You have just been hired at the local soup distributor and your new boss, Michae
ID: 380988 • Letter: Y
Question
You have just been hired at the local soup distributor and your new boss, Michael, asks you to calculate and decide between two different forecasting methods for soup: the weighted average and exponential smoothing. Based on Michael’s experience, he suggested the following weights (most recent first) using the weighted average method for five periods: 0.35, 0.25, 0.20, 0.10, and 0.10. He suggested using an alpha of .30 with exponential smoothing for comparison. You tell Michael that you can do that with no problem and can produce a forecast based on previous demand using both methods. Based on these data, which method, weighted averaging or exponential smoothing, do you recommend that should Michael use? (Hint: calculate and complete the table below and calculate the MAPE using the data for periods 6 and 7.)
Important: Round the forecast of demand to the nearest whole number. Enter forecast as ### or #,###.
Round percentage error for each period to 2 digits (e.g. 05.12%) before calculating MAPE. Calculate weighted average and exponetial smoothing for periods 6,7, and 8.
Week
Actual Demand
Weighted Average
Exponential Smoothing
1
9,301
2
9,216
3
8,436
4
9,291
9,291
5
8,707
9,291
6
9,108
7,979
7
8,207
8,067
8
7,820
Calculate the MAPE for the weighted average model using periods 6 and 7. Round the percentage error to 2 digits after the decimal point (enter as 00.00)
%
Calculate the MAPE for the Exponential Smoothing model using periods 6 and 7. Round the percentage error to 2 digits after the decimal point (enter as 00.00)
%
Which method should Michael use? (Enter weighted average or exponential smoothing)
Week
Actual Demand
Weighted Average
Exponential Smoothing
1
9,301
2
9,216
3
8,436
4
9,291
9,291
5
8,707
9,291
6
9,108
7,979
7
8,207
8,067
8
7,820
Explanation / Answer
Please find blow the filled up table as desired:
WEEK
ACTUAL DEMAND
FORECAST ( WEIGHTED AVERAGE)
ABSOLUTE DEVIATION
ABSOLUTE PERCENT ERROR
FORECAST ( Exponential smoothing)
ABSOLUTE DEVIATION
ABSOLUTE PERCENT ERROR
6
9108
7979
1129
12.40
8882.2
225.8
2.48
7
8207
8067
140
1.71
8949.94
742.94
9.05
Sum =
14.10
11.53
Please note following :
Absolute deviation = Absolute difference between Actual demand and forecast
Absolute percentage error = Absolute deviation / Actual demand x 100
Formula for exponential smoothing :
Ft = alpha x Ft-1 + ( 1 – alpha) x At-1 , Ft. Ft-1 = Forecast for period t and t-1 respectively
= 0.3 x Ft-1 + 0.7 x At-1 At-1 = Actual demand for period t-1
Alpha = Exponential smoothing factor = 0.3
Forecast ( Exponential smoothing) for week 6
= 0.3 x Forecast for period 5 + 0.7 x Actual demand = 0.3 x 9291 + 0.7 x 8707 = 2787.3 + 6094.9 = 8882.2
Thus,
Sum of Absolute percentage error ( weighted average method ) for period 6 and 7 = 14.10
Hence MAPE = 14.10/2 = 7.05 %
Sum of absolute percentage error ( weighted average method) for period 6 and 7 = 11.53
Hence MAPE = 11.53/2 = 5.765 %
Since MAPE for Exponential smoothing method < MAPE for Weighted average method,
Michael must choose Exponential smoothing method
MAPE FOR WEIGHTED AVERAGE METHOD = 7.05%
MAPE FOR WEIGHTED AVERAGE METHOD = 5.76%
MICHAEL SHOULD USE EXPONENTAIL SMOOTHING METHOD
WEEK
ACTUAL DEMAND
FORECAST ( WEIGHTED AVERAGE)
ABSOLUTE DEVIATION
ABSOLUTE PERCENT ERROR
FORECAST ( Exponential smoothing)
ABSOLUTE DEVIATION
ABSOLUTE PERCENT ERROR
6
9108
7979
1129
12.40
8882.2
225.8
2.48
7
8207
8067
140
1.71
8949.94
742.94
9.05
Sum =
14.10
11.53
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