cpm examples1
TRANSCRIPT
EXAMPLE 1
Example 1. CPM with Single Time Estimate
Consider the following consulting project:
Develop a critical path diagram and determine
the duration of the critical path and slack times
for all activities.
Activity Designation Immed. Pred. Time (Weeks) Assess customer's needs A None 2 Write and submit proposal B A 1 Obtain approval C B 1 Develop service vision and goals D C 2 Train employees E C 5 Quality improvement pilot groups F D, E 5 Write assessment report G F 1
Example 1. CPM with Single Time Estimate
Consider the following consulting project:
Activity Designation Immed. Pred. Time (Weeks) Assess customer's needs A None 2 Write and submit proposal B A 1 Obtain approval C B 1 Develop service vision and goals D C 2 Train employees E C 5 Quality improvement pilot groups F D, E 5 Write assessment report G F 1
Develop a critical path diagram and determine
the duration of the critical path and slack times
for all activities.
Example 1: First draw the network
A(2) B(1) C(1)
D(2)
E(5)
F(5) G(1)
A None 2
B A 1
C B 1
D C 2
E C 5
F D,E 5
G F 1
Act. Imed. Pred. Time
Example 1: Determine early starts and early finish times
ES=9 EF=14
ES=14 EF=15
ES=0 EF=2
ES=2 EF=3
ES=3 EF=4
ES=4 EF=9
ES=4 EF=6
A(2) B(1) C(1)
D(2)
E(5)
F(5) G(1)
Hint: Start with ES=0 and go forward in the network from A to G.
Example 1: Determine late starts and late finish times
ES=9 EF=14
ES=14 EF=15
ES=0 EF=2
ES=2 EF=3
ES=3 EF=4
ES=4 EF=9
ES=4 EF=6
A(2) B(1) C(1)
D(2)
E(5)
F(5) G(1)
LS=14 LF=15
LS=9 LF=14
LS=4 LF=9
LS=7 LF=9
LS=3 LF=4
LS=2 LF=3
LS=0 LF=2
Hint: Start with LF=15 or the total time of the project and go backward in the network from G to A.
Example 1: Critical Path & Slack
ES=9 EF=14
ES=14 EF=15
ES=0 EF=2
ES=2 EF=3
ES=3 EF=4
ES=4 EF=9
ES=4 EF=6
A(2) B(1) C(1)
D(2)
E(5)
F(5) G(1)
LS=14 LF=15
LS=9 LF=14
LS=4 LF=9
LS=7 LF=9
LS=3 LF=4
LS=2 LF=3
LS=0 LF=2
Duration = 15 weeks
Slack=(7-4)=(9-6)= 3 Wks
Example 2. CPM with Three Activity Time Estimates
Task
Immediate
Predecesors Optimistic Most Likely Pessimistic
A None 3 6 15
B None 2 4 14
C A 6 12 30
D A 2 5 8
E C 5 11 17
F D 3 6 15
G B 3 9 27
H E,F 1 4 7
I G,H 4 19 28
EXAMPLE 2
A Select administrative and medical staff. — 12 B Select site and do site survey. — 9 C Select equipment. A 10 D Prepare final construction plans & layout. B 10 E Bring utilities to the site. B 24 F Interview applicants and fill positions in A 10 nursing, support staff, maintenance, and security. G Purchase and take delivery of equipment. C 35 H Construct the hospital. D 40 I Develop an information system. A 15 J Install the equipment. E,G,H 4 K Train nurses and support staff. F,I,J 6
St. Adolf’s Hospital (A sample project)
Immediate Activity Description Predecessor(s) Activity Times
*We won’t assigning “Responsibility” data, but it is important in project management.
St. Adolf’s Hospital Diagramming the Network
Finish Start
A
B
C
D
E
F
G
H
I
J
K
Immediate Predecessors
A – 12
B – 9
C A 10
D B 10
E B 24
F A 10
G C 35
H D 40
I A 15
J E,G,H 4
K F,I,J 6
Activity Times (wks)
St. Adolf’s Hospital Activity Paths
Finish Start
A
B
C
D
E
F
G
H
I
J
K
Path Time (wks) A-I-K33 A-F-K28 A-C-G-J-K 67 B-D-H-J-K 69 B-E-J-K 43
Paths are sequences of activities between a project’s start and finish.
St. Adolf’s Critical Path
Finish Start
A
B
C
D
E
F
G
H
I
J
K Path Time (wks) A-I-K33 A-F-K28 A-C-G-J-K 67 B-D-H-J-K 69 B-E-J-K 43
Project Expected Time is 69 wks.
The longest path is the critical path!
Earliest Start and Earliest Finish Times
K
6
C
10
G
35
J
4
H
40
B
9
D
10
E
24
I
15
Finish Start
A
12
F
10
0
Earliest start time
12
Earliest finish time
0 9
9 33
9 19 19 59
22 57 12 22
59 63
12 27
12 22 63 69
© 2013 Lew Hofmann
Earliest Start and Earliest Finish Times
Critical Path
The Critical Path takes 69 weeks
K
6
C
10
G
35
J
4
H
40
B
9
D
10
E
24
I
15
Finish Start
A
12
F
10
0 9
9 33
9 19 19 59
22 57 12 22
59 63
12 27
12 22 63 69 0 12
Path Time (wks) A-I-K33 A-F-K28 A-C-G-J-K 67 B-D-H-J-K 69 B-E-J-K 43
© 2013 Lew Hofmann
K
6
C
10
G
35
J
4
H
40
B
9
D
10
E
24
I
15
Finish Start
A
12
F
10
0 9
9 33
9 19 19 59
22 57 12 22
59 63
12 27
12 22 63 69 0 12
Latest Start and Latest Finish Times (You start with the last activity and work toward the first activity)
48 63
53 63
59 63
24 59
19 59
35 59
14 24
9 19
2 14
0 9
Latest finish time
63 69
Latest start time
© 2013 Lew Hofmann
Activity Slack Analysis
K
6
C
10
G
35
J
4
H
40
B
9
D
10
E
24
I
15
Finish Start
A
12
F
10
0 9
9 33
9 19 19 59
22 57 12 22
59 63
12 27
12 22 63 69 0 12
48 63
53 63
59 63
24 59
19 59
35 59
14 24
9 19
2 14
0 9
63 69
Slack is the difference between LS and ES or EF and LF
Node Duration ES LS Slack
A 12 0 2 2
B 9 0 0 0
C 10 12 14 2
D 10 9 9 0
E 24 9 35 26
F 10 12 53 41
G 35 22 24 2
H 40 19 19 0
I 15 12 48 36
J 4 59 59 0
K 6 63 63 0
© 2013 Lew Hofmann