The document discusses critical path calculations and Gantt charts for project scheduling. It defines key terms like critical path, critical activities, and float. It describes the two phases of critical path calculations - the forward pass and backward pass. The forward pass calculates earliest occurrence times while the backward pass calculates latest occurrence times. It provides an example problem calculating the minimum time and identifying critical path activities. Finally, it outlines the benefits of Gantt charts for illustrating time-based activities on a horizontal timescale and monitoring project progress.

1. Chapter 8
Scheduling
Project Management
A Managerial Approach

2. Solving the Network

4. The expected time, TE, Standard deviation
and variance
 TE = (a +4m +b2)/6
 where
 a optimistic time estimate
 b pessimistic time estimate
 m most likely time estimate, the mode

9. CRITICAL PATH CALCULATIONS
Critical Path: is the path through the network that takes
the longest total time. It therefore determines the earliest
possible time the project can be completed.
Critical path requires more careful monitoring, because if
they are not completed on time, the project will be late –
unless the subsequent activities are completed in less than
the scheduled time.

10. CRITICAL PATH CALCULATIONS
Critical Activity: An activity that has total float equal to zero. All
Activities on the critical path are known as Critical Activities.
Float/Slack: Float is the time available to retard or advance
the start time of an activity without delaying the completion of
the project.

11. CRITICAL PATH CALCULATIONS
The critical path calculations include two phases.
Forward Pass
Backward Pass
Forward Pass: The first phase is called the forward pass, where calculations
begin from the “start” node and move to the “end” node. At each node a
number is computed representing the earliest occurrence time of the
corresponding event.
Backward Pass: The second phase, called the backward pass, begins
calculations from the “end” node and moves to the “start” node. The number
computed at each node (shown in triangles Δ) represents the latest
occurrence time of the corresponding event.

12. Activity Days Precedents
a Schedule of liabilities 3 -
b Mail confirmation 15 a
c Test pension plan 5 a
d Vouch selected liabilities 60 a
e Test accruals 6 d
f Process confirmations 40 b
g Reconcile interest 10 c, e
h Verify debt compliance 7 f
i Investigate balances 6 g
j Review payments 12 h, i
Q#1 Draw the network and calculate the CP, and slack
times of activities

13. Question #2
A project consists of Six activities: A,B,C,D, E, F. A and B have no
preceding activities, but activity C requires that activity B must be
completed before C can begin. Activity D cannot start until both
activities A and B are complete. Activity F can start any time.
Activity E requires activities A and C to be completed before it can
start. If the activity times are A: 10 days; B: 4 days; C: 8 days; D: 3
days, E = 2 days, and F: 1 day,
 Find out the minimum time possible to complete this project.
 Are there any critical path activities? Which one are those?
Take no more than 20 minutes to solve the above problem. You may consult with
each other.

14. Gantt Charts
“A manner of illustrating multiple, time based
activities on a horizontal time scale”
 The Gantt chart shows planned and actual progress
for a number of tasks displayed against a horizontal
time scale
 It is an effective and easy-to-read method of
indicating the actual current status for each set of
tasks compared to the planned progress for each
item of the set
 It can be helpful in expediting, sequencing, and
reallocating resources among tasks
 Gantt charts usually do not show technical
dependencies
Chapter 8-14

15. Gantt Chart
Chapter 8-15

16. Gantt Charts
 There are several advantages to the use of Gantt
charts:
 Even though they may contain a great deal of
information, they are easily understood
 While they may require frequent updating, they are easy
to maintain
 Gantt charts provide a clear picture of the current state of
a project
 They are easy to construct
Chapter 8-16