Biology Forums - Study Force

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.