1. Project Management for Business
Week 4
LSBM , Sept 2015
Project Management for Business

2. Outline
Project Scheduling
PERT/CPM

3. University of Nottingham
8/6/2018
Project Scheduling
It is part of project management within the Planning phase of the Project Development Life Cycle.
Project Scheduling: Allocate resources to execute all activities in the project.
Maria Petridou

4. University of Nottingham
8/6/2018
Project Scheduling
Objectives:
Establish beginning, ending and duration of each activity in the project.
Calculate overall completion time of the project given the amount of usually limited resources.
Determine the critical path and its duration.
Determine the slack time for all non-critical activities and the whole project.
Maria Petridou

5. University of Nottingham
8/6/2018
Project Scheduling
Phases:
Define activities or tasks according to the project objectives.
Identify precedence relationships or dependencies
Estimate time required to complete each task.
Draw an activity-on-arrow / activity-on-node PERT diagram.
Apply CPM to calculate earliest and latest starting times, earliest and latest completion times, slack times, critical path etc.
Construct a GANTT chart.
Reallocate resources and resolve if necessary.
Continuously monitor/revise the time estimates along the project duration.
Maria Petridou

6. University of Nottingham
8/6/2018
PERT Diagrams
Program Evaluation and Review Technique
It is a network model that shows activity completion times and their precedence.
Tool used to control the length of projects.
PERT was developed in the late 1950’s for the US Navy.
It has the potential to reduce both the time and cost required to complete a project.
Maria Petridou

7. University of Nottingham
8/6/2018
PERT Diagrams 3 B D A F 1 2 5 6 C E 4
Single start
node
Single finish
node
Maria Petridou

8. University of Nottingham
8/6/2018
PERT Diagrams
Activity-on-node
Activity-on-arrow
Maria Petridou

9. CPM – Critical Path Method
University of Nottingham
8/6/2018
CPM – Critical Path Method
ET – Earliest node time for given activity duration and precedence relationships
LT – Latest node time assuming no delays
ES – Activity earliest start time
LS – Activity latest start time
EF – Activity earliest finishing time
LF – Activity latest finishing time
Slack Time – Maximum activity delay time
Maria Petridou

10. CPM – Critical Path Method
University of Nottingham
8/6/2018
CPM – Critical Path Method 2
A ( 3 )
D ( 5 ) 1 5
B ( 4 )
E ( 2 ) 3 4
C ( 7 )
Maria Petridou

11. CPM – Critical Path Method
University of Nottingham
8/6/2018
CPM – Critical Path Method
Step 1. Calculate ET for each node.
For each node i for which predecessors j are labelled with ET(j), ET(i) is given
by:
ET(i)= maxj [ET(j)+ t(j,i)]
where t(j,i) is the duration of task between nodes (j,i).
Step 2. Calculate LT for each node.
For each node i for which successors j are labelled with LT(j), LT(i) is given by:
LT(i)= minj [LT(j) – t(i,j)]
where t(j,i) is the duration of task between nodes (i,j).
Maria Petridou

12. CPM – Critical Path Method
University of Nottingham
8/6/2018
CPM – Critical Path Method 2
A ( 3 )
D ( 5 ) 1 5
B ( 4 )
E ( 2 ) 3 4
C ( 7 )
Maria Petridou

13. CPM – Critical Path Method
University of Nottingham
8/6/2018
CPM – Critical Path Method 2 3
A ( 3 )
D ( 5 ) 1 5
B ( 4 )
E ( 2 ) 3 4 4
C ( 7 )
Maria Petridou

14. CPM – Critical Path Method
University of Nottingham
8/6/2018
CPM – Critical Path Method 2 3
A ( 3 )
D ( 5 ) 1 5
B ( 4 )
E ( 2 ) 3 4 4
C ( 7 ) 11
Maria Petridou

15. CPM – Critical Path Method
University of Nottingham
8/6/2018
CPM – Critical Path Method 2 3 13
A ( 3 )
D ( 5 ) 1 5
B ( 4 )
E ( 2 ) 3 4 4
C ( 7 ) 11 15
Maria Petridou 15

16. CPM – Critical Path Method
University of Nottingham
8/6/2018
CPM – Critical Path Method 2 3 13
A ( 3 )
D ( 5 ) 8 1 5
B ( 4 )
E ( 2 ) 3 4 4
C ( 7 ) 11 16
Maria Petridou 16

17. CPM – Critical Path Method
University of Nottingham
8/6/2018
CPM – Critical Path Method 2 3 13
max
A ( 3 ) 8
D ( 5 ) 1 5
B ( 4 )
E ( 2 ) 3 4 4
C ( 7 ) 11 17
Maria Petridou 17

18. CPM – Critical Path Method
University of Nottingham
8/6/2018
CPM – Critical Path Method 2 3
A ( 3 )
D ( 5 ) 1 5 13
B ( 4 )
E ( 2 ) 3 4 4
C ( 7 ) 11
Maria Petridou

19. CPM – Critical Path Method
University of Nottingham
8/6/2018
CPM – Critical Path Method 2 3
A ( 3 )
D ( 5 ) 1 5 13 13
B ( 4 )
E ( 2 ) 3 4 4
C ( 7 ) 11
Maria Petridou

20. CPM – Critical Path Method
University of Nottingham
8/6/2018
CPM – Critical Path Method 2 3
A ( 3 )
D ( 5 ) 1 5 13 13
B ( 4 )
E ( 2 ) 3 4 4
C ( 7 ) 11 11
Maria Petridou

21. CPM – Critical Path Method
University of Nottingham
8/6/2018
CPM – Critical Path Method 2 3 8
A ( 3 )
D ( 5 ) 1 5 13 13
B ( 4 )
E ( 2 ) 3 4 4
C ( 7 ) 11 11
Maria Petridou

22. CPM – Critical Path Method
University of Nottingham
8/6/2018
CPM – Critical Path Method 2 3 8
A ( 3 )
D ( 5 ) 1 5 13 13
B ( 4 )
E ( 2 ) 3 4 4 4
C ( 7 ) 11 11
Maria Petridou

23. CPM – Critical Path Method
University of Nottingham
8/6/2018
CPM – Critical Path Method 2 3 8 5
A ( 3 )
D ( 5 ) 1 5 13 13
B ( 4 )
E ( 2 ) 3 4 4 4
C ( 7 ) 11 11 23
Maria Petridou 23

24. CPM – Critical Path Method
University of Nottingham
8/6/2018
CPM – Critical Path Method 2 3 8 5
A ( 3 )
D ( 5 ) 1 5 13 13
B ( 4 )
E ( 2 ) 3 4 4 4
C ( 7 ) 11 11 24
Maria Petridou 24

25. CPM – Critical Path Method
University of Nottingham
8/6/2018
CPM – Critical Path Method 2 3 8 5
min
A ( 3 )
D ( 5 ) 1 5 13 13
B ( 4 )
E ( 2 ) 3 4 4 4
C ( 7 ) 11 11 25
Maria Petridou 25

26. CPM – Critical Path Method
University of Nottingham
8/6/2018
CPM – Critical Path Method 2 3 8
A ( 3 )
D ( 5 ) 1 5 13 13
B ( 4 )
E ( 2 ) 3 4 4 4
C ( 7 ) 11 11
Maria Petridou

27. CPM – Critical Path Method
University of Nottingham
8/6/2018
Step 3. Calculate processing times for each activity.
CPM – Critical Path Method
Task
Duration ES EF LS LF
Slack
Critical Task A 3 5 8 No B 4
Yes C 7 11 D 13 E 2
Maria Petridou

28. CPM – Critical Path Method
University of Nottingham
8/6/2018
CPM – Critical Path Method 2 3 8
A ( 3 )
D ( 5 ) 1 5 13 13
B ( 4 )
E ( 2 ) 3 4 4 4
C ( 7 ) 11 11
Maria Petridou

29. 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

31. AON Network for General Foundry

32. Activity Time Estimates

33. 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

34. 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)

35. Forward Pass If only 1 immediate predecessor, then
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}

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

37. Forward Pass: Earliest Start and Finish Times

38. Backward Pass
Identifies latest times (LST and 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}

39. LST Rule:
LST = LFT – activity time

40. Backward Pass: Latest Start and Finish Times

41. 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

42. Project Schedule and Slack Times

43. Critical Path and Slack Times

44. Project Scheduling
Questions?

45. Reference List
1. Project Management: Achieving competitive advantage, chapter 9 2. Project Management: A managerial Approach, chapter 13, Project Termination