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Home > Operation Research calculators > Critical path, Total float, Free float, Independent float calculator
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Algorithm and examples
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PERT and CPM
Critical path, Total float, Free float, Independent float
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1-2 | 4 | 2-3 | 6 | 2-4 | 2 | 3-4 | 0 | 3-6 | 2 | 4-5 | 7 | 5-6 | 4 | 6-7 | 8 | 7-8 | 3 |
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Solution
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Solution provided by AtoZmath.com
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Critical path, Total float, Free float, Independent float calculator
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1. An assembly is to be made from two parts X and Y. Both parts must be turned on a lathe
Y must be polished where as X need not be polished. The sequence of acitivities, together with their
predecessors, is given below
Activity |
Description |
Predecessor Activity |
A |
Open work order |
- |
B |
Get material for X |
A |
C |
Get material for Y |
A |
D |
Turn X on lathe |
B |
E |
Turn Y on lathe |
B,C |
F |
Polish Y |
E |
G |
Assemble X and Y |
D,F |
H |
Pack |
G |
Draw a network diagram of activities for the project.
2. Listed in the table are the activities and sequencing necessary for a maintenance job on
heat exchangers in a refinery
Activity |
Description |
Predecessor Activity |
A |
Dismantle pipe connections |
- |
B |
Dismantle heater, closure and floating front |
A |
C |
Remove tube bundle |
B |
D |
Clean bolts |
B |
E |
Clean heater and floating head front |
B |
F |
Clean tube bundle |
C |
G |
Clean shell |
C |
H |
Replace tube bundle |
F,G |
I |
Prepare shell pressure test |
D,E,H |
J |
Prepare tube pressure test and reassemble |
I |
Draw a network diagram of activities for the project.
3. Listed in the table are the activities and sequencing necessary for the competion of a
recruitment procedure for management trainees in a firm.
Activity |
Description |
Predecessor Activity |
A |
|
- |
B |
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A |
C |
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A |
D |
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C |
E |
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B |
F |
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C |
G |
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D,E |
H |
|
G |
I |
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H |
J |
|
F |
K |
|
I,J |
L |
|
K |
M |
|
L |
N |
|
J |
O |
|
M,N |
Draw a network diagram of activities for the project.
4. An established company has decided to add a new product to its line. It will buy the
product from a manufacturing concern, package it, and sell it to a number of distributors that have been
selected on a geographical basis. Market research has already indicated the volume expected and the size
of sales force required. The steps shown in the following table are to be planned.
Activity |
Description |
Predecessor Activity |
Duration (days) |
A |
Organize sales office |
- |
6 |
B |
Hire salesman |
A |
4 |
C |
Train salesman |
B |
7 |
D |
Select advertising agency |
A |
2 |
E |
Plan advertising campaign |
D |
4 |
F |
Conduct advertising campaign |
E |
10 |
G |
Design package |
- |
2 |
H |
Setup packaging campaign |
G |
10 |
I |
Package initial stocks |
J,H |
6 |
J |
Order stock from manufacturer |
- |
13 |
K |
Select distributors |
A |
9 |
L |
Sell to distributors |
C,K |
3 |
M |
Ship stocks to distributors |
I,L |
5 |
(a) Draw an arrow diagram for the project.
(b) Indicate the criticla path.
(c) For each non-critical activity, find the total and free float.
5. An established company has decided to add a new product to its line. It will buy the
product from a manufacturing concern, package it, and sell it to a number of distributors that have been
selected on a geographical basis. Market research has already indicated the volume expected and the size
of sales force required. The steps shown in the following table are to be planned.
Activity |
Description |
Predecessor Activity |
Duration (days) |
A |
|
- |
14 |
B |
|
A |
4 |
C |
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B |
2 |
D |
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C |
1 |
E |
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A |
2 |
F |
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E |
3 |
G |
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E |
2 |
H |
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E |
4 |
I |
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H,L |
3 |
J |
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K |
12 |
K |
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D,F,G |
4 |
L |
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J |
2 |
M |
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H,L |
2 |
(a) Draw an arrow diagram for the project.
(b) Indicate the criticla path.
(c) For each non-critical activity, find the total and free float.
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