Problem 3-5

The following table contains the demand from the last 10 months:

MONTH ACTUAL DEMAND
1 31
2 33
3 34
4 42
5 45
6 44
7 42
8 44
9 41
10 43
________________________________________

a. Calculate the single exponential smoothing forecast for these data using an α of 0.40 and
an initial forecast (F1) of 31. (Round your answers to 2 decimal places.)

Month Exponential
Smoothing
1 2 3 4 5 6 7 8 9 10
________________________________________

b. Calculate the exponential smoothing with trend forecast for these data using an α of 0.40,
a of 0.30, an initial trend forecast (T1) of 1.00, and an initial exponentially smoothed forecast
(F1) of 30. (Round your answers to 2 decimal places.)

Month FITt
1 2 3 4 5 6 7 8 9 10
________________________________________

c-1. Calculate the mean absolute deviation (MAD) for the last nine months of forecasts. (Round
your answers to 2 decimal places.)

MAD
Single exponential smoothing forecast Exponential smoothing with trend forecast
________________________________________

c-2. Which is best?

Single exponential smoothing forecast

Exponential smoothing with trend forecast
Problem 3-12
Demand for stereo headphones and MP3 players for joggers has caused Nina Industries to grow almost
50 percent over the past year. The number of joggers continues to expand, so Nina expects demand
for headsets to also expand, because, as yet, no safety laws have been passed to prevent joggers
from wearing them. Demand for the players for last year was as follows:

MONTH DEMAND
(UNITS)
January 4,100
February 4,200
March 3,900
April 4,300
May 4,900
June 4,600
July 5,200
August 4,800
September 5,300
October 5,600
November 6,200
December 5,900
________________________________________

a. Using linear regression analysis, what would you estimate demand to be for each month next
year?(Do not round intermediate calculations. Round your answers to 2 decimal places.)

Month Forecast
January February March April May June
July August September October November December
________________________________________

b. To be reasonably confident of meeting demand, Nina decides to use 4 standard errors of
estimate for safety. How many additional units should be held to meet this level of confidence? (Do
not round intermediate calculations. Round your answer to the nearest whole number.)

Additional units Problem 3-16
A particular forecasting model was used to forecast a six-month period. Here are the forecasts and
actual demands that resulted:

FORECAST ACTUAL
April 260 210
May 334 258
June 409 325
July 359 310
August 384 336
September 459 412
________________________________________

a. Find the tracking signal for each month. (Negative values should be indicated by a minus
sign.)

Month Tracking Signal
April May June July August September
________________________________________

b. Is the model being used is giving acceptable answers.

No, the model’s performance is poor.

Yes, the model’s performance is good.

Problem 3-20
Your manager is trying to determine what forecasting method to use. Based upon the following
historical data, calculate the following forecast and specify what procedure you would utilize.

MONTH ACTUAL
DEMAND
1 62
2 63
3 66
4 65
5 73
6 68
7 74
8 75
9 75
10 82
11 86
12 85
________________________________________

a. Calculate the simple three-month moving average forecast for periods 4–12. (Round your
answers to 3 decimal places.)

Month Three-Month Moving Average
4 5 6 7 8 9 10
11 12 ________________________________________

b. Calculate the weighted three-month moving average for periods 4–12 using weights of 0.50
(for the period t−1); 0.30 (for the period t−2), and 0.20 (for the period t−3). (Do not round
intermediate calculations. Round your answers to 3 decimal places.)

Month Three-Month Weighted Moving Average
4 5 6 7 8 9 10
11 12 ________________________________________

c. Calculate the single exponential smoothing forecast for periods 2–12 using an initial
forecast (F1) of 65 and an α of 0.40. (Do not round intermediate calculations. Round your answers
to 3 decimal places.)

Month Single Exponential Smoothing Forecast
2 3 4 5 6 7 8
9 10 11 12
________________________________________

d. Calculate the exponential smoothing with trend component forecast for periods 2–12 using an
initial trend forecast (T1) of 1.80, an initial exponential smoothing forecast (F1) of 64, an α of
0.40, and a of 0.30. (Do not round intermediate calculations. Round your answers to 3 decimal
places.)

Month Exponential Smoothing with Trend
2 3 4 5 6 7 8
9 10 11 12
________________________________________

e-1. Calculate the mean absolute deviation (MAD) for the forecasts made by each technique in
periods 4–12. (Do not round intermediate calculations. Round your answers to 3 decimal places.)

Mean Absolute
Deviation
Three-month moving average Three-month weighted moving average Single
exponential smoothing forecast Exponential smoothing with trend
________________________________________

e-2. Which forecasting method do you prefer?

Three-month moving average

Three-month weighted moving average

Exponential smoothing with trend forecast

Single exponential smoothing forecast

Problem 3-21
After using your forecasting model for six months, you decide to test it using MAD and a tracking
signal. Here are the forecast and actual demands for the six-month period:

PERIOD FORECAST ACTUAL
May 460 485
June 510 550
July 560 385
August 585 475
September 625 655
October 705 630
________________________________________

a. Find the tracking signal. (Negative values should be indicated by a minus sign. Round your
answers to 2 decimal places.)

Period Tracking
Signal
May June July August September October
________________________________________

b. Check whether your forecasting routine is acceptable.

No

Yes

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