Download - Slide 8.1 4E1 Project Management Network Representation and Critical Path Analysis - Part 1
Slide 8.2
Key ConceptsNetworks
• Building networks, possible problems, scheduling objectives
Critical path (analysis)• Calculating the critical path, possible complications, handling constraints
Project planning software
Project Evaluation and Review Technique (PERT)• Using simulation with PERT
Project plan
Slide 8.3
Structure of SessionDeveloping a project schedule to build a garage
Starting point: specification and info on resources
From this you will create:• a WBS• a task list• an arrow diagram network of the project• a precedence diagram of the project (homework)
We will then examine the concept of critical path• You will determine the critical path through the network
We will look briefly at PERT
We will conclude with a summary of the plan
We will consider some of the software tools available to help
Slide 8.4
Specification8m x 5m garage
Concrete base
Wooden trussed & sheeted roof
Double wooden doors
No windows
Side fascia boards
Side gutter system which drains to a soakaway trench containing a drainage pipe
Doors and trusses will need to be made up
All exterior woodwork and doors to be painted
Brick walls; no plastering required
Reinforced steel joist (RSJ) required for the door
You have all materials including bricks, wood, sand, cement, aggregate, ready-made guttering and grills plus nails, screws etc. and a full set of tools (mixer, spades, saws, etc.) and labour
Assume that drainage is into an open pond and needs no connection to a main system
Slide 8.6
Building a Garage
RSJ lintel
Gutter
FasciaBoards
Drain (underground)
Sheeted roof
WoodenDoubleDoors
TrussBeams
Brick walls
Ridge beam
DoorFrame
Slide 8.7
Extract from Possible WBS1. Base
2. Drainage
3. Walls
4. Doors4.1 Make door frame
4.1.1 Cut frame timbers
4.1.2 Prime frame timbers
4.1.3 Assemble frame
4.1.4 Paint frame
4.2 Make doors4.2.1 Cut door timbers
4.2.2 Prime door timbers
4.2.3 Assemble doors
4.2.4 Fit hinges
4.2.5 Hang doors
4.2.6 Paint doors
4.2.7 Fit bolt
5. Roofing…
Slide 8.8
Some Network Concepts
We will first consider information-on-arrow representation
Information-on-arrow networks can be used to represent various problems e.g.:
• Shortest route
• Flow capacity
• Projects
The following terminology is used in networks:
• Nodes
• Sources/starts
• Sinks/ends
• Links/arcs
• Directed and undirected
• Loops
• Circuits
• Paths
Slide 8.9
Example: Shortest Route Problem
1
11
6
5
4
3
2
12
7
8
9
1020
70
30
40
20 120
50
80
100
6060
60
70
110
9070 80
90
30
110
20
8050
9040
70
100
Start
Finish
Find the shortest route through this network where numbers are distances in kilometers – have fun!
Slide 8.10
Project Networks
Arrows/links • represent a task or activity
and its duration - hence “Activity on Arrow” (AOA)
• conventionally run left-right
One and only one • starting node
• completion node
• link between each pair of nodes (why?)
At least one path from start to completion
No circuits or loops
May be • multiple paths from start to
completion
• special activities, and thus links, with zero duration
Project networks have some specific characteristics:
Slide 8.11
No. Task ID Task Duration Predecessors Resources1 START Project start 02 G0102 Dig foundation 8 1 Labourer3 G0103 Make, prime door frame 6 1 Skilled4 G0104 Dig soakaway, trench 2 1 Labourer5 G0107 Make doors 1 1 Skilled6 G0110 Cut roof timbers 1 1 Skilled7 G0205 Concrete foundations 2 2 Labourer8 G0305 Position door frame 1 3 Skilled9 G0411 Lay underground pipe 1 4 Labourer, Skilled10 G0508 Build main brick walls 10 7, 8 Skilled, Labourer11 G0509 Lay concrete base 2 7 Labourer12 G0713 Prime the doors 1 5 Skilled13 G0810 Fit RSJ lintel 1 10 Skilled, Labourer14 G0913 Lay floor screed 1 11 Skilled15 G1012 Fit roof timbers 2 6, 13 Skilled16 G1016 Case lintel, parapets 2 13 Skilled, Labourer17 G1115 Fill draining trench 1 9 Labourer18 G1214 Fit fascia boards 1 15 Skilled19 G1216 Fit roof sheets 1 15 Skilled20 G1317 Hang doors 1 10, 12, 14 Skilled, Labourer21 G1417 Fit gutters and pipes 1 9, 18 Skilled22 G1518 Concrete over trench 1 17 Labourer23 G1618 Seal the roof 2 16, 19 Skilled24 G1718 Paint all woodwork 3 20, 21 Skilled25 FINISH Finish project 0 22, 23, 24
Exercise 2: Draw This Network
Slide 8.12
Solution…
A D
B
E
C
G
F
H
I
J
M
L
N
Dig foundation 8
Cut roof Timbers 1
Dig trench 2
Make& Prime
door frame 6
Mak
e do
ors 1
Position
d/frame 1
Concrete
fdns 2
Lay under-
ground pipe 1
Build
walls 10
Concrete
base 2
Prime doors 1
Fit
RSJ 1
Lay
floor
scre
ed 1
P
OFit roof
timbers 2
Case lintel and parapets 2
K
Fill
Trench 1
Fit f
asci
abo
ards
1
Fit roof
sheets 1
Hang Doors 1
R
S
Fit g
utte
rsan
d pi
pes 1
Concrete
over trench 1
Seal
Roof 2
PaintWood 3
Q
FINISH
START
Slide 8.13
Project Network FeaturesSlack
• Typical task has earliest start and latest completion times
• Slack = LC - ES
Critical path• If all tasks on a path from start
to completion have zero slack, the path is on the critical path
Free float• Activities that can start late or
finish early have free float
• Activities on the critical path have no free float
Interfering float• An activity that can only be
delayed in its float at the expense of some other activity’s float has an interfering float
Other types of float exist
Sub-critical activities• Activities with a small free float
are sub-critical activities
Slide 8.14
Critical Path Network Objectives
May be > 1 objective
e.g. To minimise:• Total project time
• Total project cost
• Cost for a given time
• Time for a given cost
• Idle resources
CPA methods used as:• planning tools
• control tools
Many software packages can calculate the path
May be > 1 critical path
Slide 8.15
Critical Path Method (CPM)To find the critical path three steps are required
• Requires care and thought
• Easy to make a mistake
1.Forward pass
Traverse network from start, calculating earliest possible completion time of each task.
This will give you a total time for the project.
2.Backward pass
Working backwards from end, calculate latest completion time needed to complete each activity’s preceding task.
3.Identify critical path
Nodes where the forward earliest completion time equals the backward latest completion lie on the critical path.
Also single pass method
Slide 8.16
Example 1: Simple Project Network
What is the critical path through this network?
1
65
4
3
2
3
0
2
37
2
2
5
6
3 Finish
Start
0
2
e.g. Task (4,6). Duration 5 days
Slide 8.18
1
65
4
3
2
3
0
2
37
2
2
5
6
3
0
0 3
6
62
2
1319
30
6
1913
4 6
Start
Finish
Step 2: Backward Pass
Slide 8.19
1
65
4
3
2
3
0
2
37
2
2
5
6
3
Start
0
0 3
6
62
2
1319
30
6
1913
4 6
Start
Finish
Step 3: Critical Path
Slide 8.20
Exercise 3: Given the Following…
1 2 3 6 7 8
9
5
4
11103a
b
c7
4
d5
d1
d20
0
0d3
2 1ml
k3
j4
3e
2f
i98 h1 g
Find the critical path through this network
Slide 8.21
Exercise 3: Forward Pass
1 2 3 6 7 8
9
5
4
11103
40
0
0
2 1
3
4
3
2
981
0 3
10
10
8
10 16
20
23
23
24
5
7
Slide 8.22
1 2 3 6 7 8
9
5
4
11103
40
0
0
2 1
3
4
3
2
981
0 3
10
10
8
10 16
20
23
23
24
23
23
20
16
8
14
13
13
3 0 24
5
7
Exercise 3: Backward Pass
Slide 8.23
Exercise 3: Critical Path
1 2 3 6 7 8
9
5
4
11103
4
5
0
0
0
2 1
3
4
3
2
981
0 3
10
10
8
10 16
20
23
23
24
23
23
20
16
8
14
13
13
3 0 24
7
Slide 8.24
Exercise 4Find the critical path for the garage projectIgnore labour constraints and non-working days
A D
B
E
C
G
F
H
I
J
M
L
N
Dig foundation 8
Cut roof Timbers 1
Dig trench 2
Make& Prime
door frame 6
Mak
e do
ors 1
Position
d/frame 1
Concrete
fdns 2
Lay under-
ground pipe 1
Build
walls 10
Concrete
base 2
Prime doors 1
Fit
RSJ 1
Lay
floor
scre
ed 1
P
OFit roof
timbers 2
Case lintel and parapets 2
K
Fill
Trench 1
Fit f
asci
abo
ards
1
Fit roof
sheets 1
Hang Doors 1
R
S
Fit g
utte
rsan
d pi
pes 1
Concrete
over trench 1
Seal
Roof 2
PaintWood 3
Q
FINISH
START
1
6 10 20
21
8 10
12
20
21
23
2424
25
28
2 3
4
28
26
24
9 1021
24
2520
23
108
0
0
27
23 21
23
2423