Example 16.6 Forecasting Hardware Sales at Lee’s

Thomson/South-Western 2007 © South-Western/Cengage Learning © 2009Practical Management Science, Revised 3eWinston/Albright Background Information In the previous example, we saw that the moving averages method was able to provide only fair forecasts of weekly hardware sales at Lee’s. Using the best of three potential spans, its forecasts were still off by about 13.9% on average. The company would now like to try simple exponential smoothing to see whether this method, with an appropriate smoothing constant, can outperform the moving averages method. How should the company proceed?

Thomson/South-Western 2007 © South-Western/Cengage Learning © 2009Practical Management Science, Revised 3eWinston/Albright Solution We already saw in Example 16.5 that the hardware sales series meanders through time, with no apparent trends or seasonality. Therefore, this series is a good candidate for simple exponential smoothing. This is no guarantee that the method will provide accurate forecasts, but at least we cannot rule it out as a promising forecasting method.

Thomson/South-Western 2007 © South-Western/Cengage Learning © 2009Practical Management Science, Revised 3eWinston/Albright Developing the Spreadsheet Model To implement simple exponential smoothing, we must use the equation repeatedly. You can think of this procedure as climbing a ladder. The equation shows how to move from one step to the next step (from time period t-1 to time period t). However, just as in climbing a ladder, we have to get to the first step before we can continue. Choosing a value for L 0 is called initializing the procedure.

Thomson/South-Western 2007 © South-Western/Cengage Learning © 2009Practical Management Science, Revised 3eWinston/Albright Hardware Sales 2.xls The calculations for a smoothing constant of  =0.1 appear on the next slide and in this file. Using our initialization procedure, the first level, L 1, is the same as the first observation, so we enter it in cell C8 with the formula =B8. From then on, we calculate each level from the equation. The typical formula entered in cell C9 is =$B$2*B9+(1-$B$2)*C8 We then copy this formula down to cell C111. Next, because each forecast is the previous level, we enter the formula =C8 in cell D9 and copy it down to cell D112.

Thomson/South-Western 2007 © South-Western/Cengage Learning © 2009Practical Management Science, Revised 3eWinston/Albright

Thomson/South-Western 2007 © South-Western/Cengage Learning © 2009Practical Management Science, Revised 3eWinston/Albright Developing the Spreadsheet Model -- continued As with moving averages, it is useful to create plots of the sales series with the forecast series superimposed. The next slide shows this plot with  = 0.1; the slide after that shows it with  = 0.3. As we see, the forecast series is smoother with the smaller smoothing constant. In this sense, a small value of in exponential smoothing corresponds to a large span in moving averages.

Thomson/South-Western 2007 © South-Western/Cengage Learning © 2009Practical Management Science, Revised 3eWinston/Albright

Thomson/South-Western 2007 © South-Western/Cengage Learning © 2009Practical Management Science, Revised 3eWinston/Albright

Thomson/South-Western 2007 © South-Western/Cengage Learning © 2009Practical Management Science, Revised 3eWinston/Albright Developing the Spreadsheet Model -- continued If we want the forecasts to react less to random ups and downs of the series, we choose a smaller value of . This is the reasoning behind the common practiceof choosing a small smoothing constant such as 0.1 or 0.2. We show the summary measures of the forecast errors for three potential smoothing constants, 0.1, 0.2, and 0.3, on the next slide.

Thomson/South-Western 2007 © South-Western/Cengage Learning © 2009Practical Management Science, Revised 3eWinston/Albright Developing the Spreadsheet Model -- continued From these summary measures we can make two conclusions. –First, the summary measures decrease slightly as the smoothing constant increases. We tried making the smoothing constant even larger, but virtually no improvement was possible with smoothing constants larger than 0.3. –Second, the best of these results is virtually the same as the best moving averages results. The best forecasts with each method have errors in the 13% to 14% range. Again, this is due to the relatively large amount of noise inherent in the sales series.

Thomson/South-Western 2007 © South-Western/Cengage Learning © 2009Practical Management Science, Revised 3eWinston/Albright Developing the Spreadsheet Model -- continued In cases like this, we might be able to track the ups and downs of the historical series more closely with a larger smoothing constant, but this would almost surely not result in better future forecasts. The bottom line is that noise, by definition, is not predictable.