Practice Problem: Forecasting Models
Problem 1:
Auto sales at Carmen’s Chevrolet are shown below.
Develop a 3-week moving average.
|
Week |
Auto Sales |
|
1 |
8 |
|
2 |
10 |
|
3 |
9 |
|
4 |
11 |
|
5 |
10 |
|
6 |
13 |
|
7 |
- |
Problem 2:
Carmen’s decides to forecast auto sales by weighting
the three weeks as follows:
|
Weights Applied |
Period |
|
3 |
Last week |
|
2 |
Two weeks ago |
|
1 |
Three weeks ago |
|
6 |
Total |
Problem 3:
A firm uses simple exponential smoothing with 
to forecast demand.
The forecast for the week of January 1 was 500 units whereas the actual demand
turned out to be 450 units. Calculate the demand forecast for the week of
January 8.
Problem 4:
Exponential smoothing is used to forecast automobile
battery sales. Two value of 
are examined, 
and 
Evaluate the accuracy
of each smoothing constant. Which is preferable? (Assume the forecast for
January was 22 batteries.) Actual sales are given below:
|
Month |
Actual Battery
Sales |
Forecast |
|
January |
20 |
22 |
|
February |
21 |
|
|
March |
15 |
|
|
April |
14 |
|
|
May |
13 |
|
|
June |
16 |
|
Problem 5:
Use the sales data given below to determine: (a) the
least squares trend line, and (b) the predicted value for 2003 sales.
|
Year |
Sales (Units) |
|
1996 |
100 |
|
1997 |
110 |
|
1998 |
122 |
|
1999 |
130 |
|
2000 |
139 |
|
2001 |
152 |
|
2002 |
164 |
To minimize computations, transform the value of x
(time) to simpler numbers. In this case, designate year 1996 as year 1, 1997 as
year 2, etc.
Problem 6:
Given the forecast demand and actual demand for
10-foot fishing boats, compute the tracking signal and MAD.
|
Year |
Forecast Demand |
Actual Demand |
|
1 |
78 |
71 |
|
2 |
75 |
80 |
|
3 |
83 |
101 |
|
4 |
84 |
84 |
|
5 |
88 |
60 |
|
6 |
85 |
73 |
Problem: 7
Over the past year Meredith and Smunt Manufacturing
had annual sales of 10,000 portable water pumps. The average quarterly sales
for the past 5 years have averaged: spring 4,000, summer 3,000, fall 2,000 and
winter 1,000. Compute the quarterly index.
Problem: 8
Using the data in Problem 7, Meredith and Smunt
Manufacturing expects sales of pumps to grow by 10% next year. Compute next
year’s sales and the sales for each quarter.
Problem: 9
A
firm’s sales for a product line during the last 10 months are as follows:
|
Month |
Sales
units |
|
1 |
700 |
|
2 |
724 |
|
3 |
720 |
|
4 |
728 |
|
5 |
740 |
|
6 |
742 |
|
7 |
758 |
|
8 |
750 |
|
9 |
770 |
|
10 |
775 |
Provide
the forecast for months 11 and 12.
Also
compute MAD and MSE.
Problem: 10
Passenger
miles flown on Northeast airlines , a commuter firm serving the Boston hub, are
as follows for the past 12 weeks:
|
Week |
Actual
passengers miles[1000s] |
|
1 |
17 |
|
2 |
21 |
|
3 |
19 |
|
4 |
23 |
|
5 |
18 |
|
6 |
16 |
|
7 |
20 |
|
8 |
18 |
|
9 |
22 |
|
10 |
20 |
|
11 |
15 |
|
12 |
22 |
Assuming
an initial forecast for week 1 of 17,000 miles, use exponential smoothing to
compute miles for week 2 through 12. Use alpha=0.2. Also compute mean squared
errors and mean absolute deviation.
Problem: 11
Blackman’s supply stocks three-horsepower motors. Weekly
demand for 12 typical weeks is:
|
Week |
Demand |
Week |
Demand |
|
42 43 44 45 46 47 48 |
20 17 12 14 8 10 9 |
49 50 51 52 53 |
4 6 5 4 3 |
a.
Calculate a weighted moving average forecast for weeks
54 and 55 using a three-period model with the most recent period’s demand
weighted three times as heavily as each of the previous two period’s demands.
After forecasting period 54, actual demand was 6 motors for the period.
b.
Examining the data visually, what would you suggest as
a possible alternative to the weighed moving average model? Why?
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