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# Forecasting and inventory problems

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8. Tucson Machinery, Ins., manufactures numerically controlled machines, which sell for an average price of \$0.5 million each. Sales for these NCM's for the past two years were as follows:
Quarter Quantity
2004
I 12
II 18
III 26
IV 16
Quarter Quantity
2005
I 16
II 24
III 28
IV 18
a. Do a linear regression for the data.
b. Find the trend and seasonal factors.
c. Forecast sales for 2006.

17. Historical demand for a product is:

April-60
May-55
June-75
July-60
August-80
September-75
a. Using a simple four month moving average, calculate a forecast for October.
b. Using single exponential smoothing with alpha=0.2 and a September forecast=65, calculate a forecast for October.
c. Using simple linear regression, calculate the trend line for the historical data. Say the X axis is April=1, May=2, and so on, while the Y axis is demand.

10. The annual demand for a product is 15,600 units. The weekly demand is 300 units with a standard deviation of 90 units. The cost to place an order is \$31.20 , and the time from ordering to receipt is four weeks. The annual inventory carrying cost is \$0.10 per unit. Find the reorder point necessary to provide a 98 percent service probability. Suppose the production manager is ordered to reduce the safety stock by 50 Percent. If he does so, what will the new service probability be?

14. A particular raw material is available to a company at three different prices, depending on the size of the order:

Less than 100 pounds - \$20 per pound
100 pounds to 999 pounds - \$19 per pound
More than 1,000 pounds - \$18 per pound

The cost to place an order is \$40. Annual demand is 3,000 units. Holding (or carrying) cost is 25 percent of the material cost. What is the economic order quantity to buy each time?

16. Gentle Ben's Bar and Restaurant uses 5,000 quart bottles of an imported wine each year. The effervescent wine costs \$3 per bottle and is served in whole bottles only since it loses its bubbles quickly. Ben figures that it costs \$10 each time an order is placed, and holding costs are 20 percent of the purchase price. It takes three weeks for an order to arrive. Weekly demand is 100 bottles (closed two weeks a year) with a standard deviation of 30 bottles.
Ben would like to use an inventory system that minimizes inventory cost and will satisfy 95 percent of his customers who order this wine.
a. What is the economic order quantity for Ben to order?
b. At what inventory level should he place an order.