Question

cost estimation

PROB #2: LearningCurve An activity to produce 100 units was planned for 40 working days of 8 hours each, for one 5 person crew at KD 10 per hour per person. Because of owner required acceleration, the contractor worked with 2 crews of 5 people each for 10 hour per day. The contractor had to pay KD 15 per hour per person for the overtime hours above 8 hr day. For this work, LP 85% ( for learning curve with s -0.2345). What is the duration and cost of the activity with acceleration, and how much does this exceed the original estimated cost? SHOW ALL WORK. Ignore the change in productivity due to working on scheduled overtime.

Answer 1

Without acceleration each unit will take a fixed time. Here the production of 100 units takes 40*8*5 = 1600 hours

This means ideally each unit takes 1600/100 = 16 hours. This will be the base for starting time for a unit.

The total cost without learning curve is 1600*10 = 16000 KD and it takes 40 days to complete the work.

Now the learning curve equation is

Cumulative average time = aX^b

Here b = -0.2345, X = number of items = 100 and a = time for the first item = 16 hours.

This means the cumulative average for 100 items is 16*100^(-0.2345) = 5.43 hours. This means overall time needed is 100*5.43 = 543 hours

Now, since we have 2 teams of 5 people each and they both work 10 hours a day, we have a total of 10*10 = 100 hours per day. However the cost of hours per day will be 10*8*10 + 10*2*15 = 1100 per day. Hence for 4 days it will cost 1100*4 = 4400. The last day the remaining 43 hours can be completed at the cost of 430. This makes the total cost of using learning curve to be 4400 + 430 = 4830.

With learning curve the total cost is KD 4830 and it takes 5 days to complete the work.

Now, compared to the previous original cost, the difference is saving of KD 11170