Network diagrams in context PM
SOW
CHARTER
SCOPE DEFINITION
WBS
circulation, negotiation, translation
WBS
WP à activities ----- estimations
Time
AOA
GANTT
Cost
PERT
AON
-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐ planning, resource alloca7on, cost alloca7on, control -­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐-­‐ Mainly PMBOK chapter 6 WBS Network diagrams te
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PERT – Program Evalua/on & Review Technique
WBS
GANTT
PERT
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) There are more complex models, using sta7s7cs but we will eventually address them later 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) –  Ac7vity-­‐on-­‐arrow network construc7on 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
C,7
D,2
E,6
F,3
G,10
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
C,7
D,2
E,6
F,3
G,10
17 19 Examples of different nota/ons 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
C,4
B,7
D,6
10
10
Network Analysis example AOA A,3
C,4
B,7
D,6
There is a dummy ac7vity – dura7on 0 (only a logical dependency) Network Analysis example AOA A,3
C,4
B,7
D,6
Are all paths iden7fied? 10
10
Network Analysis example AOA A,3
C,4
B,7
D,6
10
11
10
No, there are three paths, not two! And that makes quite a difference!! Network Analysis example AOA A,3
C,4
Activity
A
B
C
D
Dummy
Duration
Early St
B,7
10
11
D,6
Early Fi
10
Latest St
Lat. Fi.
Float
Network Analysis example AOA A,3
B,7
10
11
D,6
C,4
10
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
Preceded by a planning effort by the
project management team. This
planning effort is part of the
Develop Project Management Plan process
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 communica/on tool documented in the schedule management plan PERTS, and projects
PERTS, and projects
Late start and backward path 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 (as we have in the table) 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 3
Activ
ity
Dura
tion
Early
St
Early
Fi
Lates
t 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
Dum
my
0
4
4
4
4
0
B,7
A,3
DUMMY,0
4
D,6
C,4
2
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 ac7vity 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 situated condi7ons (environment, resources, risk, …) 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 Network Analysis example 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 Network Analysis example 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 8 paths CP Network Analysis example AOA à AON A,3
AOA
AON
C,4
A,3
B,7
D,6
B,7
END
B
C,4
D,6
With AON you don’t have dummies Network Analysis example AON A,10
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 D,2
J,2
B
B,20
C,4
E,10
END
F,8
G,4
H,2
I,6
ADJ 14
BEJ 32
BF 28
BGI 30
CEJ 16
CF 12
CGI 14
CHI 12