/ AMA INTERNATIONAL UNIVERSITY
Manama, Kingdom of Bahrain
Course Code : ABI-201 MANAGEMENT SCIENCE – 1
FORECASTING TUTORIALS

Illustrated Example on Forecasting

The following table represent the sales of car at National Motors for the last five days:-

Month / Sales
Saturday / 10
Sunday / 9
Monday / 14
Tuesday / 12
Wenesday / 17
Thursday / 20

(A)What are the expected sales in Friday based in naïve method assuming the showroom will be open in Fridays?

Answer:-

Sales at Friday = sales at previous Thursday = 20 cars based in naive method

(B)Build two moving average 2MA models for the car forecasted sales in this week? Then find MAD to find the accuracy?

Answer:-

Month / Sales / 2Moving Average / Error
A - F
Saturday / 10 / x
Sunday / 9 / x
Monday / 14 / = (9+10)/2 = 9.5 / 4.5
Tuesday / 12 / =(14+9)/2 = 11.5 / 0.5
Wednesday / 17 / = (12+14)/2 = 13 / 4
Thursday / 20 / = (17+12)/2 = 14.5 / 5.5
= (20+17)/2 = 18.5

= = 3.625

(C)Build two weighted moving average expected the nearest period weight is 65% and the second one is 35%? Find the MAD to test the model accuracy?

Answer:-

Month / Sales / 2 weighted Moving Average / Error
Saturday / 10 / x
Sunday / 9 / x
Monday / 14 / = 0.65*9 + 0.35*10 = 9.35 / 4.65
Tuesday / 12 / = 0.65*14 + 0.35*9 = 12.25 / -0.25
Wednesday / 17 / = 0.65*12 + 0.35*14 = 12.7 / 4.3
Thursday / 20 / = 0.65*17 + 0.35*12 = 15.25 / 4.75
= 0.65*20 + 0.35*17 = 18.95

= = 3.3625

(D)Compute the forecast for year Friday using exponential smoothing; an initial forecast for Saturday is 8, and α = 0.4? Find the MAD to test the model accuracy?

Answer:-

General exponential smoothing equations

Month / Sales / Exponential Smoothing / Error
Saturday / 10 / 8 / x
Sunday / 9 / = 8 + 0.4 ( 10 – 8 ) = 8.8 / 0.2
Monday / 14 / = 8.8 + 0.4 ( 9 – 8.8 ) = 8.88 / 5.12
Tuesday / 12 / = 8.88 + 0.4 ( 14 – 8,88 ) = 10.93 / 1.072
Wednesday / 17 / = 10.93 + 0.4 ( 12 – 10.93) = 11.36 / 5.6432
Thursday / 20 / = 11.36 + 0.4 ( 17 – 11.36 ) = 13.61 / 6.38592
= 13.61 + 0.4 ( 20 – 13.61 ) = 16.17

= = 3.684224

(E)Using linear regression equations to find the car sales in Friday? Find MAD to test the accuracy of the model?

Answer:-

Days / X / Sales= Y / XY / X SQUARE
Saturday / 1 / 10 / 10 / 1
Sunday / 2 / 9 / 18 / 4
Monday / 3 / 14 / 42 / 9
Tuesday / 4 / 12 / 48 / 16
Wednesday / 5 / 17 / 85 / 25
Thursday / 6 / 20 / 120 / 36
/ 21 / 82 / 323 / 91

= 2.06 = 6.46

Days / X / Y / FORECATSED
VALUE / ERROR
Saturday / 1 / 10 / 8.52 / 1.48
Sunday / 2 / 9 / 10.58 / -1.58
Monday / 3 / 14 / 12.64 / 1.36
Tuesday / 4 / 12 / 14.69 / -2.69
Wednesday / 5 / 17 / 16.75 / 0.25
Thursday / 6 / 20 / 18.81 / 1.19

= = 1.43

(F)Which is the best accurate model? And why?

MODEL / 2 MA / 2WMA / EXP. SMOOTHING / LINEAR TREND
MAD / 3.625 / 3.3625 / 3.684224 / 1.43

THE BEST CHOICE IS LINEARTREND LINE THE LEAST MAD

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