Question

Here is a list of activity times for a project as well as crashing costs for its activities. Determine which activities should be crashed and total cost of crashing if the goal is to shorten the project by three weeks as cheaply as possible. First construct a network diagram. You can use either an AOA or and AON
Path Activity "Duration
(weeks)" Duration Total (weeks) First Crash "Second
Crash"
TOP A 5 14 $8 $10
B 6 7 9
C 3 14 15
MIDDLE D 3 13 9 11
E 7 8 9
C 3 14 15
F 5 15 10 15
BOTTOM G 5 11 13
H 5 12 14
Critical path: 1-5-6-7

Answer 1

To shorten the project by three weeks as cheaply as possible, we need to find the cheapest combination of crashing activities.

First, let's look at the current critical path:
1-5-6-7 (TOP: A-B-C / 14 weeks)

Now, we need to find activities that can help shorten the project duration:

1. Activity A (First Crash): Reduces duration by 1 week; cost: $8
2. Activity B (First Crash): Reduces duration by 1 week; cost: $7
3. Activity D (First Crash): Reduces duration by 1 week; cost: $9
4. Activity E (First Crash): Reduces duration by 1 week; cost: $8
5. Activity F (First Crash): Reduces duration by 1 week; cost: $10
6. Activity G (First Crash): Reduces duration by 1 week; cost: $11
7. Activity H (First Crash): Reduces duration by 1 week; cost: $12

Since our goal is to shorten the project by three weeks, we will choose the three activities with the lowest crashing costs:

1. Activity B (First Crash): Reduces duration by 1 week; cost: $7
2. Activity A (First Crash): Reduces duration by 1 week; cost: $8
3. Activity E (First Crash): Reduces duration by 1 week; cost: $8

Total cost of crashing: $7 + $8 + $8 = $23

By crashing activities A, B, and E by one week each, we can shorten the project by three weeks, and the total cost of crashing is $23.