Chapter 13 Forecasting

Chapter 13 Forecasting

2. Dalworth Company

a. Three-month simple moving average

Month Actual Sales Three-Month Simple Absolute Absolute Squared

(Thousands) Moving Average Error % Error Error

Forecast

Jan. 20

Feb. 24

Mar. 27

Apr. 31 (20+24+27)/3 = 23.67 7.33 23.65 53.73

May 37 (24+27+31)/3 = 27.33 9.67 26.14 93.51

June 47 (27+31+37)/3 = 31.67 15.33 32.62 235.01

July 53 (31+37+47)/3 = 38.33 14.67 27.68 215.21

Aug. 62 (37+47+53)/3 = 45.67 16.33 26.34 266.67

Sept. 54 (47+53+62)/3 = 54.00 0.00 0.00 0.00

Oct. 36 (53+62+54)/3 = 56.33 20.33 56.47 413.31

Nov. 32 (62+54+36)/3 = 50.67 18.67 58.34 348.57

Dec. 29 (54+36+32)/3 = 40.67 11.67 40.24 136.19

Total 114.00 291.48 1,762.20

Average 12.67 32.39 195.80

Such results also can be obtained from the Time Series Forecasting Solver:

b. Four-month simple moving average

Month Actual Sales Four-Month Simple Absolute Absolute Squared

(Thousands) Moving Average Error % Error Error

Forecast

Apr. 31

May 37 (20+24+27+31)/4 = 25.5 11.50 31.08 132.25

June 47 (24+27+31+37)/4 = 29.75 17.25 36.70 297.56

July 53 (27+31+37+47)/4 = 35.5 17.50 33.02 306.25

Aug. 62 (31+37+47+53)/4 = 42.00 20.00 32.26 400.00

Sept. 54 (37+47+53+62)/4 = 49.75 4.25 7.87 18.06

Oct. 36 (47+53+62+54)/4 = 54.00 18.00 50.00 324.00

Nov. 32 (53+62+54+36)/4 = 51.25 19.25 60.16 370.56

Dec. 29 (62+54+36+32)/4 = 46.00 17.00 58.62 289.00

Total 124.75 309.71 2,137.68

Average 15.59 38.71 267.21

Similarly, using Time Series Forecasting Solver, we get:

c.*e. Comparison of performance

Question Measure 3-Month 4-Month Recommendation

SMA SMA

c. MAD 12.67 15.59 3-month SMA

d. MAPE 32.39 38.71 3-month SMA

e. MSE 195.80 267.21 3-month SMA

4. Dalworth Company (continued)

a. Three-month weighted moving average (weights of 3/6, 2/6, and 1/6)

Month Actual Sales Three-Month Weighted Absolute Absolute % Squared

(000s) Moving Average Forecast Error Error Error

Jan. 20

Feb. 24

Mar. 27

Apr. 31 [(3 27)+(2 24)+(l 20)]/6 = 24.83 6.17 19.90 38.07

May 37 [(3 31)+(2 27)+(l 24)]/6 = 28.50 8.50 22.97 72.25

June 47 [(3 37)+(2 31)+(l 27)]/6 = 33.33 13.67 29.09 186.87

July 53 [(3 47)+2 37)+(l 31)]/6 = 41.00 12.00 22.64 144.00

Aug. 62 [(3 53)+(2 47)+(l 37)]/6 = 48.33 13.67 22.05 186.87

Sept. 54 [(3 62)+(2 53)+(l 47)]/6 = 56.50 2.50 4.63 6.25

Oct. 36 [(3 54)+(2 62)+(l 53)]/6 = 56.50 20.50 56.94 420.25

Nov. 32 [(3 36)+(2 54)+(l 62)]/6 = 46.33 14.33 44.78 205.35

Dec. 29 [(3 32)+(2 36)+(l 54)]/6 = 37.00 8.00 27.59 64.00

Total 99.34 250.59 1,323.91

Average 11.04 27.84 147.09

The results from Time Series Forecasting Solver give the same results:

b. Exponential smoothing (* = 0.6)

Month Dt Ft Ft+1 = Ft + *(Dt * Ft)

Absolute Absolute Squared

(t) (millions) Error % Error Error

Jan. 20 22.00 20.80

Feb. 24 20.80 22.72

Mar. 27 22.72 25.29

Apr. 31 25.29 28.72 5.71 18.41 32.60

May 37 28.72 33.69 8.28 22.38 68.56

June 47 33.69 41.67 13.31 28.32 177.16

July 53 41.67 48.47 11.33 21.38 128.37

Aug. 62 48.47 56.59 13.53 21.82 183.06

Sept. 54 56.59 55.04 2.59 4.80 6.71

Oct. 36 55.04 43.62 19.04 52.88 362.52

Nov. 32 43.61 36.64 11.61 36.28 134.79

Dec. 29 36.65 32.06 7.65 26.38 58.52

Total 93.05 232.65 1,152.29

Average 10.34 25.85 128.03

c.*e. Comparison of performance

Question Measure 3-Month Exponential Recommendation

WMA Smoothing