Question

Use 5 months moving average and exponential smoothing method (using alpha=0.3) on the following sale of Maggi. You are supposed to forecast the sale of Maggi in the 13^th Month. Compare whether there is any difference in forecast based on two methods and Comment.

Period (Month)	Actual Sale of Maggi
1	1100
2	800
3	1000
4	1050
5	1500
6	750
7	700
8	650
9	1400
10	1200
11	900
12	1000
13

Answer 1

Forecast using 5 month moving average

Forecast_{month n}= (Demand_{month n-1} + Demand_{month n-2} + Demand_{month n-3} + Demand_{month n-4} + Demand_{month n-5})/5

Forecast Error_{month n} = Demand_{month n} - Forecast_{month n}

Compute Absolute Error Deviation by taking the positive value of error

Compute Mean Absolute Deviation = Sum of Absolute value of error for all the months / number of months.

For 5 months moving average, we have the Error and Absolute error for month 6 to 12 = 7 months

Forecast_{month 13} = (Demand_{month 12} + Demand_{month 11} + Demand_{month 10} + Demand_{month 9} + Demand_{month 8}) / 5

                         = (1000 + 900 + 1200 +1400 +650) / 5 = 1030

13th month forecast using 5 month moving average is 1030

Sum of Absolute value of Error = 1750

Mean Absolute Deviation (MAD_{5 months moving average}) = 1750 / 7 = 250

Forecast using Exponential method

α = 0.3

Forecast_{month n} = Forecast_{month n-1} + α * (Demand_{month n-1} - Forecast_{month n-1})

Forecast Error_{month n} = Demand_{month n} - Forecast_{month n}

Compute Absolute Error Deviation by taking the positive value of error

Compute Mean Absolute Deviation = Sum of Absolute value of error for all the months / number of months.

For Exponential method, we have the Error and Absolute error for month 1 to 12 = 12 months

Assume the demand for Forecast for month 1 same as the demand for month 1

Forecast_{month 13} = Forecast_{month 12} + α * (Demand_{month 12} - Forecast_{month 12})

                         = 1020 + 0.3 * (1000 - 1020) = 1014

13th month forecast using Exponential method is 1014

Sum of Absolute value of Error = 1966

Mean Absolute Deviation (MAD_{Exponential method}) = 1966 / 12 = 163.8

MAD_{Exponential method} of 163.8 <MAD_{5 months moving average} of 250 thus Exponential method is giving a more accurate forecast.