In: Statistics and Probability
Office Automation, Inc., developed a proposal for introducing a new computerized office system that will standardize the electronic archiving of invoices for a particular company. Contained in the proposal is a list of activities that must be accomplished to complete the new office system project. Use the following relevant information about the activities:
Immediate | Time (weeks) | Cost ($1000s) | |||||||
Activity | Description | Predecessor(s) | Normal | Crash | Normal | Crash | |||
A | Plan needs | — | 12 | 8 | 30 | 110 | |||
B | Order equipment | A | 8 | 6 | 120 | 150 | |||
C | Install equipment | B | 10 | 7 | 100 | 160 | |||
D | Set up training lab | A | 7 | 6 | 40 | 50 | |||
E | Conduct training course | D | 10 | 8 | 50 | 75 | |||
F | Test system | C, E | 3 | 3 | 60 | — |
(i) | (ii) | ||
(iii) | (iv) |
Earliest | Latest | Earliest | Latest | Critical | ||||||||
Activity | Start | Start | Finish | Finish | Slack | Activity | ||||||
A | ||||||||||||
B | ||||||||||||
C | ||||||||||||
D | ||||||||||||
E | ||||||||||||
F |
Crash Activities | Number of Weeks | Cost ($1000s) |
A | 4 | |
B | 2 | |
C | 1 | |
D | 1 | |
E | 1 | |
Earliest | Latest | Earliest | Latest | Critical | ||||||||
Activity | Start | Start | Finish | Finish | Slack | Activity | ||||||
A | ||||||||||||
B | ||||||||||||
C | ||||||||||||
D | ||||||||||||
E | ||||||||||||
F |
Given data:
Activity | Description | Immediate Predecessor(s) | Time (weeks) Normal |
Cost ($1000s) Crash |
A | Plan needs | — | 12 | 8 |
B | Order equipment | A | 8 | 6 |
C | Install equipment | B | 10 | 7 |
D | Set up training lab | A | 7 | 6 |
E | Conduct training course | D | 10 | 8 |
F | Test system | C, E | 3 | 3 |
Q-A)
Network Diagram:
Q-B)
Slack = LS-ES
Activity | Activity Time (weeks) (T) |
Earliest Start (ES) |
Latest Start (LS) |
Earliest Finish (EF) |
Latest Finish (LF) |
Slack (LS-ES) |
A | 12 | 0 | 0 | 12 | 12 | 0 |
B | 8 | 12 | 12 | 20 | 20 | 0 |
C | 10 | 20 | 20 | 30 | 30 | 0 |
D | 7 | 12 | 13 | 19 | 20 | 1 |
E | 10 | 19 | 20 | 29 | 30 | 1 |
F | 3 | 30 | 30 | 33 | 33 | 0 |
Q-C)
Critical path is which all have slack is zero, that route is critical path.
A-B-C-F
Project completion time is 33 weeks,
Q-D)
Crash Activities | Number of Weeks can crash | |||
A | 4 | |||
B | 2 | |||
C | 3 | |||
D | 1 | |||
E | 2 |
we only crash the activity which is on critical path.
So we crash activity A first. so we can crash 4 days.
so new network diagram and critical path shown below
Activity | Activity Time (weeks) (T) |
Earliest Start (ES) |
Latest Start (LS) |
Earliest Finish (EF) |
Latest Finish (LF) |
Slack (LS-ES) |
A | 8 | 0 | 0 | 8 | 8 | 0 |
B | 8 | 8 | 8 | 16 | 16 | 0 |
C | 10 | 16 | 16 | 26 | 26 | 0 |
D | 7 | 8 | 9 | 15 | 16 | 1 |
E | 10 | 15 | 16 | 25 | 26 | 1 |
F | 3 | 26 | 26 | 29 | 29 | 0 |
So critical path is A-B-C-F and completion time is 29 weeks,
then we crash B, so we can reduce 2 days,
new diagram will be.
Activity | Activity Time (weeks) (T) |
Earliest Start (ES) |
Latest Start (LS) |
Earliest Finish (EF) |
Latest Finish (LF) |
Slack (LS-ES) |
A | 8 | 0 | 0 | 8 | 8 | 0 |
B | 6 | 8 | 9 | 14 | 15 | 1 |
C | 10 | 14 | 15 | 24 | 25 | 1 |
D | 7 | 8 | 8 | 15 | 15 | 0 |
E | 10 | 15 | 15 | 25 | 25 | 0 |
F | 3 | 25 | 25 | 28 | 28 | 0 |
we can crash D activity
new diagram will be
Activity | Activity Time (weeks) (T) |
Earliest Start (ES) |
Latest Start (LS) |
Earliest Finish (EF) |
Latest Finish (LF) |
Slack (LS-ES) |
A | 8 | 0 | 0 | 8 | 8 | 0 |
B | 6 | 8 | 8 | 14 | 14 | 0 |
C | 10 | 14 | 14 | 24 | 24 | 0 |
D | 6 | 8 | 8 | 14 | 14 | 0 |
E | 10 | 14 | 14 | 24 | 24 | 0 |
F | 3 | 24 | 24 | 27 | 27 | 0 |
Now we got intresting , we have two critical path, A-B-C-F & A-D-E-F
so we have to crash both E & C
then only it reduce to 1 week, else only critical path will chenge, the total time for completing the activities will not change.
new network diagram will be:
Activity | Activity Time (weeks) (T) |
Earliest Start (ES) |
Latest Start (LS) |
Earliest Finish (EF) |
Latest Finish (LF) |
Slack (LS-ES) |
A | 8 | 0 | 0 | 8 | 8 | 0 |
B | 6 | 8 | 8 | 14 | 14 | 0 |
C | 9 | 14 | 14 | 23 | 23 | 0 |
D | 6 | 8 | 8 | 14 | 14 | 0 |
E | 9 | 14 | 14 | 23 | 23 | 0 |
F | 3 | 23 | 23 | 26 | 26 | 0 |
Project completion time is 26weeks.
So the creshe activities
Crash Activities | Number of Weeks crashed | |
A | 4 | |
B | 2 | |
D | 1 | |
C | 1 | |
E | 1 |
e)
Activity | Activity Time (weeks) (T) |
Earliest Start (ES) |
Latest Start (LS) |
Earliest Finish (EF) |
Latest Finish (LF) |
Slack (LS-ES) |
A | 8 | 0 | 0 | 8 | 8 | 0 |
B | 6 | 8 | 8 | 14 | 14 | 0 |
C | 9 | 14 | 14 | 23 | 23 | 0 |
D | 6 | 8 | 8 | 14 | 14 | 0 |
E | 9 | 14 | 14 | 23 | 23 | 0 |
F | 3 | 23 | 23 | 26 | 26 | 0 |
f)
Crash Activities | Number of Weeks can crash | Cost for crashing ($1000s*weeks) |
A | 4 | 4000 |
B | 2 | 2000 |
D | 1 | 1000 |
C | 1 | 1000 |
E | 1 | 1000 |
Total Cost | 9000 |
added cost due to crashing is $9000