1. Chapter 7 Project Management
© 2007 Pearson Education

2. Project Management Used to manage large complex projects
Has three phases:
Project planning
Project scheduling
Project controlling

3. 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?

4. 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?

5. 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?

6. 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?

7. 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

8. Work Breakdown Structure (WBS)
Divides the project into its various subcomponents and defines hierarchical levels of detail
Level
1 Project
2 Major tasks in project
3 Subtasks in major tasks
Activities to be completed

9. Example Work Breakdown Structure

10. Identify for Each Activity:
Which other activities must be completed previously (predecessors)
Time required for completion
Resources required
This completes the project planning phase.

11. Project Scheduling Phase
Commonly used techniques:
Program Evaluation and Review Technique (PERT)
Critical Path Method (CPM)

12. 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

14. 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

15. AON Network for General Foundry

16. Activity Time Estimates

17. 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

18. 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)

19. 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}

20. EFT Rule:
EFT = EST + activity time
Node Notation:

21. Forward Pass: Earliest Start and Finish Times

22. 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}

23. LST Rule:
LST = LFT – activity time

24. Backward Pass: Latest Start and Finish Times

25. 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 Critical Activities
The Critical Path is a continuous path through the network from start to finish that include only critical activities

26. Project Schedule and Slack Times

27. Critical Path and Slack Times

28. 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

29. 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

30. 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)

31. Expected activity time (t) t = (a + 4m + b) 6
Variance = [ (b – a) / 6 ]2
Standard deviation = SQRT(variance)
= (b – a)
Go to file 7-1.xls

32. Project Variance and Standard Deviation
Project variance (σp2)
= ∑ (variances of all critical path activities)
σp2 =
= 3.11
Project standard deviation (σp)
= SQRT (Project variance)
σp = SQRT ( 3.11) = 1.76

33. 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

34. Normal Probability Calculations
Z = (Target time – expected time) σp
Z = ( ) = 0.57
1.76
This means 16 weeks is 0.57 standard deviations above the mean of 15 weeks.

35. Probability Based on Standard Normal Table
Prob (proj completion < 16 weeks) =

36. Project Duration for a 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

37. Z = (? ) = 2.33
1.76
So ? = x 1.76 = 19.1 weeks

38. 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

43. 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)

45. 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

46. 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.

48. Crashing Using Linear 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

49. There is a maximum amount that each activity can be crashed
Constraints
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