Page 95 - DMGT523_LOGISTICS_AND_SUPPLY_CHAIN_MANAGEMENT

Logistics and Supply Chain Management

Notes There are no specific rules of selecting the value for ‘ ’. If more weight has to be given to recent
data, then the value should be closer to ‘1’. Values between 0.1 and 0.3 are most commonly used.
However, a method of choosing the best fit is by choosing the value of such that the error
variance is the minimum. This is shown in the worked example below:

Practical Problems
Problem – Choosing the Best Fit
Saluja Brothers manufactures simple lathes for the export market. The manufacturing manager
uses exponential smoothing technique to arrive at his forecasts. He has made a forecast using a
smoothing constant of 0.2.
The sales manager has also made his forecast using the exponential smoothing method, but has
used a smoothing constant of 0.5.

Compare the forecasts for the series data under two situations and determine which forecast
will you accept and why?

Period 1 2 3 4 5 6 7 8 9 10
Observations 30 32 35 34 31 30 33 36 36 34

Solution:
The basic exponential smoothing model is F =  D + (1 –  ) F
t t t–1
Where: D is the actual value
t
F is the forecasted value
t
 is the smoothing constant or weighting factor, and

F is the current time period.
t–1
Assume that the smoothed value of the time series for the first period is equal to the actual first
value of the time series. You can calculate the values as shown in the table below. The calculations
are simple.
The table shows the forecasts under the two specified conditions i.e.  = 0.2 and  = 0.5:

ά = 0.2 ά = 0.5
Period Dt Dt- Ft-1 ά* Dt- Ft-1 Ft (Dt- Ft-1)² Dt- Ft-1 ά* Dt- Ft-1 Ft (Dt- Ft-1)²
1 30 0.00 0.00 30.00 0.00 0.00 0.00 30.00 0.00
2 32 2.00 0.40 30.40 4.00 2.00 1.00 31.00 4.00
3 35 4.60 0.92 31.30 21.16 3.00 1.50 33.00 9.00
4 34 2.70 0.54 31.85 7.29 1.00 0.50 33.5 1.00
5 31 -0.85 -0.17 31.68 0.73 -2.50 -1.25 32.25 6.25
6 30 -1.68 -0.34 31.35 2.83 -2.25 1.13 31.13 5.06
7 33 1.65 0.33 31.68 2.73 1.88 0.94 32.06 3.54
8 36 4.32 0.86 32.54 18.67 2.94 1.97 34.03 8.65
9 36 3.46 0.69 33.23 11.97 1.97 0.99 35.00 3.88
10 34 0.77 0.15 33.38 0.60 -1.00 -0.50 34.50 1.00
Total 69.98 42.38

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