Scheduling Problems Complete the following problems covering project scheduling methods. 1. Put the following project management activities in order, by defining immediate predecessors by placing one or more letters in the column labeled “Immediate predecessor”. One of them has been done for you. Activity Immediate predecessor a) Calculate durations along all project paths b) Calculate Te c) Define immediate predecessors h d) Develop WBS e) Draw a network diagram f) Estimate task durations g) Find the critical paths h) Generate a complete, detailed task list i) Identify project objectives j) Write project scope statement 2. Draw network diagram for the following list of activities and their immediate predecessors. Draw start and end nodes. Activity Immediate predecessor A -- B -- C A, B D C E C F D G E H F, G I C 3. Given the following detailed task list, draw a network diagram, including starting and ending nodes. Task Immediate predecessor A -- B A C A D B E C F D, E 4. Identify all paths and their summed durations from the following detailed task list. Task Estimated duration Immediate Predecessors A-define info req 2 wks - B- analyze existing infrastruc 1.5 wks - C-define network req 1 wk. B D-design database 3 wks. A E-design network 2.5 wks. C F-implement 7 wks. D, E G-test 4 wks. F H-document database 1 wk. D I-user documentation 2 wks. C 5. What is/are the critical path(s) amongst the following paths through a project? Path 1: A-B-D = 8.5 mos. Path 2: B-C-I-J = 10 mos. Path 3: A-B-E = 5.5 mos. Path 4: B-F-G-J = 12 mos. 6. What is the shortest possible completion time for a project, given the following paths through a project from start to finish? A-B-D-F = 14 weeks A-G = 22 weeks A-C-H-I-J = 19 weeks 7. Identify all non-critical activities in the project with the following paths: A-B-C = 22 weeks B-J-K = 18 weeks A-B-D-E = 22 weeks A-B-I = 14 weeks B-L = 20 weeks 8. Identify all non-critical activities for a project with the following paths A-B-C = 10 days A-B-D = 8 days A-B-E-F = 8 days A-B-G = 9 days 9. Develop an early start early finish (ES/EF) schedule for the following project. Activity Duration Predecessor ES EF A Develop specifications 2 wks B Design 4 A C Documentation 5 A D Implementation 8 B, C E Testing 4 D 10. Develop an early start, early finish (ES/EF) schedule for the following project. Activity Duration Predecessor ES EF A Develop specifications 6 wks B Design 5 wks A C User Documentation 7 wks A D Implementation 11 wks B, C E Acceptance Testing 8 wks D F Develop marketing literature 8 wks A G Technical documentation 7 wks B, C, F PAGE 3 Example Scheduling Problem 1 v3 Before we can schedule a project, we will need to have done the following, in order: -        Identify project objectives -        Write project scope statement -        Develop a WBS -        Generate a co.

1. Scheduling Problems
Complete the following problems covering project scheduling
methods.
1. Put the following project management activities in order, by
defining immediate predecessors by placing one or more letters
in the column labeled “Immediate predecessor”. One of them
has been done for you.
Activity
Immediate predecessor
a) Calculate durations along all project paths
b) Calculate Te
c) Define immediate predecessors
h
d) Develop WBS
e) Draw a network diagram
f) Estimate task durations
g) Find the critical paths
h) Generate a complete, detailed task list
i) Identify project objectives
j) Write project scope statement
2. Draw network diagram for the following list of activities and
their immediate predecessors. Draw start and end nodes.
Activity
Immediate predecessor

2. A
--
B
--
C
A, B
D
C
E
C
F
D
G
E
H
F, G
I
C

3. 3. Given the following detailed task list, draw a network
diagram, including starting and ending nodes.
Task
Immediate predecessor
A
--
B
A
C
A
D
B
E
C
F
D, E
4. Identify all paths and their summed durations from the
following detailed task list.
Task

4. Estimated duration
Immediate Predecessors
A-define info req
2 wks
-
B- analyze existing infrastruc
1.5 wks
-
C-define network req
1 wk.
B
D-design database
3 wks.
A
E-design network
2.5 wks.
C
F-implement
7 wks.

5. D, E
G-test
4 wks.
F
H-document database
1 wk.
D
I-user documentation
2 wks.
C
5. What is/are the critical path(s) amongst the following paths
through a project?
Path 1: A-B-D = 8.5 mos.
Path 2: B-C-I-J = 10 mos.
Path 3: A-B-E = 5.5 mos.

6. Path 4: B-F-G-J = 12 mos.
6. What is the shortest possible completion time for a project,
given the following paths through a project from start to finish?
A-B-D-F = 14 weeks
A-G = 22 weeks
A-C-H-I-J = 19 weeks
7. Identify all non-critical activities in the project with the
following paths:
A-B-C = 22 weeks
B-J-K = 18 weeks
A-B-D-E = 22 weeks
A-B-I = 14 weeks
B-L = 20 weeks
8. Identify all non-critical activities for a project with the
following paths
A-B-C = 10 days
A-B-D = 8 days
A-B-E-F = 8 days
A-B-G = 9 days
9. Develop an early start early finish (ES/EF) schedule for the
following project.

7. Activity
Duration
Predecessor
ES
EF
A
Develop specifications
2 wks
B
Design
4
A
C
Documentation
5
A
D
Implementation
8
B, C
E
Testing
4
D
10. Develop an early start, early finish (ES/EF) schedule for the

8. following project.
Activity
Duration
Predecessor
ES
EF
A
Develop specifications
6 wks
B
Design
5 wks
A
C
User Documentation
7 wks
A
D
Implementation
11 wks
B, C
E
Acceptance Testing
8 wks
D

9. F
Develop marketing literature
8 wks
A
G
Technical documentation
7 wks
B, C, F
PAGE
3
Example Scheduling Problem 1 v3
Before we can schedule a project, we will need to have done the
following, in order:
- Identify project objectives
- Write project scope statement
- Develop a WBS
- Generate a complete detailed task list
The above can be considered progressive elaboration of scope,
And then we need to:
- Define immediate predecessors
If we do all of these things, we can then define a network
diagram that illustrates the interrelationship among activities,
and the various paths throughout the project.

10. Before we can develop a schedule, using the critical path
method, we also have to:
- Estimate task durations
The three (3) inputs to using the critical path method for
scheduling are, therefore, (a) develop a detailed activity list
with (b) immediate predecessors and (c) estimated task
durations.
What I am going to show you now is how to develop a project
schedule, in the following basic steps:
- Draw a network diagram
- Calculate durations along all project paths
- Find the critical path(s)
- Calculate Te
1. Draw network diagram for the following list of activities and
their immediate predecessors. Draw start and end nodes. The
project is to put a consulting company’s marketing plan on the
Internet. (Olson 2004, p. 207 #12).
Activity Immediate predecessor
A none
B none
C D
D A
E A, B
F A, B
G E, F
H C
I C, G
J H, I
K J

11. L K
( See Network Diagram on Next)
2. Identify all paths from the network diagram above.
Paths
Path 1 – A-D-C-H-J-K-L
Path 2 – A-D-C-I-J-K-L
Path 3 – A-E-G-I-J-K-L
Path 4 – A-F-G-I-J-K-L
Path 5 – B-E-G-I-J-K-L
Path 6 – B-F-G-I-J-K-L
2. Identify all paths and their summed durations from the
following
detailed task list.
Activity
Predecessor(s) Duration
A-obtain your boss’s approval of your plan
none 8 days
B-obtain budget approval
none 12 days
C-obtain systems development approval D
10 days
D-develop user specifications A
1 day
E-obtain a marketing program from mktg A, B
120 days
F-obtain a mktg program from consultant A, B

12. 60 days
G-review and select mktg program E,
F 5 days
H-perform systems dev of module contents
C 80 days
I-design system interface C,
G 50 days
J-review and approve systems development H,
I 5 days
K-test prototype
J 10 days
L-revision and final systems development K
20 days
Path = Summed duration
Path 1 – A-D-C-H-J-K-L = 8+1+10+80+5+10+20 = 19 +
80 + 35 = 134 days
Path 2 – A-D-C-I-J-K-L = 19 + 50 + 35 = 104 days
Path 3 – A-E-G-I-J-K-L = 8 + 120 + 5 + 50 + 35 = 218
days
Path 4 – A-F-G-I-J-K-L = 8 + 60 + 5 + 50 + 35 = 158
days
Path 5 – B-E-G-I-J-K-L = 12+120+5+50+35 = 222 days
Path 6 – B-F-G-I-J-K-L = 222 – 120 + 60 = 162 days
3. What is/are the critical path(s) from the paths above?
Path 5 – B-E-G-I-J-K-L = 12+120+5+50+35 = 222 days
4. What is the shortest possible completion time for the project,
Te?
222 days

13. 5. Identify all non-critical activities in the project:
Activities A, C, D, and H do not fall on the critical path.
6. Develop an early start, early finish (ES/EF) schedule for the
following project.
Activity
Predecessor
Duration
ES
EF
A
obtain your boss’s approval of your plan
none
8
0
8
B
obtain budget approval
none
12
0
12
C
obtain systems development approval
D
10
9
19
D
develop user specifications
A
1

14. 8
9
E
obtain a marketing program from mktg
A, B
120
12
132
F
obtain a mktg program from consultant
A, B
60
12
72
G
review and select mktg program
E, F
5
132
137
H
perform systems dev of module contentS
C
80
19
99
I
design system interface
C, G
50
137
187
J
review and approve systems development
H, I
5

15. 187
192
K
test prototype
J
10
192
202
L
revision and final systems development
K
20
202
222
Example Problem - Network Diagram :