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# Learning Curve Sample Problem

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### Learning Curve Sample Problem

1. 1. CASE 1: LEARNING CURVE ANALYSIS Group 7
2. 2. Problem #1 The ABC Company has just been given the following production schedule for ski-lift gondola cars. This product is considerably different from any others the company has produced. Historically, the company‘s learning rate has been 80% on large projects. The first unit took 1,000 hours to produce.
3. 3. Month Units Cumulative 1 3 3 2 7 10 3 10 20 4 12 32 5 4 36 6 2 38 a. Estimate how many hours would be required to complete the 38th unit.
4. 4. Solution a) a. We use the learning curve formulas to calculate the time required for the 38th unit: a. Given: L=0.80 T1= 1000 hrs. T38 = T1 (N (log L/log 2)) = 1000 (38 log 0.80/log 2) = 310.04 hrs
5. 5. • b. If the budget only provides for a maximum of 30 direct labor employees in any month and a total of 15,000 direct labor hours for the entire schedule, will the budget be adequate? Assume that each direct labor employee is productive for 150 work hours each month.
6. 6. Cumulative Hours Mont hs Units Cummulative Units Cumulative Average Cumulative Average Time per Unit Cumulative Total Hours for all Units 1 3 3 0.834034568 834.034568 2502.103704 2 7 10 0.631537303 631.5373025 6315.373025 3 10 20 0.524247142 524.2471422 10484.94284 4 12 32 0.45870687 458.7068697 14678.61983 5 4 36 0.443285172 443.2851721 15958.26619 6 2 38 0.436342826 436.3428259 16581.02738
7. 7. Number of hours per month. Month 1 2502.103704 - 0 = 2502.103704 hrs 2 6315.373025-2502.103704= 3813.269321 hrs 3 10484.94284-6315.373025 = 4169.569815 hrs. 4 14678.61983-10484.94284= 4193.67699 hrs. 5 15958.26619-14678.61983= 1279.64636 hrs. 6 16581.02738-15958.26619= 622.76119 hrs.
8. 8. Direct Labor Hours Month Direct Labor Workers by Month 1 (2,502.1 hr)/(150 hr) = 16.7, or 17 2 (3,813.3 hr)/(150 hr) = 25.4, or 26 3 (4,169.6 hr)/(150 hr) = 27.8, or 28 4 (4,193.7 hr)/(150 hr) = 27.9, or 28 5 (1,279.7 hr)/(150 hr) = 8.5, or 9 6 (622.5 hr)/(150 hr) = 4.2, or 5
9. 9. Conclusion: *The schedule is sufficient in terms of the maximum direct labor required in any month because it never exceeds 30 employees. However, the total cumulative hours are 16,581, which exceeds the budgeted amount by 1,581 hours. Therefore, the budget will not be adequate.
10. 10. Problem 2 XYZ Company has \$200,000 in cash, no inventory, and a 90 percent learning curve. To reduce the complexity of this problem, ignore the hiring and training costs associated with dramatically increased production. Employees are paid \$20 per hour every Friday for that week‘s work. XYZ has received an order to build 1,000 oak desks over the next 15 weeks. Materials cost \$400 per desk. Suppliers make deliveries each Monday and insist on cash upon delivery. The first desk takes 100 hours of direct labor to build. XYZ will be paid \$1,500 per desk two weeks after the desks are delivered. Should XYZ take this order? Additional Assumptions: • Products are delivered at the end of each week. Cash inflow from sales occurs at the end of the week.
11. 11. Given: \$ 20 per hour 100 hours per desk \$ 400 material cost per desk \$ 20 per hour x 100 hours per desk = \$ 2000 per desk Cost: \$ 400 material cost per desk + \$ 2000 per desk = \$ 2400 per desk
12. 12. Week Units Total cost Inflows every after 2 weeks 1 2 4800 2 4 9600 3 8 19200 3000 4 12 28800 6000 5 14 33600 12000 6 24 57600 18000 7 64 153600 21000 8 128 307200 36000 9 128 307200 96000 10 128 307200 192000 11 88 211200 192000 12 100 240000 192000 13 100 240000 132000 14 100 240000 150000 15 100 240000 150000 150000 150000 Cash Outflows & Inflows
13. 13. 350000 300000 250000 200000 150000 100000 50000 0 Cash Flow Chart 0 2 4 6 8 10 12 14 16 Values Weeks Total cost Inflows every after 2 weeks
14. 14. Conclusion: The company should not take the order, because the total cost exceed the cash inflow every after two weeks.