# Problem 3-5

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 a 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 a 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 a 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 a 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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