1. Project Management and scheduling
Objectives of project scheduling
Network analysis
Scheduling techniques

2. Objectives of project scheduling
Produce an optimal project schedule in terms of cost, time, or risk.
Usually, it is difficult to optimize the three variables at the same time. Thus,
setting an acceptable limit for two of the three varaibles and optimizing the project in terms of the third variable.

3. Critical Path Method (CPM)
Produce the earliest and lastest starting and finishing times for each task or activity.
Calculate the amount of slack associated with each activity.
Determine the critical tasks (Critical path).
Forward pass and backward pass computational procedures.

4. Network control
Track the progress of a project on the basis of the network schedule and taking corrective actions when necessary.
Evaluate the actual performance against expected performance.

5. PERT/CPM
Node
Merge point
Successor
Burst point
Arrow
Predecessor

6. Two models of PERT/CPM
Activity-on-Arrow (AOA): Arrows are used to represent activities or tasks. Nodes represent starting and ending points of activities.
Activity-on-Node (AON): Nodes are used to represent activities or tasks, while arrows represent precedence relationships.

7. Recap - purpose of CPM Critical path Earliest starting time ES
Earliest completion time EC
Latest starting time LS
Latest completion time LC
Activity Capital letter
Duration t

8. Example Activity Predecessor Duration A - 2 B - 6 C - 4 D A 3 E C 5
F A 4
G B, D, E 2

9. Activity on Node Network

10. Forward pass analysis

11. Backward pass analysis

12. Slack Time in Triangles

13. Critical path

14. Computational analysis of network
Forward pass: each activity begins at its earliest time. An activity can begin as soon as the last of its predecessors is finished.
Backward pass: begins at its latest completion time and ends at the latest starting time of the first activity in the project network.

15. Rules for implementation - forward pass
The earliest start time (ES) for any node (j) is equal to the maximum of the earliest completion times (EC) of the immediate predecessors of the node.
The earliest completion time (EC) of any activity is its earliest start time plus its estimated time (its duration).
The earliest completion time of the project is equal to the earliest completion time the very last activity.

16. Rules for implementation - backward pass
The latest completion time (LC) of any activity is the smallest of the latest start times of the activity’s immediate successors.
The latest start time for any activity is the latest completion time minus the activity time.

17. Calculate slack time for each activity
Slack time: the difference in time between the two dates at the beginning of a job or the two dates at the end of the job. Slack time represents the flexiblity of the job.
Thus, slack time = LS - ES or LC - EC

18. PERT PERT is an extension of CPM.
In reality, activities are usually subjected to uncertainty which determine the actual durations of the activities.
It incorporates variabilities in activity duration into project entwork analysis.
The poetntial uncertainties in activity are accounted for by using three time estimates for each activity

19. Variation of Task Completion Time
Task A 2 4 6
Task B 3 4 5
Average 4 4

20. PERT Estimates & Formulas
a+4m+b
(b-a) 2
te =
s2 = 6 36
a = optimistic time estimate
m = most likely time estimate
b = pessimistic time estimate (a < m < b)
te = expected time for the activity
s2=variance of the duration of the activity

21. PERT Calculate the expected time for each activity
Calculate the variance of the duration of each activity
Follow the same procedure as CPM does to calculate the project duration, Te
Calculate the variance of the project duration by summing up the variances of the activities on the critical path.

22. Sources of the Three Estimates
Furnished by an experienced person
Extracted from standard time data
Obtained from historical data
Obtained from regression/forecasting
Generated by simulation
Dictated by customer requirement

23. A PERT Example
Activity Predecessor a m b te s2 A B C
D A
E C
F A
G B, D, E

24. What do Te & S2 tell us?
How likely to finish the project in a specified deadline.
For example, suppose we would like to know the probability of completing the project on or before a deadline of 10 time units (days)

25. Probability of finishing the project in 10 days
Te = 11
S2 = V[C] + V[E] + V[G] = = S=
( 10-Te )
P( T<=Td ) = P(T<=10) = P(z<= ) S
(10-11)
= P(z<=
) = P(z<= )
0.7817 =
About 10% probabilty fo finishing the project within 10 days

26. Probability of finishing the project in 13 days
Te = 11
S2 = V[C] + V[E] + V[G] = = S=
( 13-Te )
P(T<=Td ) = P(T<=10) = P(z<= ) S
(13-11)
= P(z<=
) = P(z<= )
0.7817 =
About 99% probabilty of finishing the project within 13 days

27. Gantt Chart
Gantt chart is a matrix of rows and columns. The time scale is indicated along the horizontal axis. Activities are arranged along the vertical axis.
Gantt charts are usually used to represent the project schedule. Gantt charts should be updated periodically.

28. Gantt Chart G F E D C B A 1 2 3 4 5 6 7 8 9 10 11

29. Gantt Chart Variations
Linked Bars
Progress - monitoring
Milestone
Task - combinations
Phase-Based
Multiple-Projects
Project-Slippage-tracking

30. Linked Bars Gantt ChartF E D C B A 1 2 3 4 5 6 7 8 9 10 11