1. Hoppy Foods Manufactures Peanut Butter. It Purchases Its Peanuts from the Carter Farm

ISDS 361B Dr. Goldstein

E X A M #3

1. Hoppy Foods manufactures peanut butter. It purchases its peanuts from the Carter Farm Cooperative. Peanuts normally cost Hoppy $0.45 per pound, but Carter offers its customers the following all units discount pricing schedule: Purchase Amount Discount Under $10,000 none $10,000–$24,999 5% $25,000–$49,999 7% $50,000–$69,999 8% $70,000–$89,999 9% $90,000 or more 10% Hoppy uses 10,000 pounds of peanuts per day, and the Hoppy plant operates 365 days a year. The cost of placing an order with Carter is $90, and the lead-time is two weeks. The company requires a safety stock of 40,000 pounds of peanuts. If the annual holding cost rate for peanuts is 22%, answer the following questions (before you start, notice that the discount chart above presents the discount intervals in $ s, not in quantities): a. Focus on the 8% discount. Show how you would calculate the optimal order quantity Q* and how you would modify this quantity to fit the discount schedule. b. Determine the annual holding cost and annual ordering cost for the 8% discount price category. Show your work. c. From the template determine the optimal inventory policy if Hoppy’s warehouse space for peanut storage is limited to 125,000 pounds. d. If weekly demand is normally distributed with a mean of 70,192 and standard deviation of 15,000 pounds, show how you would determine the reorder point for 85% service level. Recall that lead time is 2 weeks so adjustment of parameters is needed. e. What service level can be achieved by holding a safety stock of 40,000 pounds of peanuts? Again, recall that lead time is 2 weeks. Show your calculations. f. Bonus: With the optimal ordering policy you have found in part ‘c’, and the service level you have found in part ‘e’, in how many cycles per year on the average do you expect to have a stock out? 2. For the following PERT/CPM network the mean time and the standard deviation provided are in days. The standard deviations of all the activities are 6 days.

a. Use the Excel template, and find how long the whole project is expected to take. b. The standard deviation of the project completion time is 12. Show how it was calculated. c. Consider the additional information: i. Activity ‘A’ can be expedited for a cost of $5,000. ii. If A is expedited, its new mean time and the standard deviation of its time will be 8 and 6 days respectively. iii. A bonus of $10,000 is paid if the project is completed in 57 days; neither bonus is granted nor a penalty is paid if the project is completed between 57 and 65 days, but a penalty of $15000 is paid if the project is not completed in 65 days. Should activity A be expedited based on the expected cost criterion?

3. A glass manufacturer produces Mason jars. Quarterly sales (in millions of dollars) over the past five years are shown in the table below.

Time 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Sales 1.2 1.7 2.3 .5 1.5 2 2.1 1 1.8 2.3 2.6 1.3 1.9 2.5 2.9 1.4 2.6 3.2 3.7 2.4

a. The manufacturer noticed that the 4 period moving average doesn’t produce good forecasts. Explain statistically (build a test, use alpha = .01) why the moving average should not be used. b. Use Excel to determine what is the linear regression model for forecasting the quarterly sales. Show this equation (Ft = a + b*t = …..) c. Use the linear regression equation to answer. On the average, by how much do sales change each year? d. Make the following forecasts by hand: F3, F4. Show the equations you use. Do not use the template. Use alpha = .2 and gamma = .5. e. Now use the template and Solver in order to determine the best values of alpha and gamma for the Holt’s model. Your objective should be minimum MSE. What are the optimal values of alpha and gamma you find?