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 8.5

Exercise 1

Draw up a work breakdown structure

From this, draw up a task list

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 8.17

1

65

4

3

2

3

0

2

37

2

2

5

6

3

0

0 3

6

19

62

13

2

Start

Finish

Step 1: Forward Pass

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