Answer:
a. To construct the project network using Activity on Node (AON), we can create a diagram that shows each activity as a node and the arrows represent the dependencies between activities. The diagram is as follows:
A(16)
/ \
/ \
/ \
B(9) C(6)
/ / \
/ / \
D(2) E(10) F(7)
\ /
\ /
G(15)
Note: The numbers in parentheses next to each activity represent the normal time for that activity.
b. To determine the critical path, we need to identify the longest path through the network in terms of duration. The critical path is as follows:
A -> B -> D -> F -> G
This path has a duration of 32 weeks.
c. To determine the earliest start, earliest finish, latest start, and latest finish times for each activity, we can use the following formulas:
Earliest Start (ES) = Maximum of the Earliest Finish times of all predecessor activities
Earliest Finish (EF) = ES + Normal time
Latest Finish (LF) = Minimum of the Latest Start times of all successor activities
Latest Start (LS) = LF - Normal time
Using these formulas, we can calculate the following times:
Activity ES EF LS LF
A 0 16 0 16
B 16 25 16 25
C 16 22 22 28
D 25 27 25 27
E 25 35 28 38
F 27 34 27 34
G 34 49 32 47
d. To crash the project, we can identify the activities that are on the critical path and crash them first. We can then continue crashing activities with the highest crash cost per week until we reach the desired project duration.
The crash cost per week for each activity is given in the table. We can calculate the cost to crash each activity by multiplying the crash cost per week by the reduction in time. For example, to crash activity A from 16 weeks to 14 weeks, the cost would be:
Cost to crash A = (3600 - 2000) / (16 - 14) * $300 = $1800
Using this method, we can calculate the following costs to crash each activity as much as possible:
Activity Normal time Crash time Normal cost Crash cost Cost to crash per week
A 16 14 2000 3600 1800
B 9 2 1000 8740 3870
C 6 4 500 800 150
D 2 2 1500 1650 75
E 10 7 3000 3450 150
F 7 5 6000 8000 1000
G 15 10 5000 14400 980
Based on these costs, we can crash activities B and F by a total of 7 weeks, which will reduce the project duration to 25 weeks. This is the shortest duration that we can achieve by crashing activities. The total cost for the project at this duration is:
Total cost = Normal cost
The total cost for the project at this duration is:
Total cost = Normal cost + Cost to crash = $23,200 + $5,340 = $28,540
Note that the cost to crash the project includes both direct and indirect costs. Direct costs are the costs associated with crashing the individual activities, while indirect costs are the costs incurred for each week that the project duration is shortened.
The new project network with the crashed activities is as follows:
A(14)
/ \
/ \
/ \
B(2) C(6)
/ / \
/ / \
D(2) E(7) F(5)
\
\
G(10)
The critical path has now changed to A -> C -> E -> G, with a duration of 23 weeks.
The earliest start, earliest finish, latest start, and latest finish times for each activity can be recalculated using the same formulas as before:
Activity ES EF LS LF
A 0 14 0 14
B 14 16 14 16
C 14 20 16 22
D 16 18 16 18
E 20 27 22 29
F 27 32 27 32
G 32 42 29 39
By crashing the project, we were able to reduce the duration by 9 weeks and the total cost increased by $5,340.