Transcript:

Let us look at an example of forecasting using the time series methods. The past data for the demand of a product is given to us in this table so for the month of June 2013 the demand was 584 units for Feb. 2013 The demand was 610 units for March 2013 The demand was 655 units and so on till July 2013 which has a demand of 963 units. So these are basically the actual demand for each of these months now. If a five month moving average is used to forecast the next month’s, demand compute the forecast for the month of August 2013 So basically, this point number A is to find the forecast for month of August using the moving average Method B compute a weighted three-month moving average for August 2013 where the weights are 0.5 for the latest month 0.3 and point 2 for the other months, respectively, So B is to find the forecast for August 2013 using the weighted average method and C is find an exponential smoothing forecast for the month of August 2013 taking alpha as 0.33 so C is to find the forecast using the exponential smoothing method, So let us find out the forecast for the month of August, using the three time series methods, simple, moving average weighted average and exponential smoothing, so let us first find out the simple moving average now. The forecast for simple moving average can be found by the formula sum of n periods divided by N. Now we have already been given that we have to take a 5 month. Moving average, so N is 5 so since we have to find the forecast for August, we will take the last 5 months so 1 2 3 4 & 5 till March 2013 So for March 2013 The demand is 655 for April 747 for May 862 for June 913 and for July 9 63 And this is all divided by 5 so this is equal to 4 1 4 0 divided by 5 5 841 carry over 5 Twos are 10 for carry over 5 AIDS of 40 so 828 units next, let’s find out the forecast for August using the weighted moving average. Now here we have been asked to find out the weighted three month moving average for the month of August and the weights are 0.5 for the latest month 0.3 and point 2 for the older months so here our forecasts can be calculated as the weight for the month of July multiplied by the demand for July, plus the weight for June multiplied by the demand for June, Plus the weight for me multiplied by the demand for me. So this is equal to the weight for the latest month has been given as 0.5 so 0.5 multiplied by the demand is 963 plus the weight for June, which is 0.3 and the demand is 9 and 3 plus. The weight for me is 0.2 multiplied by the demand, which is 862 so this is equal to nine twenty seven point eight units. So this is the forecast for the month of August 2013 using the weighted moving average method. Now let’s move to the third part, which is to find the forecast using the exponential smoothing method – exponential smoothing method now. The formula for the exponential smoothing method is FP that is forecast for the period. T is equal to F T minus 1 that is a forecast for the period T minus 1 plus alpha multiplied by the actuals for the period T minus 1 minus the forecast for T minus 1 Now in our case, T is August and T minus 1 will be July. Now let’s see which of the values do. We already have in order to calculate the forecast for August? So we have been given that Alpha is 0.33 and the actual 40 minus 1 would be the actuals for July and we have been given the actual demand for July as 963 So this also we have, which is 963 but we don’t have the forecast for the month of July and we need the forecast in order to calculate the forecast for the month of August. So now the question is that how do we proceed? So let’s assume that The actual for Jan is also the forecast for February. So this is the actual and let me put the forecast here, so we are assuming that For February, the forecast is the same as the actual for Jan, which is 584 now. Using these two values and using this exponential smoothing method, let’s find out the forecast for the remaining months so forecast for March, so F March will be equal to the forecast for February, which is 584 plus alpha, which is 0.33 multiplied by the actual for the previous month, which is 610 – the forecast 584 and this comes out to 592 0.58 Now, similarly, let’s find out The forecast for April, so forecast for April is equal to the forecast for March, which is 500 two point five eight plus zero point three three actual for March, which is 655 minus the forecast five ninety two point, five eight and this is equal to six one three point one eight now forecast for May so forecast for April, which is six one three point one eight plus zero point three three multiplied by the Actuals for April, which is seven forty seven minus six one three point one eight and this is equal to 650 seven point. Three four so forecast for June is equal to the forecast for May, which is 650 700 point three, four plus zero point 3 3 multiplied by actual for me, which is 862 minus the forecast for May, which is 650 seven point three four and this is equal to seven twenty four point eight eight and forecast for July forecast for June, which is seven the four point eight eight plus zero point three three multiplied by the Actuals for June, which is 9 1 3 minus the forecast for June, which is seven twenty four point eight eight and this is equal to seven eighty six point nine, six, So now we have. F T minus one, which is seven eighty six point. Nine, six eighty minus 1 which is nine sixty three and alpha is zero point three three, so let’s find out the value of the forecast, so F T minus one, which is seven eighty six point nine, six plus alpha, which is zero point three three multiplied by the Actuals, which is 960 3 minus the forecast, which is seven eighty six point nine six, so this turns out to be eight, forty five point zero five. So this is the forecast using the exponential smoothing method, So let’s compare the three forecast numbers that we got so using the simple moving average, we had a forecast of eight twenty eight units for the month of August. Using the weighted moving average, the forecast was nine, twenty seven point eight units and using the exponential smoothing. The forecast is eight. Forty five point. Zero Five units you.