COURSE: INDUSTRIAL ENGINEERING LESSON: TYPES OF FORECASTING-PART-11)
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WEIGHTED MOVING AVERAGE (ii) Weighted moving average: This method gives unequal weight to each demand data in such a manner that the summation of all weights always equals to one. The most recent data is given the highest weight and the weight assigned to the oldest data is the least If n number of periods, then first forecast (n+1)th period. Method to find the weights 1) Find the summation of n natural numbers Zn n (n+1)/2 2) Arrange in decreasing order as n n-1 n-2 n-3 Zn ,Zn ,Zn ,Zn Example: For n = 4, first forecast will be from 5th period and n = 10 10 10 10 10
WEIGHTED MOVING AVERAGE Year Actual demand (DForecasted demand (F) 1. 2003 2. 2004 3. 2005 4. 2006 5. 2007 6. 2008 108 127 113 121 129 143 118.5 123.2 F2007 0.4* 121 0.3 113 + 0.2*127 +0.1*108 118.5 F2008 0.4* 129 0.3 121 0.2 113 +0.1*127 123.2
EXPONENTIAL SMOOTHING (iv) Exponential Smoothing: In this method we require only the actual demand data and the forecasted value for the last period to get the next forecast. This method gives weight to all the previous data and the weight assigned are in exponentially decreasing order. The most recent data is given the highest weight and the weight assigned to older data decreases exponentially General case: Since Forecast error, eDt-Ft Therefore Ft Ft-1 + { et-1 } Forecast (F) at any period (t) is given by Where F-1 is forecasted value for the previous period (t-1) is known as smoothing constant and is equivalent to F, Dt-1 + (1- ) Ft-1 2 n+1 n- number of period
EXPONENTIAL SMOOTHING Note: If for the initial period forecast value is not known then it can be determined by either of the following methods: Ist Method (Naive Method): Take the actual demand data for the first period equal to 2(Applying Na ve method) F2004 F2003 + 0.3 (0) = 100 F2005 F2004 0.3 (20) 106 F2006-F2005 + 0.3 (-16) = 101.24 F2007F2000.3 (43.8) 114.34 F2008 F2000.3 (45.66) 128.03 the forecast for the first period i.e. take D Fiand proceed. IInd Method: Take the mean or average value of actual demand data as the forecast for first period and proceed For 0.3 Year Actual demand (D) Forecasted demand (F) Error (e) 1. 2003 2. 2004 3. 2005 4. 2006 5. 2007 6. 2008 100 120 90 145 160 100 100 106 101.2 114.34 128.03 20 -16 43.8 45.66
QUESTION The sales of a product during the last four years were 860, 880, 870 and 890 units. The forecast for the fourth year was 876 units. If the forecast for the fifth year, using simple exponential smoothing, is equal to the forecast using a three period moving average, the value of the exponential smoothing constant a is: (a) (c)
SOLUTION Using simple exponential smoothing, new forecast-old forecast + (Actual-old forecast) and forecast using a three period moving average = (880 870 890)/3 and equate Ans : c
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