1. Project Scheduling
Lecture # 1

2. Project Scheduling
Gantt chart
CPM

3. Critical Path
“The specific set of sequential tasks upon which the project completion date depends”
or “the longest full path”
All projects have a Critical Path
Accelerating non-critical tasks do not directly shorten the schedule

4. CPM What is the total time required to complete the project
What are the start and the completion times for individual activities?
Which critical activities must be completed as scheduled to meet the estimated project completion time?
How much delay can be tolerated for non-critical activities without incurring a delay in the estimated project completion time?
What is the least expensive way to speed up a project to meet a targeted completion time?

5. Continued
The most widely used scheduling technique is the critical path method (CPM) for scheduling.
This method calculates the minimum completion time for a project along with the possible start and finish times for the project activities.

6. Critical Path Example

7. Continued Critical Path Method
The process for determining and optimizing the critical path
Non-CP tasks can start earlier or later w/o impacting completion date
Note: Critical Path may change to another as you shorten the current

8. Activity on Arrow
In the second approach, the project activities are reported on arcs and nodes represent the starting or the completion of activities.

9. Activity on Arrow

10. Activity on Node
In the first approach, the nodes of the network represent the project activities and the arcs show their precedence relationships.

11. Activity on Node

12. CPM
The earliest start time (EST): the earliest time at which an activity can start if no delays occur in the project;
The earliest finish time (EFT): The earliest time at which an activity can finish if no delays occur in the project;
The latest start time (LST): The latest time at which an activity can start without delaying the completion of the project;
The latest finish time (LFT): The latest time at which an activity can finish without delaying the completion of the project.

13. Continued
A forward pass (from the starting node to the finish node) is used to compute the EST and EFT, whereas a backward pass (from the finish node to the starting node) is used for the LST and LFT.

14. Forward Pass
The forward pass to obtain the EST and the EFT can be summarized as follows:
1. For each activity with no predecessor, set EST 0.
2. For each activity with known EST, calculate EFT that is,
EFT= EST + t.
3. For each new activity where all immediate predecessors have known EFT values, apply the EST rule to obtain the EST and step 2 to calculate EFT.
4. Repeat step 3 until EST and EFT have been obtained for all activities.

15. Backward Pass
For backward pass the procedure can be summarized as follows: 1. For each of the activities without successors (including the finish node), set LFT equal to EFT of the finish node. 2. For each activity with known LFT value, calculate LST that is, LST= LFT- t. 3. For each new activity where immediate successors have known LST values, apply, respectively, the LFT rule to obtain the corresponding LFT and step 2 to calculate LST. 4. Repeat step 3 until LFT and LST have been obtained for all activities.

16. Slack Time
The slack time for an activity refers to the length of time that can be tolerated without incurring a delay in the scheduled project completion time. The slack time per activity needs to be calculated first to identify the critical path(s), by considering either the start times or the finish times. Hence, for each of the activities in the project network, the slack time can be calculated as follows:
Slack= LST-EST or LFT-EFT

17. CPM Example

18. CPM

19. CPM

20. CPM

21. Gantt Chart

22. CPM(Assignment Question)

23. Example of Gantt chart