1. PLANNING ENGINEERING AND PROJECT MANAGEMENT
Lecture#08
PLANNING ENGINEERING AND PROJECT MANAGEMENT By
Lec. Junaid Arshad
DEPARTMENT OF ENGINEERING MANAGEMENT

2. Topics Covered CPM Calculations for AOA and AON Networks
Slack Time / Float
Critical Path, Critical Activity
Practice Problems

3. CPM Calculations for AON Network
Provides activity information
Early start (ES) & late start (LS)
Early finish (EF) & late finish (LF)
Slack (S) / Float (FL)
Identifies critical path
This and the next several slides illustrate the definitions of terms appropriate to critical path analysis.
There are many opportunities for good managers to truly manage a project once they have a PERT network established. For instance, sub-contractors know early start and late start times and the managers know the activities on the critical path upon which to focus effort.

4. Forward and Backward Pass
Forward pass is a technique to move forward through network diagram. Backward pass is its opposite.
Early Start (ES) and Early Finish (EF) use the forward pass technique.
Late Start (LS) and Late Finish (LF) use the backward pass technique.
Note: If the float of the activity is zero, the two starts (ES and LS) and the two finish (EF and LF) are the same. Hence, If float of activity is zero, ES = LS and EF = LF.

5. Early Start and Early Finish Steps
Begin at starting event and work forward
ES = 0 for starting activities
ES is earliest start
EF = ES + Activity time
EF is earliest finish
ES = Maximum EF of all predecessors for non- starting activities

6. Late Start and Late Finish Steps
Begin at ending event and work backward
LF = Maximum EF for ending activities
LF is latest finish; EF is earliest finish
LS = LF - Activity time
LS is latest start
LF = Minimum LS of all successors for non-ending activities

7. AON Network CalculationsES LS EF LF
Earliest Finish
Latest Start
Earliest Start
Activity Name
Activity Duration
Latest Finish

8. CPM Calculations for an AON Network
Problem 04
Activity
Preceding Activity
Duration (days) A - 10 B 07 C 12 D 18 E 14 F 13 G 16 H
D, E I
F, G 06
CPM Calculations for an AON Network

9. Slack Time/Float
Slack Time is the amount of time an activity may be delayed without affecting the project deadline. This is also referred as float.
Total Slack Time / Total Float:
Time shared among more than one activity.
Free Slack Time /Free Float: Time associated with a single activity.

10. Critical Activity
An activity having zero slack time is called critical activity.
The concept of critical activities is that it draws the attention of the project manager to the activities that needs the closest monitoring.
Any delay of a critical activity leads to an equivalent delay of the total project.

11. Critical Path
A path having longest duration (completion time) in the network is called critical path.
Shortest time project can be completed
Any delay on critical path activities, delays project
Critical path activities have zero slack

12. Explanation of Total Float
Total Float is valid for a chain and not for a single activity. In the under discussion example, C and G have a float of 06 days. This means that the sum of delays for C and G may run up to 06 days without affecting the project finish time. Analysis of float is a particularly neat tool for calculating consequences of schedule variance.

13. Assume the following data with respect to
schedule (for problem 04)
B will be delayed by 04 days
D will be delayed by 01 day
E will be delayed by 05 days
G will be delayed by 03 days

14. It is recognized that D is critical, hence a delay of at least one day to the overall project is unavoidable. Activity G has a float of 06 days. Since no other activity on that chain has a delay, the float will accommodate the 03 day delay of G.

15. Further, B and E are both on the same chain
Further, B and E are both on the same chain. The float along the chain is 07 days and the total delay is 4+5=9 days. This means a 02 day delay of the project. In conclusion, the project will be delayed by 02 days and B-E-H will be the new critical path. A-D will have a float of one, and C-G a float of 04.

16. CPM Calculations for AON Network
CPM calculation for AON Network is same as for AOA network, but the calculation of events is omitted.

17. Problem 05: General Hospital’s Activities and Predecessors
Activity
Immediate Predecessors
Duration (days) A - 2 B 3 C D
A, B 4 E F G
D, E 5 H
F, G

18. AON Network for General Hospital Includes Critical Path
Start A B C D F G H 13 2 15 8 5 4 10 3 7 E 1
Slack=0
Slack=6
Slack=1
Slack=0

19. Critical Path for General Hospital
Start H B D G

20. Explanation of Free Float
Consider slack time of activity F. Delaying this activity decreases only its slack time and does not impact the slack time of any other activity. This type of slack time is referred as free slack / free float.

21. Gantt Chart for General Hospital Early Start and Finish
A Build internal components
B Modify roof and floor
C Construct collection stack
D Pour concrete and install frame
E Build high-temperature burner
F Install pollution control system
G Install air pollution device
H Inspect and test
This and the following slide illustrate the translation of Early and Late Start and Finish time to Gantt charts.

22. Gantt Chart for General Hospital Late Start and Finish
A Build internal components
B Modify roof and floor
C Construct collection stack
D Pour concrete and install frame
E Build high-temperature burner
F Install pollution control system
G Install air pollution device
H Inspect and test
GENERAL HOSPITAL
This and the following slide illustrate the translation of Early and Late Start and Finish time to Gantt charts.

23. Table for Network Scheduling
Problem 06
Table for Network Scheduling

24. Problem 06 Solution - AOA Method

25. Early Event Time (TE)

26. Finding TE Values

27. Late Event Time (TL)

28. Finding TL Values

29. Critical Path

30. Activity Scheduling
An activity’s early starting time equals the TE of its beginning event: ES = TE.
An activity’s late finishing time equals the TL for its ending event: LF = TL.
From these, Two times are computed using the expected activity completion time t:
Early finishing time: EF = ES + t.
Late starting time: LS = LF - t.

31. Problem 06 Solution - AOA Method
Scheduled Times must fall between ES and LF and allow at least time t to complete.

32. CPM Calculations for an AOA Network
Problem 07
Activity
Preceding Activity
Duration (weeks) A - 10 B 07 C 12 D 18 E 14 F 13 G 16 H
D, E I
F, G 06
CPM Calculations for an AOA Network

33. Predecessors (Dependencies) Table for Network Scheduling
Problem 08
Activity
Predecessors (Dependencies)
Time (Weeks) A - 3 B 5 C 7 D 8 E F G 4 H I 6 J
G - H
Table for Network Scheduling

34. Q&A