activity time (hours) preceding activities decorating & furnishing a spare bedroom 1 remove old...
TRANSCRIPT
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
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
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
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
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
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
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 9 hours – lasts 5hrs
must start at 14 hours – lasts 2hrs
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
3Remove old furnitureRemove carpetTake down curtains & railRemove wallpaper
2
12
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
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
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
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