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CRITICAL PATH ANALYSIS
aka NETWORK PATH ANALYSIS
DESIGNED to help managers who are planning complex projects that involve many interrelated tasks
The idea is to help identify which of these interrelated task are the CRITICAL ones. Any change in these ‘critical’ tasks will have a significant impact* on the overall project
* “impact”, relates firstly to time delays in this context
The general ideaBUILDING A BRIDGE
Lots of interrelated tasks eg
To build the bridge you need both the passway and the base.
They are in fact interrelated by by TIME. To build the passway you FIRST have to build the base.
Any delay in the building of the base, is going to cause a delay in the building of the passway
Building of the base is a critical activity
Don’t copy any of these down !
THE CRITICAL PATHWAY is made up of NODES.
Node number[in order of the network]
Earliest Start Time
Latest Finishing Time
Activity / task
Duration of activity
A node for each independent activity/task
On the very first node these will both be ZERO
For the preceding task
For this task
= EST of following node - Duration of current activity
For node 5 the Latest Finishing Time [for activity D & E] is 10. They must both be finished by the 10th week or else the Final Finishing Time will be delayed. This makes sense because if the activity F cannot be started until the 11th week and takes 1 week itself, the Final Finishing Time will be week 12! Therefore all activities preceding Node 5 must be finished by week 10 at the latest. It can be calculated by the “EST of node 6 (11) – Duration of F (1) = 10”
Node number[in order of the network]
Earliest Start Time
Latest Finishing Time
Activity / task
Duration of activity
For the preceding task
For this task
= EST - Duration
The LFT [for activity 4] recorded in Node 8 will be the same as the EST in Node 8 because there is no following node and no activity
The EST means ‘what is the earliest the ‘end’ can start’ and will be : the EST of node 7 + Duration of Activity 4
The activity of the final node is not shown as it is the ‘end’
Lets try a simple example
You cannot leave the classroom until you have
finished your work and tidied up
0
0
a. Finish work
30 mins
30
30
b. Tidy up
7 mins
37
37
ESTs & LFTs are the same because this is a simple example with no parallel tasks
Lets try one that’s a little harder
You cannot leave the classroom until you have all
finished your work, girls should then tidy up and put up the
chairs while guys put away the laptops
0
0
a. Finish work
30 mins
30
30
b. Tidy up
7 mins
45
45
37
39
c. clear laptops
15 mins
d. Put up chairs
6 mins
EST’s
Duration of task is the next issue to identify…
1 : same as before = 0
2 : same as before = 30
3 : 30 + 7 = 37
4: 37 + 6 = 43 or 30 + 15 = 45 ?
Always the LONGER therefore = 45
LFT’s
Go in reverse
4: 45, remember it’s the same.
3 :45-6 = 39
2 : 39 – 7 = 32 or 45 – 15 = 30
Always the SHORTER therefore 30
1. 0, remember it’s the same.
A
A
A
B
B
B
C
C
D
Neither task C nor D can start until tasks A and B are completed
Neither task B nor D can start until tasks A and C are completed
Task D can be started when Task C is completed
Neither task B nor C can start until tasks A is completed
Task A will be divided up into two tasks : B & C
Task B cannot be started before Task A is complete
Task A must be started before Task B, but either could finish first
BUT AT THIS STAGE WE HAVE NOT YET LOOKED AT THIS IDEA
OF ‘CRITICAL’
“TASKS THAT CANNOT BE ALTERED WITHOUT AFFECTING
THE WHOLE PRODUCTION PROCESS”
0
0
a. Finish work
30 mins
30
30
b. Tidy up
7 mins
45
45
37
39
c. clear laptops
15 mins
d. Put up chairs
6 mins
To identify the critical tasks Lets assume a universal small change of 1 minute
Now last 31 minutes. That will affect the EST of Node 2 – & push it up to 31 min.
Now last 8 minutes. That will affect the EST of Node 3 and push it up to 39 min.
Now last 16 minutes. That will affect the EST of Node 4 and push it up to 47 min.
Now last 7 minutes. That will affect the EST of Node 4 and push it up to 46 min.
?
The Critical Tasks are A and B, so the Critical Path is shown by the route connecting Nodes 1, 2 and 3
ALL CRITICAL tasks WILL HAVE E.S.T.s THAT ARE EQUAL TO THEIR L.F.T.s
Common Error
a
b
c
c
2 tasks starting at the same time, with the same follow-on task.
You cant draw it as we see because this would indicate that task a & b are the same duration
It would need to be as we have drawn before [see left]
A
B
C
(Code) Task Preceded by
Duration (mins)
A. Take a shower - 10
B. Have breakfast A 15
C. Text friends A 6
D. Get dressed C 10
E. Drive to interview B & D 25
1. Draw the NETWORK Diagram
2. Identify the Critical Path
3. How long should you allow yourself to get to the interview on time?
0
0
15
10
B
C
A10
10
6
26
26
16
16
D 10
25
E 51
51
We also talk about a FLOAT
Is an activity which has an amount of time by which it can be extended and not affect the overall project time frame
Which task here has a float? And how large is this float?
Activity B! 1 minute
P719 -722 readingp723 Q5.8.1
7
3
A
BF
0
0
5
7
7
5
5
D
5
2
C 9
10
10
10
13
13
E
3
P723 readingp724 Q5.8.2
0
0
6 weeks
1 week
A. foundation1
1
7
7
3
8
11
11
B. Construction
C. Pool E&F
2 weeks
D. Pool T&S
2 weeks
E. House ID&F
3 weeks 10
10
F. Final Testing
1 week
Explain why its important?..... 4 marks
P724 -726 readingp727 Q5.8.3
FREE FLOAT = EST (of next) – Duration (of current) – EST (of current)The amount of time that an activity can be delayed without affecting the EST of the next activity
TOTAL FLOAT = [ LFT (of next) – Duration (of current) – EST (of current) ] You then add up all the Total FloatsThe amount of time a sequence of tasks can be delayed without affecting the whole process
0
0
4
4
A. 4
4
8
11
7
7
B.
C.
311
11
14
14
16
16
21
215
E.
5
H
4
D
3
F
2G
FF =
ActB = 8-4-4 = 0
ActE = 16-5-8 = 3
TF =
ActB = 11-4-4 = 3
ActE = 16-5-8 = 3
= 6
P727 -728 readingp729 Q5.8.4
P729 - 730 reading
The revised times are:
CODE TASK
D 45
E 120
F 30
Recalculate the network diagram and show the new time for the whole project. State whether the critical path has changed [3 marks]
3. Using this information and evidence from the case itself evaluate whether Max should go ahead and build the cottages [6 marks]
MAXS COTTAGES [revised] QUESTION
2. continued
[6 marks]
0
0 30
A
45
B
45
45
60
C105
105
75
10530
D
195
90
E
5
J
20
I20
F
235
235
255
255
260
260
215
215
30
G
20
H
275
275
15K
195
Assume you need to B.Build Access Road in order to bring in the cement needed to C.Lay Foundationie Task C is preceded by A&B
Assume also that you need to B.Build Access Road in order to bring in the materials needed to C.Lay Cables + Water Pipes ie Task D is preceded by A&B too
0
0
MAXS COTTAGES [revised] ANSWER
0
0 30
A
45
B
45
45
60
C105
105
75
10530
D
225
90
E
5
J
20
I20
F
275
275
295
295
300
300
255
255
30
G
20
H
315
315
15K
225
Assume you need to B.Build Access Road in order to bring in the cement needed to C.Lay Foundationie Task C is preceded by A&B
Assume also that you need to B.Build Access Road in order to bring in the materials needed to C.Lay Cables + Water Pipes ie Task D is preceded by A&B too
0
0
45
120
30
MAXS COTTAGES [revised] ANSWER
QUANTITATIVE
You originally reduced the Project Time by 90 days, to 275 days. Which is a 25% reduction.
He then, in his re-estimations, bought it back up again by 55 days. Which is 20% increase (in relation to your New Project Time.)
However 15 of those 55 days where part of the Float in Activity D so the Project Time only went up by 40 days which represents a 15% increase (in relation to your New Project Time).
The Final Revised Project Time is now 315 days, which is still 50 days less than originally quoted. Or 14% less.
He has bought his final prices down by $30 000 which represents 20%.
His prices have gone from $411/day to $381/day (although this ignores material costs)
QUALITATIVE
He seems to be an over-charger, and requires careful watching. Do we want to get into a relationship with him? HOWEVER Do we have other options? Will they be any better.
What is the likelihood of getting the Planning Permission? On time? If there is delays not caused by the Builders, what will be their overtime charge rates?
Significant saving possible with Just-in-Time, provided motivation sand weather remain predictable
Conclusion :
We seem to have got a more competitive prices now and if we are willing to commit time to building a positive relationship with our supplier then I would recommend we go ahead. We should of course bear in mind that the CPA has limitations and numerous unforeseen factors might extend the actual task time.
MAXS COTTAGES [revised] ANSWER
The revised times are:
CODE TASK
D 45
E 120
F 30
Recalculate the network diagram and show the new time for the whole project. State whether the critical path has changed [3 marks]
3. Using this information and evidence form the case itself evaluate whether Max should go ahead and build the cottages [8 marks]
MAXS COTTAGES [original] QUESTION
2. continued
0
0 30
A
45
B
30
..
60
C
45
260
90
90
60
6030
D
180
90
E
5
J
20
I20
F
220
220
240
240
245
245
200
200
30
G
20
H
260
260
15K
180
Assume you need NOT B.Build Access Road in order to C.Lay Foundation
MAXS COTTAGES [original] ANSWER
0
0 30
A
45
B
30
30
60
C
45
300
90
90
75
6030
D
210
90
E
5
J
20
I20
F
260
260
280
280
285
285
240
240
30
G
20
H
300
300
15K
210
Assume you need NOT B.Build Access Road in order to C.Lay Foundation
45
120
30
MAXS COTTAGES [original] ANSWER
QUANTITATIVE
You originally reduced the Project Time by 105 days, to 260 days. Which is a 29% reduction.
He then, in his re-estimations, bought it back up again by 55 days. Which is 21% increase (in relation to your New Project Time.)
However 15 of those 55 days where part of the Float in Activity D so the Project Time only went up by 40 days which represents a 15% increase (in relation to your New Project Time).
The Final Revised Project Time is now 300 days, which is still 65 days less than originally quoted. Or 18% less.
He has bought his final prices down by $30 000 which represents 20%.
His prices have gone from $411/day to $400/day (although this ignores material costs)
QUALITATIVE
He seems to be an over-charger, and requires careful watching. Do we want to get into a relationship with him? HOWEVER Do we have other options? Will they be any better.
What is the likelihood of getting the Planning Permission? On time? If there is delays not caused by the Builders, what will be their overtime charge rates?
Conclusion :
We seem to have got a more competitive prices now an dif we are willing to commit time to building a positive relationship with our supplier then I would recommend we go ahead
MAXS COTTAGES [original] ANSWER
