Use exponential smoothing with a smoothing constant of 0.3 to
a) What is the MAD?
b) What is the MSE?
a)
To determine: Forecast the registrations at the seminar using exponential smoothing and hence compute MAD.
Introduction: Forecasting is used to predict future changes or demand patterns. It involves different approaches and varies with different time periods. Exponential Smoothing and Naïve forecasting methods are two of the time series methods of forecasting which use past data to forecast the future.
Answer to Problem 11P
Using exponential smoothing, the registrations at the seminar are forecasted and the computed MAD is 2.44.
Explanation of Solution
Given information:
Year | Registrations (000) |
1 | 4 |
2 | 6 |
3 | 4 |
4 | 5 |
5 | 10 |
6 | 8 |
7 | 7 |
8 | 9 |
9 | 12 |
10 | 14 |
11 | 15 |
Formula to calculate the forecasted demand
Where,
Calculation to forecast demand using exponential smoothing:
Year | Registrations (000) | Ft (000) |
1 | 4 | 5 |
2 | 6 | 4.700 |
3 | 4 | 5.090 |
4 | 5 | 4.763 |
5 | 10 | 4.834 |
6 | 8 | 6.384 |
7 | 7 | 6.869 |
8 | 9 | 6.908 |
9 | 12 | 7.536 |
10 | 14 | 8.875 |
11 | 15 | 10.412 |
Table 1
Excel calculation:
Calculation of forecast for year 2:
To calculate the forecast for year 2, substitute the value of the forecast of year 1, smoothing constant, and difference of actual and forecasted demand in the above formula. The result of forecast for year 2 is 4.70
Calculation of forecast for year 3:
To calculate the forecast for year 3, substitute the value of the forecast of year 1, smoothing constant, and difference of actual and forecasted demand in the above formula. The result of forecast for year 3 is 5.09
Calculation of forecast for year 4:
To calculate the forecast for year 4, substitute the value of the forecast of year 3, smoothing constant, and difference of actual and forecasted demand in the above formula. The result of forecast for year 3 is 4.763
Calculation of forecast for year 5:
To calculate the forecast for year 5, substitute the value of the forecast of year 4, smoothing constant, and difference of actual and forecasted demand in the above formula. The result of forecast for year 5 is 4.834
Calculation of forecast for year 6:
To calculate the forecast for year 6, substitute the value of the forecast of year 5, smoothing constant, and difference of actual and forecasted demand in the above formula. The result of forecast for year 5 is 6.384
Calculation of forecast for year 7:
To calculate the forecast for year 7, substitute the value of the forecast of year 6, smoothing constant, and difference of actual and forecasted demand in the above formula. The result of forecast for year 7 is 6.869
Calculation of forecast for year 8:
To calculate the forecast for year 8, substitute the value of the forecast of year 7, smoothing constant, and difference of actual and forecasted demand in the above formula. The result of forecast for year 8 is 6.908
Calculation of forecast for year 9:
To calculate the forecast for year 9, substitute the value of the forecast of year 8, smoothing constant, and difference of actual and forecasted demand in the above formula. The result of forecast for year 8 is 7.536
Calculation of forecast for year 10:
To calculate the forecast for year 10, substitute the value of the forecast of year 9, smoothing constant, and difference of actual and forecasted demand in the above formula. The result of forecast for year 9 is 8.875
Calculation of forecast for year 11:
To calculate the forecast for year 11, substitute the value of the forecast of year 10, smoothing constant, and difference of actual and forecasted demand in the above formula. The result of forecast for year 10 is 10.412
The forecasted value of registrations using exponential smoothing is provided in table 1
Calculation of MAD using exponential smoothing
Formula to calculate MAD
Table 1 provides the adequate forecasted data to compute MAD.
Year | Registrations (000) | Ft (000) | Absolute error |
1 | 4 | 5.000 | 1 |
2 | 6 | 4.700 | 1.30 |
3 | 4 | 5.090 | 1.09 |
4 | 5 | 4.763 | 0.24 |
5 | 10 | 4.834 | 5.17 |
6 | 8 | 6.384 | 1.62 |
7 | 7 | 6.869 | 0.13 |
8 | 9 | 6.908 | 2.09 |
9 | 12 | 7.536 | 4.46 |
10 | 14 | 8.875 | 5.13 |
11 | 15 | 10.412 | 4.59 |
Total | 26.81 | ||
MAD | 2.44 |
Table 2
Excel calculation:
Mean Absolute Deviation:
Mean Absolute Deviation is obtained by dividing the summation of absolute values by the number of years. Absolute error is obtained by taking modulus for the difference between actual and forecasted values.
Calculation of absolute error for year 1
The absolute error for year 1 is the modulus of the difference between 4 and 5, which corresponds to 1. Therefore absolute error for year 1 is 1.
Calculation of absolute error for year 2
The absolute error for year 2 is the modulus of the difference between 6 and 4.7, which corresponds to 1.30. Therefore absolute error for year 2 is 1.30
Calculation of absolute error for year 3
The absolute error for year 3 is the modulus of the difference between 4 and 5.09, which corresponds to 1.09. Therefore absolute error for year 1.09
Calculation of absolute error for year 4
The absolute error for year 4 is the modulus of the difference between 5 and 4.763, which corresponds to 0.24. Therefore absolute error for year 4 is 0.24
Calculation of absolute error for year 5
The absolute error for year 5 is the modulus of the difference between 10 and 4.834, which corresponds to 5.17. Therefore absolute error for year 5 is 5.17
Calculation of absolute error for year 6
The absolute error for year 6 is the modulus of the difference between 8 and 6.384, which corresponds to 1.62. Therefore absolute error for year is 1.62
Calculation of absolute error for year 7
The absolute error for year 7 is the modulus of the difference between 7 and 6.869, which corresponds to 0.13. Therefore absolute error for year is 0.13
Calculation of absolute error for year 8
The absolute error for year 8 is the modulus of the difference between 9 and 6.908, which corresponds to 2.09. Therefore absolute error for year is 2.09
Calculation of absolute error for year 9
The absolute error for year 9 is the modulus of the difference between 12 and 7.536, which corresponds to 4.46. Therefore absolute error for year is 4.46
Calculation of absolute error for year 10
The absolute error for year 10 is the modulus of the difference between14 and 8.875, which corresponds to 5.13. Therefore absolute error for year is 5.13
Calculation of absolute error for year 11
The absolute error for year 11 is the modulus of the difference between 15 and 10.412, which corresponds to 4.59. Therefore absolute error for year is 4.59
Calculation of MAD using exponential smoothing
Upon substitution of summation, the value of absolute error for 11 years, that is, 26.81 is divided by number of years, that is, 11 yields MAD of 2.44
Hence, using exponential smoothing, the registrations at the seminar are forecasted and the computed MAD is 2.44
b)
To determine: Forecast the registrations at the seminar using exponential smoothing and hence compute MSE.
Answer to Problem 11P
Using exponential smoothing, the registrations at the seminar are forecasted and the computed MSE is 9.53
Explanation of Solution
Given information:
Year | Registrations (000) |
1 | 4 |
2 | 6 |
3 | 4 |
4 | 5 |
5 | 10 |
6 | 8 |
7 | 7 |
8 | 9 |
9 | 12 |
10 | 14 |
11 | 15 |
Formula to calculate MSE
Table 1 provides the required forecasted data which in turn is used to compute MSE.
Year | Registrations (000) | Ft (000) | Error2 |
1 | 4 | 5 | 1 |
2 | 6 | 4.700 | 1.69 |
3 | 4 | 5.090 | 1.19 |
4 | 5 | 4.763 | 0.06 |
5 | 10 | 4.834 | 26.69 |
6 | 8 | 6.384 | 2.61 |
7 | 7 | 6.869 | 0.02 |
8 | 9 | 6.908 | 4.38 |
9 | 12 | 7.536 | 19.93 |
10 | 14 | 8.875 | 26.27 |
11 | 15 | 10.412 | 21.05 |
Total | 104.87 | ||
MSE | 9.53 |
Table 3
Excel calculation:
Error is the difference between actual and forecasted values. Table 2 provides the value of Error for the forecasted and given values.
Calculation of MSE
MSE is obtained by dividing the summation of the square of error (refer to Table (3)) with the n number of periods, that is, 11.
Hence, using exponential smoothing, the registrations at the seminar are forecasted and the computed MSE is 9.53.
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Chapter 4 Solutions
Principles Of Operations Management
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