Activity- JobsTime

(hours)Preceding

Activities-Jobs

Decorating & furnishing a spare bedroom

1Remove old furnitureRemove carpetTake down curtains & railRemove wallpaper

0.5

0.52

A

B C

A

B

CD

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

Lay new carpetPut up curtain rail & 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

Latest finish time

Earliest start time

Activity

DurationHow long it takes

1

BLatest finish time

Earliest start time

Activity

Duration

0.51.5

Activity B

Remove carpet

Using Labels to Identify the Activity

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 1

0

3.5

3.5

1.5

4 9

J2

14

14

16

17 17

Draw an activity networkShow the time needed for each activity

14

8

H

5

A starts at 0 and takes 1 hrSo B starts at 1C starts at 0 and takes 0.5 hrSo D could start at 0.5 hrsB starts at 1 and takes 0.5 hrSo D must start at 1.5 hrs as both B and C must be finished.D starts at 1.5 and takes 2 hrSo E and F must start at 3.5 hrsI starts at 9 and takes 5 hrSo J, K and M must start at 14 hrsH starts at 5 and takes 8 hr = 13hrs But J and K must start after both H and I so use 14 hrs

L starts at 16 and takes 1 hr = 17 hrs So End is at 17 hrsK starts at 14 and takes 1 hr = 15 hrsM starts at 14 and takes 0.5 hr = 14.5 hrs But End must occur after M,L and K are finished so use 17 hrs

Put up posters

1Remove old furnitureRemove carpetTake down curtains & railRemove wallpaper

0.50.52

A

B C

ABCD

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

Lay new carpetPut up curtain rail & hang curtainsArrange new furniture

Paint walls & ceiling 2nd coat (& dry)

EFGHIJKLM

0.51.5585211

0.5

DDEFG

H IH I

JI

Carry out a forward pass to show earliest possible start times

Latest finish time

Earliest start time

Activity

Duration

1.5

0.5

13

14

13

14 14.5

15

17

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 reverse pass to show latest possible finish times

Show the time needed for each activity

14

8

H

5 14

M ends at 17 and takes 0.5 hr so I could end at 17 – 0.5 = 16.5 hrs

But J ends at 16 and takes 2 hrs so I ends at 16 – 2 = 14 hrs

K ends at 17 and takes 1 hr so I could end at 17 – 1 = 16 hrs

But I must end before M,J and K start so use 14 hrs – lowest value

J ends at 16 and takes 2 hr so H ends at 16 – 2 = 14 hrs

K ends at 17 and takes 1 hr so H could end at 17 – 1 = 16 hrs

But H must end before J and K start so use 14 hrs – lowest value

L ends at 17 and takes 1 hr so J ends at 17 – 1 = 16 hrsE ends at 4 and takes 0.5 hr so D ends at 4 – 0.5 = 3.5 hrs

F ends at 6 and takes 1.5 hr so D could end at 6 – 1.5 = 4.5 hrs

But D must end before E and F start so use 3.5 hrs – lowest value

16.5 14 16

1614

Critical activities must start on time if the project is not to be delayed.

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 networkShow 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

Earliest start time + duration = Latest finish time

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.

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 – lasts 1hr

must start at 1 hour – lasts 0.5hrs

must start at 1.5 hours – lasts 2hrs

must start at 3.5 hours – lasts 0.5hrs

must start at 4 hours – lasts 5hrs

must start at 9 hours – lasts 5hrs

must start at 14 hours – lasts 2hrs

must start at 16 hours

Earliest start time + duration = Latest finish time

They are those for which:

Start A B D E G I J L End

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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17A B D E G I J L

CF

H

K

Put the critical activities along the bottom

M

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

14

8

H

5 14

Gantt Chart

These activities must be started and completed on timeNow put in the non–critical activities at their earliest start timeFinally show the float time

How many people are needed to complete the job?

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17A B D E G I J L

C F H K M

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

14

8

H

5 14

Gantt Chart

One person can do the critical activities

If activity M is completed after K then the 2nd person can do the other jobs.

Alternative Gannt Chart – this is the version needed in the exam

Duration RedFloat BlueThe critical activities have no float