© Nuffield Foundation 2011

Nuffield Free-Standing Mathematics Activity

Refurbishing a room

© Nuffield Foundation 2011

Refurbishing a room

You can answer such questions by using critical path analysis.

This activity will show you how to do this.

Where shall I start? What order shall I do things in? How soon can it be ready?’

The techniques of critical path analysis were developed in the late 1950s by two American companies, Dupont and Remington Rand.

They were used to plan large-scale projects such as the development of the Polaris Missile.

The algorithm determines the minimum time for a project to be completed and optimises manpower and resources to achieve this minimum completion time.

Critical Path Analysis

ActivityTime

(hours)Precedingactivities

Decorating and furnishing a spare bedroom

1Remove old furnitureRemove carpetTake down curtains and railRemove wallpaper

0.5

0.52

A

B C

A

B

CD

Prepare wallsPrepare woodworkPaint walls & ceiling 1st coat (& dry)Paint woodwork (and dry)

Lay new carpetPut up curtain rail and hang curtainsArrange new furniture

Paint walls & ceiling 2nd coat (& dry)

EF

GH

I

JKL

M

0.5

1.5

58

52

11

0.5Put up posters

DD

EF

GH I

H IJ

I

Think about…What else needs to be done?Which jobs need to be done before others?How long each job will take?

K

1

End0

M

0.5

L

1

I5

G5

F

1.5

E

0.5

D

2

C0.5

B

0.51

A

Start

00 0

0 1 1 1.5

0 1.5

3.5 4

3.5 6

1.5 3.5

4 9 9 14

J2 16

14 17

14 17

16 17

17 17

Draw an activity network

Carry out a forward pass to show earliest possible start times

Carry out a reverse pass to show latest possible finish times

Show the time needed for each activity

14

Find a critical path Start A B D E G I J L End

8

H

5 14

Think about…What will the rest of the network look like?

Critical path analysis

Step 1 List the activities with a time estimate for each.

Step 2 Note which activities must precede others.

Step 3 Draw an activity network, including the time for each activity.

Step 4 Carry out a forward pass to find the earliest possible start times.

Step 5 Carry out a reverse pass to find the latest possible finish times.

Step 6 Identify critical activities and find a critical path.

Critical activities must start on time if the project is not to be delayed. They are those for which:

A Furniture removal

B Carpet removal

D Wallpaper removal

E Wall preparation

G 1st coat on walls

I 2nd coat on walls

J Carpet laying

L Arranging new furniture

must start at 0 hours

must start at 1 hours

must start at 1.5 hours

must start at 3.5 hours

must start at 4 hours

must start at 9 hours

must start at 14 hours

must start at 16 hours

Latest finish time = earliest start time + duration

Think about…What comes next?

ActivityEarliest

startLatest finishDuration Float

The other activities have some flexibility in their start time.

C Remove curtain & rail

F Prepare woodwork

H Paint woodwork

K Put up curtain & rail

M Put up posters

0 1.5 1 h

3.5 6 1 h

5 14 1 h

14 17 2 h

14 17 2.5 h

Float = latest finish time – (earliest start time + duration)

0.5

1.5

8

1

0.5

Think about…Which activities have float?

Reflect on your work

• Summarise the steps in working out a critical path.

• Describe what is meant by ‘float’.

• What effect will the number of helpers involved have on the minimum completion time?

• When on your finished network will there be the need for at least one helper to allow some of the activities to take place simultaneously?

• What practical considerations need to be taken into account when working out the minimum completion time?

Refurbishing a room