Problems:
Forecast
Question 1.
Data collected on the yearly demand for 50-pound bags of fertilizer at Wallace Garden Supply are shown in the following table:
|
Year
|
Demand for Fertilizer (1,000s of bags)
|
|
1
|
4
|
|
2
|
6
|
|
3
|
4
|
|
4
|
5
|
|
5
|
10
|
|
6
|
8
|
|
7
|
7
|
|
8
|
9
|
|
9
|
12
|
|
10
|
14
|
|
11
|
15
|
a) Develop a three-year moving averages to forecast sale.
b) Then estimate demand again with a weighted moving average in which sales in the most recent year are given a weight of 2 and sales in the other two years are each given a weight of 1.
c) Which method do you think is best?
Question 2.
Use exponential smoothing with a smoothing constant 0.3 to forecast the demand for fertilizer given in problem (question 1). Assume that last period's forecast year 1 is 5,000 bags to begin the procedure. Would you prefer to use the exponential smoothing model or the weighted average model developed in problem (question 1)? Explain your answer.
Question 3.
Emergency calls to Winter Park, Florida's 911 system, for the past 24 weeks are as follows:
|
Week
|
Calls
|
Week
|
Calls
|
Week
|
Calls
|
|
1
|
50
|
9
|
35
|
17
|
55
|
|
2
|
35
|
10
|
20
|
18
|
40
|
|
3
|
25
|
11
|
15
|
29
|
35
|
|
4
|
40
|
12
|
40
|
20
|
60
|
|
5
|
45
|
13
|
55
|
21
|
75
|
|
6
|
35
|
14
|
35
|
22
|
50
|
|
7
|
20
|
15
|
25
|
23
|
40
|
|
8
|
30
|
16
|
55
|
24
|
65
|
(A) Compute the exponential smoothing forecast of calls for each week. Assume an initial forecast of 50 calls in the first week and use α = 0.1. What is the forecast of the 25th week?
(B) Reforecast each period using α = 0.6.
(C) Actual calls during the 25th week were 85. Which smoothing constant provides a superior forecast?
Question 4.
A major source of revenue in Texas is a state sales tax on certain types of goods and services. Data are compiled and the state comptroller uses them to project future revenues for the state budget. One particular category of goods is classified as Retail Trade. Four years of quarterly data (in $millions) for one particular area of southeast Texas follow:
|
Quarter
|
Year 1
|
Year 2
|
Year 3
|
Year 4
|
|
1
|
218
|
225
|
234
|
250
|
|
2
|
247
|
254
|
265
|
283
|
|
3
|
243
|
255
|
264
|
289
|
|
4
|
292
|
299
|
327
|
356
|
(A) Compute seasonal indices for each quarter based on a CMA (centered moving average).
(B) Deseasonalize the data and develop a trend on the deseasonlized data.
(C) Use the trend line to forecast the sales for each quarter of year 5.
(D) Use the seasonal indices to adjust the forecasts found in part (C.) to obtain the final forecasts.
Question 5.
In the past, Judy Holmes's tire dealership sold an average of 1,000 radials each year. In the past two years, 200 and 250, respectively, were sold in fall, 350, and 300 in winter, 150 and 165 in spring, and 300 and 285 in summer. With a major expansion planned, Judy projects sales next year to increase to 1,200 radials. What would the demand be each season?