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Project Management
CPM
Example - Music DM, Inc.
Solution - CPM
1) Construct the network
2) Event analysis - forward pass
- backward pass
3) Activity analysis - critical activities
- noncritical activities
___________________________________________________________________________
Quantitative Methods of Management
 Jan Fábry
Project Management
CPM
Example - Music DM, Inc.
1) Construct the network
One start node & one end node
Each activity  one arc
Two nodes are connected maximally by one arc
___________________________________________________________________________
Quantitative Methods of Management
 Jan Fábry
Project Management
CPM
Example - Music DM, Inc.
1) Construct the network
i
j
3
2
i<j
2
3
___________________________________________________________________________
Quantitative Methods of Management
 Jan Fábry
Project Management
CPM
Example - Music DM, Inc.
Activity
Description
Duration
Predecessors
A
Songs Selection
15
None
B
Mastering
8
A
C
Promotion Material Elaborating
6
A
D
Customers Analysis
7
A
E
Promotion Material Production
4
C, D
F
Promotion Material to PH
5
E
G
Customers Selection
3
D
___________________________________________________________________________
Quantitative Methods of Management
 Jan Fábry
Project Management
CPM
Example - Music DM, Inc.
Activity
Description
Duration
Predecessors
H
Make CD Copies
12
B, D
I
Data to PH
3
G
J
Laser Print
9
F, I
K
Mailing
8
H, J
___________________________________________________________________________
Quantitative Methods of Management
 Jan Fábry
Project Management
CPM
Example - Music DM, Inc.
H
9
4
B
1
A
D
2
C
3
D2
G
7
I
D1
5
K
10
J
8
F
E
6
___________________________________________________________________________
Quantitative Methods of Management
 Jan Fábry
Project Management
CPM
Example - Music DM, Inc.
12
4
9
8
10
8
9
0
1
15
7
2
6
3
3
7
3
8
0
5
5
4
6
___________________________________________________________________________
Quantitative Methods of Management
 Jan Fábry
Project Management
CPM
Example - Music DM, Inc.
2) Event analysis - forward pass
The earliest event time for a node is the earliest time at
which all the preceding activities have been completed.
j
ETj
ET j  max ( ETi  t ij )
i
___________________________________________________________________________
Quantitative Methods of Management
 Jan Fábry
Project Management
CPM
Example - Music DM, Inc.
2) Event analysis - forward pass
Ascending order:
ET1  ET2  ET3  …  ETn
The earliest event time for completing a project is the
earliest time of the last event.
T = ETn
___________________________________________________________________________
Quantitative Methods of Management
 Jan Fábry
Project Management
CPM
Example - Music DM, Inc.
2) Event analysis - backward pass
The latest event time for a node is the latest time at
which the event can occur without delaying the
determined completion time of the project.
LTi  min ( LT j  tij )
j
i
LTi
___________________________________________________________________________
Quantitative Methods of Management
 Jan Fábry
Project Management
CPM
Example - Music DM, Inc.
2) Event analysis - backward pass
Descending order:
LT1  LT2  LT3  …  LTn
The latest event time for completing a project can be
set in the planning process or can be considered as the
earliest event time for completing a project.
LTn = T = ETn
or LTn = TPL > T
___________________________________________________________________________
Quantitative Methods of Management
 Jan Fábry
Project Management
CPM
Example - Music DM, Inc.
3) Activity analysis
Total float:
i
ETi LTi
TFij  ( LT j  ETi  t ij )
tij
j
ETj LTj
___________________________________________________________________________
Quantitative Methods of Management
 Jan Fábry
Project Management
CPM
Example - Music DM, Inc.
3) Activity analysis
Critical activity:
TFij = 0
if LTn = T = ETn
TFij = TPL - T if LTn = TPL > T
Noncritical activity: TFij > 0
if LTn = T = ETn
TFij > TPL - T if LTn = TPL > T
___________________________________________________________________________
Quantitative Methods of Management
 Jan Fábry
Project Management
CPM
Example - Music DM, Inc.
3) Activity analysis
4
Critical path:
B
1
A
D
2
C
3
D2
G
H
7
9
I
D1
5
K
10
J
8
F
6
E
___________________________________________________________________________
Quantitative Methods of Management
 Jan Fábry
Project Management
CPM
Example - Music DM, Inc.
3) Activity analysis
Noncritical activity
1) Start of the activity can be postponed
2) Duration of the activity can be extended
3) Combination of 1 and 2
___________________________________________________________________________
Quantitative Methods of Management
 Jan Fábry