Question
In: Statistics and Probability
Office Automation, Inc., developed a proposal for introducing a new computerized office system that will standardize...
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 | — | |||
- Which project network is correct?
(i) (ii) (iii) (iv)
- Develop an activity schedule. If your answer is zero, enter
“0”.
Earliest Latest Earliest Latest Critical Activity Start Start Finish Finish Slack Activity A B C D E F - What are the critical activities, and what is the expected
project completion time?
Critical Path:
Expected project completion time = weeks. - Assume that the company wants to complete the project in six
months or 26 weeks. What crashing decisions do you recommend to
meet the desired completion time at the least possible cost? Work
through the network and attempt to make the crashing decisions by
inspection.
Crash Activities Number of Weeks Cost ($1000s) A 4 B 2 C 1 D 1 E 1 - Develop an activity schedule for the crashed project. If your
answer is zero, enter “0”.
Earliest Latest Earliest Latest Critical Activity Start Start Finish Finish Slack Activity A B C D E F - What added project cost is required to meet the six-month
completion time?
Total added cost due to crashing $
Solutions
Expert Solution
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
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