activity time (hours) preceding activities decorating & furnishing a spare bedroom 1 remove old...

ActivityTime

(hours)PrecedingActivities

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 start time

Earliest start time

Using Labels to Identify the Activity

Draw an activity networkShow the time needed for each activity – Activity on Arc

Put up posters


0.50.52

A

B C

ABCD




EFGHIJKLM

0.51.5585211

0.5

DDEFG

H IH I

JI

A1

C0.5

B0.5D2

H8

G5 I5

A and C have no predecessors.B follows AD follows B and C

E and F follow D

G follows E and I followsGF follows D and H follows F

E0.5

F1.5

Draw an activity networkShow the time needed for each activity

Put up posters


0.50.52

A

B C

ABCD




EFGHIJKLM

0.51.5585211

0.5

DDEFG

H IH I

JI

A1

C0.5

B0.5D2

E0.5

F1.5H8

G5 I5M0.5

L1

0

J2

K1

K and J follow H and I – need a dummyM follows IL follows J

End

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

Show the early start time needed for each activity

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 hrsCarry out a forward pass to show earliest possible start times

0

1A1

C0.5

B0.5D2

E0.5

F1.5H8

J2

G5

M0.5I5

L1

K101.5 3.5

4

5

9 14

14

16

17

Put up posters


0.50.52

A

B C

ABCD




EFGHIJKLM

0.51.5585211

0.5

DDEFG

H IH I

JI

Show the early start time needed for each activity

Use the largest number when doing a forward pass

i.e. For the 3rd label1 + 0.5 = 1.50 + 0.5 = 0.5So Use 1.5

0

1A1

C0.5

B0.5D2

E0.5

F1.5H8

J2

G5

M0.5I5

L1

K101.5 3.5

4

5

9 14

14

16

17

Carry out a reverse pass to show latest possible start times

Show the latest start time needed for each activity

0

1A1 B0.5D2

E0.5

F1.5H8

J2

G5

M0.5I5

L1

K101.5 3.5

4

5

9 14

14

16

17 17

14

16

1494

17 – 1 = 16 Using activity L16 – 2 = 14 using activity J17 – 1 = 16 using activity K Use the smallest17 – 0.5 = 16.5 using activity M14 – 0 = 14 using dummy activity Use the smallest14 – 5 = 9 using activity I9 – 5 = 4 using activity G

C0.5

Show the latest start time needed for each activity

0

1A1 B0.5D2

E0.5

F1.5H8

J2

G5

M0.5I5

L1

K101.5 3.5

4

5

9 14

14

16

17 173.5

14

16

14

6

941

1.50

4 – 0.5 = 3.5 Using activity E6 – 1.5 = 4.5 using activity F Use the smallest3.5 – 2 = 1.5 Using activity D1.5 – 0.5 = 1 Using activity B1 – 1 = 0 Using activity A1.5 – 0.5 = 1 Using activity C Use the smallest

C0.5

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

delayed.

Finding the critical path

Start A B D E G I J L End

0

1A1 B0.5D2

E0.5

F1.5H8

J2

G5

M0.5I5

L1

K101.5 3.5

4

5

9 14

14

16

17 173.5

14

16

14

6

941

1.50

Critical activities connect 2 nodes where:

latest start time of next activity – early start time of previous activity – duration = 0Right of right node – left of left node – duration = 0

C0.5

Critical path analysis – summary of steps

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 start 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 16 hours

They are those for which:

Start A B D E G I J L End

Activity

Earliest start

previous activity

Latest start next

activityDuration 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 start time next activity – earliest start time previous activity – duration

0.5

1.5

8

1

0.5

Right of right node – left of left node – duration = Float

RR – LL – D = Float = 0 if critical

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

Put the critical activities along the bottom

M

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

0

1A1 B0.5D2

E0.5

F1.5H8

J2

G5

M0.5I5

L1

K101.5 3.5

4

5

9 14

14

16

17 173.5

14

16

14

6

941

1.50

C0.5

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

C F H K

M

Gantt Chart

How many people are needed to complete the job?One person can do the critical activitiesIf activity M is completed after K then the 2nd person can do the other jobs.

0

1A1 B0.5D2

E0.5

F1.5H8

J2

G5

M0.5I5

L1

K101.5 3.5

4

5

9 14

14

16

17 173.5

14

16

14

6

941

1.50

C0.5

Gantt Chart

The exam board like Gantt Charts like this!!!

The Critical Activities clearly follow on from each other with no float

i.e A, B, D, E, G, I, J, L

Resource Histogram

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

This job appears to need 2 people if one person does the critical activities and the other person does the rest.

However some activities may require more than one person.

This means that the Gantt Chart needs amending

Decorating & furnishing a spare bedroom

ActivityNo.

people


2

12

A

B

CD




EF

GH

I

JKL

M

1

1

22

23

13

1Put up posters

Resource Histogram

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

A

B D

E

G I

J

L

C

F

H K

M

ActivityNo.

people3Remove old furniture

Remove carpetTake down curtains & railRemove wallpaper

222

ABCD




EFGHIJKLM

112223121Put up posters

1

3

2

4

5

No. people

Resource Histogram

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

A

B D

E

G I

J

L

C

H K

M

1

3

2

4

5

5 people are needed to complete this job .

Now try and reduce the number of people by levelling the histogram

C must be completed by 1.5hrs so drop it into the gap after AK must be completed by 17hrs so drop it into the gap after J

M must be completed by 17hrs so drop it down

Now 4 people are needed

F

F

Note how F is split so that there are no “holes” in the histogram

F

activity time (hours) preceding activities decorating & furnishing a spare bedroom 1 remove old...

Documents

activity activity

activity j

activity e

activity networkshow

latest start time

activity gc0

activity i9

activity cuse