SOW
CHARTER
SCOPE DEFINITION
PM
WBS
circulation, negotiation, translation
WP
à
activities --- estimation
Time
Cost
GANTT
PERT
AOA
AON
Network diagrams in context
-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐ planning, resource alloca7on, cost alloca7on, control -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐
WBS
Network diagrams
PERT, what
does it stat
e
for?
WBS
GANTT
Network Analysis
(PERT – Program Evalua/on & Review Technique;
CPM – Cri/cal Path Method)
Network modula7on approach used in planning, scheduling and controlling projects. Beyond the analysis they facilitate, they represent a common ground to discuss op7ons so they are excellent communica7on tools. They facilitate thema7c brain-‐storming analysis
Network diagrams are en7ty/rela7onship models (interrela7ons among instances of resources) usually used in project planning, namely on scheduling and 7me management
Using these models we need to take into account:
• interrela7on of ac7vi7es (sequencing rela7ons) and
• rela7ons among ac7vi7es and resources (alloca7on)
Cri7cal Path Method (CPM) (determinis7c)
A schedule network analysis technique used to determine the amount of scheduling flexibility (the amount of float) on various logical network paths in the project schedule network, and to determine the minimum total project dura7on. Early dates are calculated by means of a forward pass, using a specified start date. Late dates are calculated by means of a backward pass, star7ng from a specified comple7on date, which some7mes is the project early finish date calculated during the forward pass calcula7on.
Program Evalua7on and Review Technique (PERT) (probabilis7c)
A technique used to improve the accuracy of the cost or dura7on es7mates of project components when there is uncertainty. PERT uses weighted averages of op7mis7c, pessimis7c, and most likely es7mates (the well-‐known three-‐point es7mates) of the components' cost or dura7on. Different weigh7ng schemes represent different probability distribu7ons of the possible cost or dura7on of a component. For instance, the typical formula is [(op/mis/c + 4 /mes the most likely + pessimis/c) divided by 6], approximates a beta distribu7on.
CPM/PERT
• Cri7cal Path Method (CPM)– DuPont & Remington-‐Rand (1956)
– Determinis7c task 7mes
– Ac7vity-‐on-‐node network construc7on
• Project Evalua7on and Review Technique (PERT)
– US Navy, Booz, Allen & Hamilton
– Mul7ple task 7me es7mates (probabilis7c)
PERT elements
Events (states), ac7vi7es (nature and 7me), preceding, alloca7on, context (context must always be defined and clarified)
Some examples of PERT representa7on -‐ AOA – ac/vity on arrow, or ADM -‐ arrow diagramming method;
and AON – ac7vity on node
A,3
B,5
E,6
C,7
D,2
PERT elements
Events (states), ac7vi7es (nature and 7me), preceding, alloca7on, context (context must always be defined and clarified)
Some examples of PERT representa7on -‐ AOA – ac7vity on arrow, or ADM -‐ arrow diagramming method;
and AON – ac7vity on node
A,3
B,5
E,6
C,7
D,2
F,3
G,10
17
19
AOA -‐ Parallel ac/vi/es signaled as we exemplify are not allowed
A
B
A,B
A
B
dummy
Task B can only be started acer ac7vity A is completed. The same with D and C
A,3
B,7
C,4
D,6
10
A,3
B,7
C,4
D,6
Network Analysis example AOA
A,3
B,7
C,4
D,6
10
10
Are all paths iden7fied?
A,3
B,7
C,4
D,6
10
10
No, there are
three
paths, not two!
And that makes quite a difference!!
11
A,3
B,7
C,4
D,6
10
10
11
Activity Duration Early St Early Fi Latest St Lat. Fi. Float
A
B
C
D
Dummy
A,3
B,7
C,4
D,6
10
10
11
Activity Duration Early St Early Fi Latest St Lat. Fi. Float
A
3
0
3
1
4
1
B
7
4
11
4
11
0
C
4
0
4
0
4
0
D
6
4
10
5
11
1
Dummy
0
4
4
4
4
0
PERTS, and projects
1. Define the project and all its ac7vi7es. The project is made of tasks and all tasks should have a
single start and a single finish
2. Develop the rela7onships among the ac7vi7es. Decide which ac7vi7es must precede, which
must follow others, and the ones that can be executed in parallel. If you are short in 7me try to put in parallel as much ac7vi7es as you can
3. Draw the network diagram connec7ng all the ac7vi7es. Each ac7vity is unique. Dummy
ac7vi7es are immaterial in 7me but relevant in sequence, they impose logical dependences 4. You can assign 7me and cost to each ac7vity
5. Compute the longest 7me path through the network. This path is called the Cri/cal Path
6. Use the network to help plan, schedule, monitor and control the project and also as a
communica7on tool
Preceded by a planning effort by the
project management team. This
planning effort is part of the
Develop Project Manage-
ment Plan process
backward pass
Early dates are calculated forwards, using the forward path. Late dates are calculated in reverse direc7on,
star7ng at the date of the finishing of the project – this is the backward path
In this example one backward path leads us to “event 3” through ac7vity B. So we have:
• Total project 7me (cri7cal path) = 11
• 11-‐7 = 4. This means that the late start for ac7vity B is 4
Rela7ng to “event 2” we have to evaluate two paths, Dummy and D. Through Dummy we have 4 -‐ 0 = 4, this
means that Dummy late start is 4 and through D we have 11 -‐ 6 = 5, so ac7vity D late start is 5
A,3
C,4
D,6
B,7
2
3
4
D
UMMY,0
Activ ity Dura tion Early St Early Fi Lates t St Lat. Fi. FloatA
3
0
3
1
4
1
B
7
4
11
4
11
0
C
4
0
4
0
4
0
D
6
4
10
5
11
1
Dum my0
4
4
4
4
0
So you already have the rule to compute early starts and late starts. Early starts are
computed in the
forward path
from the beginning to the end, adding dura7on
and late starts are computed in the
backwards path
, subtrac7ng dura7on from the end
Project management tools compute this for you, you just have to manage according to
Your project is to design and develop an electric motor. Ac7vity dura7ons and predecessors
are iden7fied at the following table. A) construct a PERT; B) Which is the dura7on of every
path? Which path is the cri7cal one? C) What happens if ac7vity E dura7on becomes 8?
Ac7vity dura7on predecessor A 10 -‐ B 20 -‐ C 4 -‐ D 2 A E 10 B,C F 8 B,C G 4 B,C H 2 C I 6 G,H J 2 D,E
Ac7vity dura7on predecessor A 10 -‐ B 20 -‐ C 4 -‐ D 2 A E 10 B,C F 8 B,C G 4 B,C H 2 C I 6 G,H J 2 D,E
Ac7vity dura7on predecessor A 10 -‐ B 20 -‐ C 4 -‐ D 2 A E 10 B,C F 8 B,C G 4 B,C H 2 C I 6 G,H J 2 D,E
Network Analysis example AOA
8 paths
A,3
B,7
C,4
D,6
Network Analysis example AOA
à
AON
A,3
B,7
C,4
D,6
With AON you don’t have dummies
END
B
AOA
Ac7vity dura7on predecessor A 10 -‐ B 20 -‐ C 4 -‐ D 2 A E 10 B,C F 8 B,C G 4 B,C H 2 C I 6 G,H J 2 D,E A,10 B,20 C,4 D,2 E,10 F,8 G,4 H,2 I,6 J,2
