1. Gantt Chart
Graph or bar chart with a bar for each project activity that shows passage of time
Provides visual display of project schedule
Slack
amount of time an activity can be delayed without delaying the project

2. Example of Gantt Chart Month 0 2 4 6 8 10 | | | | | 1 3 5 7 9 Activity
| | | | |
Activity
Design house and obtain financing
Lay foundation
Order and receive materials
Build house
Select paint
Select carpet
Finish work
Month

3. The Project Network Use of nodes and arrows
Arrows  An arrow leads from tail to head directionally
Indicate ACTIVITY, a time consuming effort that is required to perform a part of the work.
Nodes  A node is represented by a circle
- Indicate EVENT, a point in time where one or more activities start and/or finish.

4. CPM/PERT Critical Path Method (CPM)
DuPont & Remington-Rand (1956)
Deterministic task times
Activity-on-node network construction
Project Evaluation and Review Technique (PERT)
US Navy, Booz, Allen & Hamilton
Multiple task time estimates
Activity-on-arrow network construction

5. Project Network Activity-on-node (AON) Node Activity-on-arrow (AOA)
nodes represent activities, and arrows show precedence relationships
Activity-on-arrow (AOA)
arrows represent activities and nodes are events for points in time
Event
completion or beginning of an activity in a project 1 3 2
Branch/Activity
Node

6. AON Network for House Building Project1 3 2 4 5 6 7
Start
Design house and obtain financing
Order and receive materials
Select paint
Select carpet
Lay foundations
Build house
Finish work

7. Critical Path Critical path 4 2 7 1 Start 3 6 5
A: = 9 months
B: = 8 months
C: = 8 months
D: = 7 months
Critical path
Longest path through a network
Minimum project completion time

8. Activity Start Times 4 2 7 1 3 6 5 Start at 5 months
Finish at 9 months
Finish

9. Calculation of Required Time (Te)
t tm tp
Te= 6
te=weighted arithmetic average time
to= Optimistic Time
tm= most likely time
tp= pessimistic time

10. Networking 2 15 13 5 2 1 2 12 8 3 4

11. Calculation of Required Time (Te)
Activity
optimistic
Most likely
Pessimistic
Average
Time (Te)
A 1-2 9 12 21 13
B 1-3 6 18
C 2-4 1
1.5 5 2
D 3-4 4
8.5 10 8
E 2-5 14 24 15
F 4-5 3

12. Slack=LF-EF, LS-ES Activity Slack
Each event has two important times associated with it :
Earliest time , Te , which is a calendar time when a event can occur when all the predecessor events completed at the earliest possible times
Latest time , TL , which is the latest time the event can occur with out delaying the subsequent events and completion of project.
Difference between the latest time and the earliest time of an event is the slack time for that event
Slack=LF-EF, LS-ES
Positive slack : Slack is the amount of time an event can be delayed without delaying the project completion

13. Mode Configuration 1 3 Activity number Earliest start Earliest finish3
Latest finish
Activity duration
Latest start

14. Forward Pass
Start at the beginning of CPM/PERT network to determine the earliest activity times
Earliest Start Time (ES)
earliest time an activity can start
ES = maximum EF of immediate predecessors
Earliest finish time (EF)
earliest time an activity can finish
earliest start time plus activity time
EF= ES + t

15. Earliest Activity Start and Finish Times1 3 2 5 4 6 8 7 9
Start
Design house and obtain financing
Select paint
Lay foundations
Select carpet
Build house
Finish work
Order and receive materials

16. Earliest Activity Start and Finish Times1 3 2 5 4 6 8 7 9
Start
Design house and obtain financing
Select paint
Lay foundations
Select carpet
Build house
Finish work
Order and receive materials *
0+3
3+1
* For forward pass maximum EF time would be taken in calculating ES time

17. Backward Pass
Determines latest activity times by starting at the end of CPM/PERT network and working forward
Latest Start Time (LS)
Latest time an activity can start without delaying critical path time
LS= LF - t
Latest finish time (LF)
latest time an activity can be completed without delaying critical path time
LS = minimum LS of immediate predecessors

18. Latest Activity Start and Finish Times1 3 2 5 4 6 7 8 9
Start
Design house and obtain financing
Select pain
Lay foundations
Select carpet
Build house
Finish work
Order and receive materials

19. Activity Slack Slack S EF LF ES LS Activity * Critical Path 9 8 *7 1 79 8 *7 1 7 6 5 *4 4 3 *2 *1
Slack S EF LF ES LS
Activity