Your boss is the project manager for a large contract assembly plant. A new customer has come to you with a product they want 20 units of assembled. The customer estimates that the time to assemble a unit is about 15 hours to assemble each one and is willing to pay you at that rate. She accepts the terms and offers you the project. You want to impress the boss but you don’t want to take the project if it will lose money and make you look bad. She tells you that the first unit took 25 hours and the second one took 20 hours. a) What is the learning rate for this project? How many hours do you expect the third unit to take? How many hours do you expect the 20th unit to take? What is the percentage change in productivity from the first unit to the 20th unit? b) What is the total number of hours required for all 20 units? What is the average time to assemble all of the units? Should you accept the project? Why or why not? c) After you have finished the project, the company comes back and asks for 20 more units. How long do believe the first unit of the order would take to produce? The 20th? How many labour hours would be required for the second order? What is the labour time per unit? d) Suppose your company can supply 503 labour hours per month to this product. What is your “capacity” to produce this product (i.e. how many can you produce in the first month)?

a. Learning rate = time taken for 2nd unit/time taken for 1st unit = 20/25 = 80%.
Hours required by 3rd unit will be computed using the formula: Tn = T1*c where Tn is the time requirement for 3rd unit. T1 = 25. C = 0.702 (from learning curve coefficient table) for 80% and n = 3.
Thus T3 = 25*0.702 = 17.55 hours.
Hours required for 20th unit: T20 = T1*C (for n=20, 80%) = 25*0.381 = 9.53
Productivity for 1st unit = 1/25 = 0.04. Productivity for 20th unit = 1/9.53 = 0.1050
% change in productivity = (0.1050-0.04)/0.04 = 162.47%
b. Total no. of hours required for 20th unit = no. of hours for 1st unit*learning curve coefficient for total time (80%,20) = 25*10.485 = 262.13
Average time to assemble all units = 262.13 hours/20 units = 13.11 hours per unit.
The project should be accepted as average time of 13.11 hours is less than customer estimated time of 15 hours. This will lead to higher profitability.
c. For 20 more units the first unit will be = 20+1 = 21st unit. The first unit will take = 25 hours*C for 21,80% = 25*0.355 = 8.88 hours.
Time taken for 20th unit (20+20=40) = 25 hours*C for 40,80% = 25*0.305 = 7.63 hours
Labor hours required for 2nd order = time to produce 40 units – time to produce the 1st lot of 20 units = 25*total time coefficient for 40,80% – 262.13 (as computed earlier) = (25*17.193)-262.13 = 167.70
Labor time per unit = 167.7/20 = 8.39 hours per unit
d. Total labor hours = 503. Let the C coeffieicent be x. Thus 25*x = 503
or x = 503/25 = 20.12. From the coefficient table (in the 80% column) we can see that C coefficient (total time) pertains to N = 50.
Thus 50 units can be produced in the 1st month.
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