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## Forecasting and Inventory models

1. For the data below:
Year
Automobile Sales
Year
Automobile Sales
1990
116
1977
119
1991
105
1998
34
1992
29
1999
34
1993
59
2000
48
1994
108
2001
53
1995
94
2002
65
1996
27
2003
111
(a) Develop a scatter diagram.
(b) Develop a six-year moving average forecast.
_________________________________________________________________________________________
2. Use simple exponential smoothing with α = 0.3 to forecast battery sales for February through May. Assume that the forecast for January was for 22 batteries.
Month
Automobile Battery Sales
January
52
February
43
March
38
April
69
3. A large school district is reevaluating its teachers’ salaries. They have decided to use regression analysis to predict mean teacher salaries at each elementary school. The researcher uses years of experience to predict salary. The raw data is given in the table below.
Salary
Yrs Exp
\$24,265.00
8
\$27,140.00
5
\$22,195.00
2
\$37,950.00
15
\$32,890.00
11
\$40,250.00
14
\$36,800.00
9
\$30,820.00
6
\$44,390.00
21
\$24,955.00
2
\$18,055.00
1
\$23,690.00
7
\$48,070.00
20
\$42,205.00
16
(a) Develop a scatter diagram., (b) What is the correlation coefficient?, (c) What is the coefficient of determination?
4. David and Beth Sheba run a health food store. Their top selling item is called Heavenly Kelp. The annual demand for this is 810 units, and demand is constant throughout the year. The cost of placing an order is \$20, while the holding cost per unit per year is \$4.
(a) How many orders per year should be placed if they wish to minimize their total cost?
(b) What is the minimum possible annual holding and ordering cost?
5. Mattress Plus Store sells waterbeds and supplies. The best selling bed in the store has an annual demand of 400 units. The ordering cost is \$40, while the holding cost is \$5 per unit per year. There are 250 working days per year, and the lead-time is 6 days.
(a) To minimize total cost, how many units should be ordered each time an order is placed?
(b) If the holding cost per unit was \$6 instead of \$5, what would the optimal order quantity be

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