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Here are the actual tabulated demands for an item for a nine-month period (January through September). Your supervisor wants to test two forecasting methods to see which method was better over this period.

MONTH ACTUAL
January 110
February 130
March 150
April 170
May 160
June 180
July 140
August 130
September 140

Required:
a. Forecast April through September using a three-month moving average.
b. Use simple exponential smoothing with an alpha of 0.3 to estimate April through September, using the average of January through March as the initial forecast for April. (Do not round intermediate calculations. Round your answers to 2 decimal places.)
c. Calculate MAD for each method.
d. Use MAD to decide which method produced the better forecast over the six-month period.

Respuesta :

batolisis

Answer:

a) 130, 150,160, 170,160,150

B) 130, 142, 147.4, 157, 152, 145

C) MAD using three month method = 23.333

  MAD using simple exponential method = 22.5

D) Exponential smoothing method produces a better Forecast because its MAD result is lower than that produced when 3 month method was used

Explanation:

A) Forecasting April through September using A three-month moving average

we use this formula :[tex]f_{t}[/tex]  = [tex]\frac{A_{t-1}+ A_{t-2}---- A_{t-n} }{n}[/tex]

where : [tex]f_{t}[/tex]  = Forecast for coming period

            At-1 = actual demand in the past period

               N = number of periods to be averaged for a three-month moving average = 3

lets term the first month A, second month Ma , third month Ju,

Forecast for month April = ( month J + month F  + month M ) / 3

                                    =  (110 + 130 + 150 )/ 3 =  130 (next forecast fr month A)

Forecast for month May = ( month f + Month A + Month ma ) / 3

                                = ( 130 + 150 + 170 ) / 3 = 150

Forecast for month June = ( Month M + Month A + Month Ma ) / 3

                               = (150 + 170 + 160 ) / 3 = 160  

Forecast for month July = ( Month A + Month Ma + Month Ju )

                                = (170 + 160 + 180 ) / 3 = 170

Forecast for month August = ( Month Ma + month Ju + month Jy ) / 3

                                 = (160 + 180 + 140 )/3 = 160

Forecast for month September = ( month Ju + month Jy + month Au ) / 3

                                 = ( 180 + 140 + 130 ) / 3 = 150

B ) Using simple exponential smoothing with an alpha of 0.3 to estimate April through September

The smoothed value for the month of the month of April = 130  i.e. value of forecast for month of April

to calculate the simple exponential forecast we apply the given formula below

single exponential smoothing (Ft) = [tex]f_{t-1} + \alpha ( A_{t-1}- F_{t-1} )[/tex]

where : [tex]\alpha[/tex] = smoothing constant

            Ft = forecast for coming period

             A = actual demand , F = forecasted demand

Exponential value for the month of May

  Forecast ( Ma ) = 142 + 0.3 [160-142]

                            = 142

Smoothed value for the month of Ju

 Forecast ( Ju ) = 142 + 0.3 [ 160 - 142 ]

                          = 147.4

Smoothed value for the month of July (Jy)

Forecast ( Jy ) = 147 + 0.3 [ 180 - 147]

                      = 157

Smoothed value for the month of August ( Au )

Forecast ( Au ) = 157  + 0.3[140 - 157 ]

                       = 152

Smoothed value for the month of September ( s )

Forecast ( s ) = 152 + 0.3 [ 130 - 152 ]

                     = 145

C) Formula for calculating MAD is attached below

using the formula to calculate MAD for each method using the three month moving average forecast

Absolute deviation

for Month April ( A ) = 40

for month May ( Ma ) = 10

for Month June ( Ju ) = 20

for month July ( Jy ) = 30

for month August ( Au ) = 30

for month September ( s ) = 10

total deviation = 140

Hence the MAD = 23.333333

Calculate the MAD using the exponential smoothing method

for Month April ( A ) = 40

for month May ( Ma ) = 18

for Month June ( Ju ) = 33

for month July ( Jy ) = 17

for month August ( Au ) = 22

for month September  ( s ) = 10

total deviation = 135

MAD = 22.5

D) Exponential smoothing method produces a better Forecast because its MAD result is lower than that produced when 3 month method was used

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