cha 5.xls

Develop a four-month moving average forecast for Wallace Garden Supply and compute the MAD. A three-month moving average forecast was developed in the section on the moving averages in Table 5.3.

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

Next period MAD

Actual Shed sales Forecast 10 12 13 16 19 12.750 23 15.000 26 17.750 30 21.000 28 24.500 18 26.750 16 25.500 14 23.000

19.0 7.781

Error

6.250 8.000 8.250 9.000 3.500 -8.750 -9.500 -9.000

Absolute error

6.250 8.000 8.250 9.000 3.500 8.750 9.500 9.000

Using MAD, determine whether the forecast in Problem 5-12 or the forecast in the section concerning Wallace Garden Supply is more accurate.

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

3 month MAD=58.33/9 4 month MAD=62.25/8

Actual Shed Forecast(3sales period MA) 10 12 13 16 19 23 26 30 28 18 16 14

11.667 13.667 16.000 19.333 22.667 26.333 28.000 25.333 20.667

Error

4.333 5.333 7.000 6.667 7.333 1.667 -10.000 -9.333 -6.667

Absolute error

4.333 5.333 7.000 6.667 7.333 1.667 10.000 9.333 6.667 58.333

Forecast(4Absolute period MA) Error error

12.750 15.000 17.750 21.000 24.500 26.750 25.500 23.000

6.25 8.00 8.25 9.00 3.50 -8.75 -9.50 -9.00

6.25 8.00 8.25 9.00 3.50 8.75 9.50 9.00 62.25

6.481 7.78

Looking at the MAD values, it can be said that the 3 period moving average is more accurate as it has lower MAD among the two.

Data collected on the yearly demand for 50-pound bags of fertilizer at Wallace Garden Supply are shown in the following table. Develop a three-year moving average to forecast sales. 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 the weight of 1. Which method do you think is best? 3 period moving averages Year 1 2 3 4 5 6 7 8 9 10 11 Next period MAD

Year

Demand Forecast 4 6 4 5 10 8 7 9 12 14 15

4.67 5.00 6.33 7.67 8.33 8.00 9.33 11.67

Error

Absolute error

0.33 5.00 1.67 -0.67 0.67 4.00 4.67 3.33

0.33 5.00 1.67 0.67 0.67 4.00 4.67 3.33

13.67 2.54 Weighted moving averages Actual value Weights Forecast Error

1 2 3 4 5 6 7 8 9 10 11

4 6 4 5 10 8 7 9 12 14 15

Next period MAD

14.00 2.313

Absolute error

1 1 2 4.50 5.00 7.25 7.75 8.00 8.25 10.00 12.25

0.50 5.00 0.75 -0.75 1.00 3.75 4.00 2.75

0.50 5.00 0.75 0.75 1.00 3.75 4.00 2.75

Weighted moving average is slightly more accurate than 3-period moving average as MAD for Weighted moving average is less among the two.

D for Weighted

Sales of Cool-Man air conditioners have grown steadily during the past five years. The sales manager had predicted, before the business started, that year 1’s sales would be 410 air conditioners. Using the exponential smoothing with a weight of alpha = 0.30, develop forecasts for years 2 through 6.

Year

Sales

1 2 3 4 5

450 495 518 563 584

Alpha Year 6 forecast

0.3

521.83

Forecast Error 410.00 422.00 443.90 466.13 495.19

73.00 74.10 96.87 88.81

Absolute error 73.00 74.10 96.87 88.81

Using the trend projection method, develop a forecasting model for the sales of Cool-Man air conditioners (see problem 5-18).

Year

Sales(Y)

1 2 3 4 5

450 495 518 563 584

Intercept Slope

421.2 33.6

Period no(X) Forecast 1 2 3 4 5

454.80 488.40 522.00 555.60 589.20 Average

Trend equation: Y=421.2+33.6X Year 6 forecast 622.8 6

Error -4.80 6.60 -4.00 7.40 -5.20

Absolute error 4.80 6.60 4.00 7.40 5.20 5.6 MAD

ners (see problem 5-18).

Management of Davis’s Department Store has used time-series extrapolation to forecast retail sales for the next four quarters. The sales estimates are $100,000, $120,000, $140,000, and $160,000 for the respective quarters before adjusting for seasonality. Seasonal indices for the four quarters have been found to be 1.30, 0.90, 0.70, and 1.10, respectively. Compute a seasonalized or adjusted sales forecast. As the seasonal indices are already given, Adjusted sales forecast is calculated using following formula: Ajusted sales forecast=Sales estimate*Seasonal index

Sales Seasonal Adjusted estimates index sales forecast

Quarter 1 2 3 4

$100,000 $120,000 $140,000 $160,000

1.30 0.90 0.70 1.10

$130,000 $108,000 $98,000 $176,000

next four quarters. The ng for seasonality. pute a seasonalized or