CRITICAL PATH
ANALYSIS:
COOKING
BOLOGNESE
When you leave home, you will need to start being
able to cook your own meals.
You would like to cook a spaghetti bolognese for tea
tonight but your friends would also like to go to the
cinema with you.
It is your task to find out the quickest time it takes
to cook spaghetti bolognese, so that you can tell
your friends what the earliest film showing you can
go and see is.
USEFUL INFORMATION
You start cooking at exactly 7pm.
 The possible film times available are:
7.30pm, 7.45pm, 8.00pm, 8.15pm, 9.00pm or
9.30pm
 It will take you a total of 1 hour to eat your tea
and wash up after.
 It will take you 15 minutes to walk to the cinema.


You have managed to find a very simple recipe
online outlining the different tasks you need to
complete to cook your spaghetti bolognese. Here
are the tasks and their durations:
Duration
(minutes)
5
10
7
30
A - Boil water
B - Add pasta to water and cook
C - Chop up onion, carrot and bacon
D - Cook minced/quorn meat
E - Add onion, carrot, bacon and tomato puree to
minced/quorn meat and stir
3
F - Drain pasta
2
G - Mix Bolognese and pasta together and serve 2
PRECEDENCE TABLE

Your precedence chart should like this:
Activity
Depends on
A - Boil water
-
B - Add pasta to water and cook
A
C - Chop up onion, carrot and bacon
-
D - Cook minced/quorn meat
E - Add onion, carrot, bacon and
tomato puree to minced/quorn meat
and stir
-
F - Drain pasta
G - Mix Bolognese and pasta together
and serve
B
C,D
E,F
ACTIVITY NETWORK

Using this precedence chart, it is possible to
create an activity network for the information.
Earliest Start
Time (EST)
B(10)
F(2)
A(5)
C(7)
D(30)
and Duration
(minutes)
Dummy
Activity
G(2)
E(3)
Latest Finish
Time (LFT)
CRITICAL PATH ANALYSIS
“Critical Path Analysis and their derivatives
had acquired a high reputation following
their use in American defence programme
management and procurement. In Britain,
Concorde was one of the first projects which
these techniques were used.”
Quote from “Government and British civil
aerospace” by Keith Hayward
Critical Path Analysis was used to build the
Leven viaduct on the Cumbrian Coast: “a
vital rail link between the north and south”.
Case study:
WORKING OUT THE EARLIEST START TIME (EST)
For EST, we start from the start node and end at the end node (i.e.
we work forwards).
EST = Earliest Start Time of the previous activity + Duration of the
previous activity
If there are two or more previous activities, choose the highest
EST.
6 + 6 = 12
E.g.
9 + 1 = 10
12 is therefore the
highest EST so
choose 12
4+2=6
6
0+4=4
0
A(4)
The EST of the
start node is
always 0
D(6)
B(2)
12
4
C(5)
4+5=9
9
E(1)
WORKING OUT THE LATEST FINISH TIME (LFT)
For LFT we start from the end node and end at the start node (i.e.
we work backwards).
LFT = Latest Finish Time at the end of the following activity –
Duration of the following activity
If there are two or more activities which follow on from the same
node, choose the smallest LFT.
E.g. (using the previous example)
The LFT of the
start node is
always 0
0
0
A(4)
12 – 6 = 6
B(2)
6
6
D(6)
The LFT of the
end node is
always equal to
its Earliest
Start Time
4
12
4
12
6–2=4
11 – 5 = 6
4 is therefore the smallest
LFT so choose 4
C(5)
12 – 1 = 11
9
E(1)
11
This is the shortest
time the project can
be completed in.
WHO WANTS TO BE A
MILLIONAIRE?
1. What is the formula to work out the
Earliest Start Time (EST)?
A. EST = Earliest start time of the following activity
– Earliest start time of the previous activity
B. EST = Earliest start time of the previous activity
+ Duration of the previous activity
C. EST = Latest finish time of the previous activity
+ Duration of the previous activity
£250,000!
2. What is the formula to work out the
Latest Finish Time (LFT)?
A. LFT = Duration of the previous activity – Latest
finish time of the following activity
B. LFT = Earliest start time of the following activity
+ Duration of the following activity
C. LFT = Latest finish time of the following activity
– Duration of the following activity
£500,000!
3. When we calculate the Earliest Start
Time (EST), which node do we start
from?
A. The first (i.e. the “start” node)
B. The last (i.e. the “end” node)
C. A random node
£750,000!
4. How do we work out the value of the
Latest Finish Time (LFT) of the end
node?
A. We guess a number
B. It is always equal to its Earliest Start Time (EST)
C. We add one to its Earliest Start Time (EST)
Congratulations!
You have won
£1,000,000!!!
Sorry, that’s the
Better luck next time
though! 


Using your knowledge of Earliest Start Times and Latest
Finish Times, use the activity network for cooking your
spaghetti bolognese to calculate the quickest possible time
that it takes to cook this dish.
Using this information, conclude which film showing you
Recall:
• You start cooking at exactly 7pm.
• The possible film times available are:
7.30pm, 7.45pm, 8.00pm, 8.15pm, 9.00pm or 9.30pm
• It will take you a total of 1 hour to eat your tea and wash
up after.
• It will take you 15 minutes to walk to the cinema

Your completed activity network should look like
the following:
5
21
A(5)
0
C(7)
0
D(30)
B(10)
15
31
7
30
30
F(2)
33
33
G(2)
35
35
E(3)
30
We can see here that the critical time to complete the project is 35
minutes. If we then add 60 minutes (i.e. the time it takes to eat the
meal and wash up afterwards, plus 15 minutes walking time to the
cinema, we get a total of 110 minutes. Starting at 7pm, this means that
one could get to the cinema for 8.50pm. The earliest possible film
showing which one could see would therefore be at 9.00pm.
EVALUATION
1)
2)
3)
4)
What is good about Critical Path Analysis?
What is a disadvantage of Critical Path
Analysis?
What have you found interesting about today’s
lesson?
Do you think you will use Critical Path Analysis
again? If yes, how? If no, why not?