duration
• Early Finish Time
• May include
• Slack/Late Finish Time
• Precedence Relationships

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Example Gantt Chart
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Example Gantt Chart
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Applications of Gantt Charts

• Visual representation of schedule
• More effective description than AOA or AON
  Network
• Size reflects activity duration ? Importance
• Shows concurrent activities
• Monitoring progress
• Can compare status vs. plan

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Extensions to PERT/CPM

• Precedence Diagramming
• Finish-to-start linkage
• Start-to-start linkage
• Finish-to-finish linkage
• Start-to-finish linkage

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Graphical Evaluation and Review Technique (GERT)

• Combination of
• Flow graphs
• Probabilistic networks
• Decision trees
• Additional features
• Allows loops back to earlier events
• Allows probabilistic branching