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Chapter 7 Project Management. © 2007 Pearson Education. Project Management. Used to manage large complex projects Has three phases: Project planning Project scheduling Project controlling. Phase 1: Project Planning. What is the project goal or objective?

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Chapter 7Project Management

© 2007 Pearson Education

project management
Project Management
  • Used to manage large complex projects
  • Has three phases:
    • Project planning
    • Project scheduling
    • Project controlling
phase 1 project planning
Phase 1: Project Planning
  • What is the project goal or objective?
  • What are the activities (or tasks) involved?
  • How are activities linked?
  • How much time required for each activity?
  • What resources are required for each activity?
phase 2 project scheduling
Phase 2: Project Scheduling
  • When will the entire project be completed?
  • What is the scheduled start and end time for each activity?
  • Which are the “critical” activities?
  • Which are the noncritical activities?
phase 2 project scheduling cont
Phase 2: Project Scheduling (cont.)
  • How late can noncritical activities be w/o delaying the project?
  • After accounting for uncertainty, what is the probability of completing the project by a specific deadline?
phase 3 project controlling
Phase 3: Project Controlling

At regular intervals during the project the following questions should be considered:

  • Is the project on schedule? Early? Late?
  • Are costs equal to the budget? Over budget? Under budget?
  • Are there adequate resources?
  • What is the best way to reduce project duration at minimum cost?
identifying activities
Identifying Activities
  • Subdivides a large project into smaller units
  • Each activity should have a clearly defined starting point and ending point
  • Each activity is clearly distinguishable from every other activity
  • Each activity can be a project in itself
work breakdown structure wbs
Work Breakdown Structure (WBS)

Divides the project into its various subcomponents and defines hierarchical levels of detail


1 Project

2 Major tasks in project

3 Subtasks in major tasks

4 Activities to be completed

identify for each activity
Identify for Each Activity:
  • Which other activities must be completed previously (predecessors)
  • Time required for completion
  • Resources required

This completes the project planning phase.

project scheduling phase
Project Scheduling Phase

Commonly used techniques:

  • Program Evaluation and Review Technique (PERT)
  • Critical Path Method (CPM)
project management example general foundry inc
Project Management Example:General Foundry Inc.
  • Have 16 weeks to install a complex air filter system on its smokestack
  • May be forced to close if not completed w/in 16 weeks due to environmental regulations
  • Have identified 8 activities
drawing the project network
Drawing the Project Network
  • AON – Activity on Node networks show each activity as a node and arcs show the immediate predecessor activities
  • AOA – Activity on Arc networks show each activity as an arc, and the nodes represent the starting and ending points

We will use the AON method

determining the project schedule
Determining the Project Schedule
  • Some activities can be done simultaneously so project duration should be less than 25 weeks
  • Critical path analysis is used to determine project duration
  • The critical path is the longest path through the network
critical path analysis
Critical Path Analysis

Need to find the following for each activity:

  • Earliest Start Time (EST)
  • Earliest Finish Time (EFT)
  • Latest start time (LST)
  • Latest Finish Time (LFT)
forward pass
Forward Pass
  • Identifies earliest times (EST and EFT)
  • EST Rule: All immediate predecessors must be done before an activity can begin
    • If only 1 immediate predecessor, then

EST = EFT of predecessor

    • If >1 immediate predecessors, then

EST = Max {all predecessor EFT’s}

EFT Rule:

EFT = EST + activity time

Node Notation:

backward pass
Backward Pass
  • Identifies latest times (LST an LFT)
  • LFT Rule:
    • If activity is the immediate predecessor to only 1 activity, then

LFT = LST of immediate follower

    • If activity is the immediate predeccor to multiple activities, then

LFT = Min {LST of all imm. followers}

LST Rule:

LST = LFT – activity time

slack time and critical path s
Slack Time and Critical Path(s)
  • Slack is the length of time an activity can be delayed without delaying the project

Slack = LST – EST

  • Activities with 0 slack are CriticalActivities
  • The Critical Path is a continuous path through the network from start to finish that include only critical activities
total slack time vs free slack time
Total Slack Time vs. Free Slack Time
  • Total slack time is shared by more than 1 activity

Example: A 1 week delay in activity B will leave 0 slack for activity D

  • Free slack time is associated with only 1 activity

Example: Activity F has 6 week of free slack time

variability in activity times
Variability in Activity Times
  • Activity times are usually estimates that are subject to uncertainty
  • Approaches to variability:
    • Build “buffers” into activity times
    • PERT – probability based
    • Computer simulation
pert analysis
PERT Analysis
  • Uses 3 time estimates for each activity

Optimistic time (a)

Pessimistic time (b)

Most likely time (m)

  • These estimates are used to calculate an expected value and variance for each activity (based on the Beta distribution)
Expected activity time (t)

t = (a + 4m + b)


  • Variance = [ (b – a) / 6 ]2
  • Standard deviation = SQRT(variance)

= (b – a)


Go to file 7-1.xls

project variance and standard deviation
Project Variance and Standard Deviation
  • Project variance (σp2)

= ∑ (variances of all critical path activities)

σp2 = 0.11 + 0.11 + 1.0 + 1.78 + 0.11

= 3.11

  • Project standard deviation (σp)

= SQRT (Project variance)

σp = SQRT ( 3.11) = 1.76

probability of project completion
Probability of Project Completion
  • What is the probability of finishing the project within 16 weeks?
  • Assumptions:
    • Project duration is normally distributed
    • Activity times are independent
  • Normal distribution parameters:

μp = expected completion time= 15 weeks

σp = proj standard deviation = 1.76 weeks

normal probability calculations
Normal Probability Calculations

Z = (Target time – expected time)


Z = (16 - 15) = 0.57


This means 16 weeks is 0.57 standard deviations above the mean of 15 weeks.

probability based on standard normal table
Probability Based on Standard Normal Table

Prob (proj completion < 16 weeks) = 0.7158

project duration for a given probability
Project Duration fora Given Probability
  • What project duration does General Foundry have a 99% chance of completing the project within?

i.e. Prob (proj duration < ? ) = 0.99

  • From Std. Normal Table, this corresponds to Z = 2.33
Z = (? - 15) = 2.33


So ? = 15 + 2.33 x 1.76 = 19.1 weeks

scheduling project costs
Scheduling Project Costs
  • Estimate total cost for each activity
  • Identify when cost will actually be spent

(we will assume costs are spread evenly)

  • Use EST and LST for each activity to determine how costs are spread over project
monitoring and controlling project costs
Monitoring and Controlling Project Costs
  • While the project is underway, costs are tracked and compared to the budget
  • What is the value of work completed?

Value of work completed

= (% of work completed) x (total activity budget)

  • Are there any cost overruns?

Cost difference

= (Actual cost) – (Value of work completed)

project crashing
Project Crashing
  • Reducing a project’s duration is called crashing
  • Some activities’ times can be shortened (by adding more resources, working overtime, etc.)
  • The crash time of an activity is the shortest possible duration, and has an associated crash cost
steps in project crashing
Steps in Project Crashing
  • Compute the crash cost per time period
  • Find the current critical path (CP)
  • Find the lowest cost way to crash the CP by 1 time period
  • Update all activity times. If further crashing is needed, go to step 2.
crashing using linear programming
Crashing UsingLinear Programming

Decision: How many time periods to crash each activity?

Objective: Minimize the total crash cost

Decision Variables

Ti = time at which activity i starts

Ci = number of periods to crash activity i

  • An activity cannot begin before all immediate predecessors are complete
  • There is a maximum amount that each activity can be crashed

Go to file 7-2.xls