operation management
Read the Specialty Contractors case (download) and submit your analysis of the exercise - i.e., identify which activities should be crashed and by how much time, what is the cost of doing this and how soon can the project be completed. (Hint: Use the greedy algorithm taught in class even though it is not guaranteed to always find the optimal solution.) [Please submit your assignment as an attachment.]
Solution:
According to the Specialty Contractors case, we get the critical path is PTV and the project duration is 12 weeks but it will be delayed 4 weeks in the beginning.
Greedy Algorithm:
PTV is critical path in this case. (Duration: 12 weeks)
The cheapest activity to crash on this path is T.
Marginal Crashing Cost = 4,000 $
Marginal Benefit = 9,000 $ (1 week delay reduction)
Now, PTV is still critical path. (Duration: 11 weeks)
Cut activity T by 1 week.
Cost = 4,000 $
Reduction in delay cost = 9,000 $
Then, PS, PTV, and QV are critical paths. (Duration: 10 weeks)
Since T cannot be crashed, we crash P and Q to expedite the project.
Cut activity P and Q by 1 week, respectively.
Cost = 5,000 $ + 6,000 $ = 10,000 $
Reduction in delay cost = 9,000 $
Since the cost is higher than savings, we accept two weeks delay.
Total cost of crashing = 4000 + 4000 = 8000 $
Total cost of delay = 9000 + 9000 = 18000 $ (delayed by 2 weeks)
Total cost of crashing and delay = 8000 + 18000 = 26000 $
To conclude, we cut activity T by 2 weeks. The project can be completed in 14 weeks.
Solution:
According to the Specialty Contractors case, we get the critical path is PTV and the project duration is 12 weeks but it will be delayed 4 weeks in the beginning.
Greedy Algorithm:
PTV is critical path in this case. (Duration: 12 weeks)
The cheapest activity to crash on this path is T.
Marginal Crashing Cost = 4,000 $
Marginal Benefit = 9,000 $ (1 week delay reduction)
Now, PTV is still critical path. (Duration: 11 weeks)
Cut activity T by 1 week.
Cost = 4,000 $
Reduction in delay cost = 9,000 $
Then, PS, PTV, and QV are critical paths. (Duration: 10 weeks)
Since T cannot be crashed, we crash P and Q to expedite the project.
Cut activity P and Q by 1 week, respectively.
Cost = 5,000 $ + 6,000 $ = 10,000 $
Reduction in delay cost = 9,000 $
Since the cost is higher than savings, we accept two weeks delay.
Total cost of crashing = 4000 + 4000 = 8000 $
Total cost of delay = 9000 + 9000 = 18000 $ (delayed by 2 weeks)
Total cost of crashing and delay = 8000 + 18000 = 26000 $
To conclude, we cut activity T by 2 weeks. The project can be completed in 14 weeks.