The pa follow For Problen DEMAND 221 247 228 233 240 152 163 155 167 158 PERIOD

Question

The pa follow For Problen DEMAND 221 247 228 233 240 152 163 155 167 158 PERIOD 4 10 7. ) Develop a last period forecast for periods 2 through 11. Calculate the MFE, MAD, and MAPE values for periods 2 through 10. Is this a good model? Why? 8..*) Develop a three-period weighted moving average forecast for periods 4 through 11. Use weights of 0.4, 0.35, and 0.25, with the most recent observation weighted the highest. Calculate the MFE, MAD, and MAPE values for periods 4 through 10. How do your results compare with those for Problem 7? 9. (") Develop two exponential smoothing forecasts for pe riods 2 through 11. For the first forecast, use = 0.2. the second, use = 0.7 . Assume that your forecast for pe- riod 1 was 250. Plot the results. Which model appears to work better? Why?

Explanation / Answer

7. Last period forecast method uses Demand of last period as the Forecast of Current period.

F (t) = D (t-1). The Forecast table is given below:

a) MFE is Mean Forecast Error which gives an average of error in forecasting over the period for which forecasting was done so as to measure over or under forecasting.

MFE = sum of all deviations/no. of periods

Deviation = Demand- Forecast = D (t)-F (t)

As can be seen from the table,

MFE = -63/9 = -7

A negative MFE is over forecasting where Actual demand is less than the forecasted demand.

b)MAD is mean absolute deviation takes an average of absolute error in forecasting whether negative or positive . It helps to decide which forecasting is better. The lower MAD value shows that there is less distance between forecast and demand and the forecasting is been done better than a forecasting having a higher MAD value .

MAD = sum of all absolute deviations/no. of periods

Absolute Deviation = | D (t)-F (t)|

MAD = sum of |D-F| / periods

Absolute deviation

|D-F|

As per given table, MAD = 185/9 = 20.6

c) MAPE is Mean absolute percentage error where a probable percentage of error over demand is taken to calculate the correctness of forecast.

MAPE = ( sum of 100*|(D-F)/D|)/no. of periods

As per above table,

MAPE = 106.6/9 = 11.8%

A low MAPE score shows that forecast calculation had a low percentage of error and was accurate.

So as can be seen from above calculation, it is not a good model to follow last period demand as a forecast of current period. This results in forecasts changing radically for every perios when the new actual comes in and there is huge difference between actual demand and forecast for that period.

8.

For 3 month weighted moving average forecasting is done as per weights provided. The summation of all the weights given is one and the highest weightage is given to the most recent demand as the change of recent demand to be equal to next period demand is higher compares to others.

Weights given are: 0.4, 0.35, 0.25 and most recent demand will be assigned the highest weight to calculate average.

For example, period 4 will have forecast of F(t)= 0.4*D(t-1) +0.35 * D(t-2) +0.25 * D(t-3)

similar calculation done for MFE, MAD and MAPE:

MFE= -201.4/7 =-28.8

MAD = 205.8/7 = 29.4

MAPE = 128.3 /7 =18.3%

Compared to previous problem, there is big deviation in all the values and the first method seems to have lesser error calculation.

9. Exponential Smoothing Forecast for alpha = 0.2

Forecast calulation in the exponential method are:

F(t+1) = F(t) + alpha * (D(t)-F(t)) = alpha *D(t) + (1-alpha)*F(t)

Since first Forecast is not given, forecast equal to Demand will be taken for only the first period.

MFE= -291.6/9 =-64.8

MAD = 297.8/9 = 66.2

MAPE = 183.4 /9 = 20.4%

Exponential Smoothing Forecast for alpha = 0.7

MFE= -99.6/9 =-22.1

MAD = 167/9 = 37.1

MAPE = 99.1 /9 = 11%

Thus from above numbers, the last model seems better as the margin of error is less and the high level of forecasting accuracy is there

Period Demand (D) Forecast (F) Deviation (D-F) 1 221 2 247 221 26 3 228 247 -19 4 233 228 5 5 240 233 7 6 152 240 -88 7 163 152 11 8 155 163 -8 9 167 155 12 10 158 167 -9 Total (summation) -63

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