The following table contains a list of activities, with precedence requirements and crash costs. All start and finish times and crash costs are on a per-week basis

a. Determine the project cost and duration without crashing.
b.

Determine the least expensive project cost if the duration is to be 10% shorter than normal project duration.
c. Determine the least expensive project cost if the duration is to be 20% shorter than normal project duration.
d. Create a graph that shows project expediting cost plotted as a function of the reduction in project duration.

Activity Normal Time Crash Time Normal Cost Crash Cost Predecessor
A 10 7 2000 2600
B 12 8 1500 2000 A
C 16 12 2200 3000 A
D 8 7 2500 3000 B
E 13 10 1950 2275 C
F 9 8 800 1000 D
G 24 29 3650 4000 E, F
H 17 14 1200 1800 G

a. Crash costs per week are shown in the table. The uncrashed project duration is 80 weeks at a cost of $15,800.

Activity Normal Time Crash Time Normal Cost Crash Cost Crash cost/week
A 10 7 2000 2600 $ 200
B 12 8 1500 2000 125
C 16 12 2200 3000 200
D 8 7 2500 3000 500
E 13 10 1950 2275 108.33
F 9 8 800 1000 200
G 20 15 3650 4000 70
H 17 14 1200 1800 200

b. The least expensive way to reduce the project duration by 10% (eight weeks) is by crashing activity G by five weeks at a cost of $70 per week, followed by activity B for three weeks at a cost of $125 per week. The total cost of the 72 week project is $725 extra, or $16,525.

c. Reducing the project by 20% from normal duration requires the actions indicated in part b, plus these actions. The reduction of activity B by another week for $125, activity A by three weeks at $200/week, activity H for three weeks at $200 per week, and activities E and F for one week each at $108.33 and $200 respectively. The total cost for the 64 week project is $2358.33 above the normal cost, or $18,158.33.

d.