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Table of Contents Chapter 10 Forecasting

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Table of Contents Chapter 10 Forecasting

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    1. © The McGraw-Hill Companies, Inc., 2008 10.1 Table of Contents Chapter 10 (Forecasting) An Overview of Forecasting Techniques (Section 10.1) 10.2–10.8 A Case Study: The Computer Club Warehouse Problem (Section 10.2) 10.9–10.13 Applying Time-Series Forecasting to the Case Study (Section 10.3) 10.14–10.30 The Time-Series Forecasting Methods in Perspective (Section 10.4) 10.31–10.35 Causal Forecasting with Linear Regression (Section 10.5) 10.36–10.40 Judgmental Forecasting Methods (Section 10.6) 10.41

    2. © The McGraw-Hill Companies, Inc., 2008 10.2 Forecasting at Fastchips Fastchips is a leading producer of microprocessors. Six months ago, it launched the sales of its latest microprocessor. Month-by-month sales (in thousands) over the initial six months have been 17 25 24 26 30 28 Question: What is the forecast for next month’s sales?

    3. © The McGraw-Hill Companies, Inc., 2008 10.3 The Last-Value Forecasting Method The last-value forecasting method ignores all data points in a time series except the last one. Forecast = Last value Fastchips: Month-by-month sales (in thousands) over the initial six months: 17 25 24 26 30 28 Forecast = 28

    4. © The McGraw-Hill Companies, Inc., 2008 10.4 The Averaging Forecasting Method The averaging forecasting method uses all the data points in the time series and simply averages these points. Forecast = Average of all data to date Fastchips: Month-by-month sales (in thousands) over the initial six months: 17 25 24 26 30 28 Forecast = (17+25+24+26+30+28) / 6 = 25

    5. © The McGraw-Hill Companies, Inc., 2008 10.5 The Moving-Average Forecasting Method The moving-average forecasting method averages the data for only the most recent time periods. n = Number of recent periods to consider as relevant for forecasting Forecast = Average of last n values Fastchips: Month-by-month sales (in thousands) over the initial six months: 17 25 24 26 30 28 Forecast (n=3) = (26+30+28) / 3 = 28

    6. © The McGraw-Hill Companies, Inc., 2008 10.6 The Exponential Smoothing Forecasting Method The exponential smoothing forecasting method provides a more sophisticated version of the moving-average method. It gives the greatest weight to the last month and then progressively smaller weights to the older months. Exponential smoothing with trend adjusts exponential smoothing by also directly considering any current upward or downward trend in sales.

    7. © The McGraw-Hill Companies, Inc., 2008 10.7 Linear Regression Linear regression uses a two-dimensional graph with sales measured along the vertical axis and time measured along the horizontal axis. After plotting the sales data, this method finds a line passing through the midst of the data as closely as possible. The extension of the line into future months provides the forecast of sales in these future months.

    8. © The McGraw-Hill Companies, Inc., 2008 10.8 Measuring the Forecast Error The mean absolute deviation (called MAD) measures the average forecasting error. MAD = (Sum of forecasting errors) / (Number of forecasts) The mean square error (often abbreviated MSE) measures the average of the square of the forecasting error. MSE = (Sum of square of forecasting errors) / (Number of forecasts). The MSE increases the weight of large errors relative to the weight of small errors.

    9. © The McGraw-Hill Companies, Inc., 2008 10.9 The Computer Club Warehouse (CCW) The Computer Club Warehouse (CCW) sells computer products at bargain prices by taking telephone orders (as well as website and fax orders) directly from customers. Products include computers, peripherals, supplies, software, and computer furniture. The CCW call center is never closed. It is staffed by dozens of agents to take and process customer orders. A large number of telephone trunks are provided for incoming calls. If an agent is not free when a call arrives, it is placed on hold. If all the trunks are in use (called saturation), the call receives a busy signal. An accurate forecast of the demand for agents is needed. Question: How should the demand for agents be forecasted?

    10. © The McGraw-Hill Companies, Inc., 2008 10.10 25 Percent Rule (Current Forecasting Method) Since sales are relatively stable through the year except for a substantial increase during the Christmas season, assume that each quarter’s call volume will be the same as the preceding quarter, except for adding 25 percent for Quarter 4. Forecast for Quarter 2 = Call volume for Quarter 1 Forecast for Quarter 3 = Call volume for Quarter 2 Forecast for Quarter 4 = 1.25(Call volume for Quarter 3) Forecast for next Quarter 1 = (Call volume for Quarter 4) / 1.25

    11. © The McGraw-Hill Companies, Inc., 2008 10.11 Average Daily Call Volume (3 Years of Data) Figure 10.1 The average number of calls received per day at the CCW call center in each of the four quarters of the past three years.Figure 10.1 The average number of calls received per day at the CCW call center in each of the four quarters of the past three years.

    12. © The McGraw-Hill Companies, Inc., 2008 10.12 Applying the 25-Percent Rule Figure 10.2 This spreadsheet records the results of applying the 25-percent rule over the past three years to forecast the average daily call volume for the upcoming quarter.Figure 10.2 This spreadsheet records the results of applying the 25-percent rule over the past three years to forecast the average daily call volume for the upcoming quarter.

    13. © The McGraw-Hill Companies, Inc., 2008 10.13 Measuring the Forecast Error The mean absolute deviation (called MAD) measures the average forecasting error. MAD = (Sum of forecasting errors) / (Number of forecasts) The mean square error (often abbreviated MSE) measures the average of the square of the forecasting error. MSE = (Sum of square of forecasting errors) / (Number of forecasts). The MSE increases the weight of large errors relative to the weight of small errors.

    14. © The McGraw-Hill Companies, Inc., 2008 10.14 Considering Seasonal Effects When there are seasonal patterns in the data, they can be addressed by forecasting methods that use seasonal factors. The seasonal factor for any period of a year (a quarter, a month, etc.) measures how that period compares to the overall average for an entire year. Seasonal factor = (Average for the period) / (Overall average) It is easier to analyze data and detect new trends if the data are first adjusted to remove the seasonal patterns. Seasonally adjusted data = (Actual call volume) / (Seasonal factor)

    15. © The McGraw-Hill Companies, Inc., 2008 10.15 Calculation of Seasonal Factors for CCW Table 10.1 Calculation of the seasonal factors for the CCW problem.Table 10.1 Calculation of the seasonal factors for the CCW problem.

    16. © The McGraw-Hill Companies, Inc., 2008 10.16 Excel Template for Calculating Seasonal Factors Figure 10.3 The Excel template in your MS Courseware for calculating seasonal factors is applied here to the CCW problem.Figure 10.3 The Excel template in your MS Courseware for calculating seasonal factors is applied here to the CCW problem.

    17. © The McGraw-Hill Companies, Inc., 2008 10.17 Seasonally Adjusted Time Series for CCW Figure 10.4 The seasonally adjusted time series for the CCW problem obtained by dividing each actual average daily call volume in Figure 10.1 by the corresponding seasonal factor obtained in Figure 10.3.Figure 10.4 The seasonally adjusted time series for the CCW problem obtained by dividing each actual average daily call volume in Figure 10.1 by the corresponding seasonal factor obtained in Figure 10.3.

    18. © The McGraw-Hill Companies, Inc., 2008 10.18 Outline for Forecasting Call Volume Select a time-series forecasting method. Apply this method to the seasonally adjusted time series to obtain a forecast of the seasonally adjusted call volume for the next time period. Multiply this forecast by the corresponding seasonal factor to obtain a forecast of the actual call volume (without seasonal adjustment).

    19. © The McGraw-Hill Companies, Inc., 2008 10.19 The Last-Value Forecasting Method The last-value forecasting method ignores all data points in a time series except the last one. Forecast = Last value The last-value forecasting method is sometimes called the naďve method, because statisticians consider it naďve to use just a sample size of one when other data are available. However, when conditions are changing rapidly, it may be that the last value is the only relevant data point.

    20. © The McGraw-Hill Companies, Inc., 2008 10.20 The Last-Value Method Applied to CCW’s Problem Figure 10.5 The Excel template in your MS Courseware for the last-value method with seasonal adjustments is applied here to the CCW problem.Figure 10.5 The Excel template in your MS Courseware for the last-value method with seasonal adjustments is applied here to the CCW problem.

    21. © The McGraw-Hill Companies, Inc., 2008 10.21 The Averaging Forecasting Method The averaging forecasting method uses all the data points in the time series and simply averages these points. Forecast = Average of all data to date The averaging forecasting method is a good one to use when conditions are very stable. However, the averaging method is very slow to respond to changing conditions. It places the same weight on all the data, even though the older values may be less representative of current conditions than the last value observed.

    22. © The McGraw-Hill Companies, Inc., 2008 10.22 The Averaging Method Applied to CCW’s Problem Figure 10.6 The Excel template in your MS Courseware for the averaging method with seasonal adjustments is applied here to the CCW problem.Figure 10.6 The Excel template in your MS Courseware for the averaging method with seasonal adjustments is applied here to the CCW problem.

    23. © The McGraw-Hill Companies, Inc., 2008 10.23 The Moving-Average Forecasting Method The moving-average forecasting method averages the data for only the most recent time periods. n = Number of recent periods to consider as relevant for forecasting Forecast = Average of last n values The moving-average forecasting method is a good one to use when conditions don’t change much over the number of time periods included in the average. However, the moving-average method is slow to respond to changing conditions. It places the same weight on each of the last n values even though the older values may be less representative of current conditions than the last value observed.

    24. © The McGraw-Hill Companies, Inc., 2008 10.24 The Moving-Average Method Applied to CCW Figure 10.7 The Excel template in your MS Courseware for the moving-average method with seasonal adjustments is applied here to the CCW problem.Figure 10.7 The Excel template in your MS Courseware for the moving-average method with seasonal adjustments is applied here to the CCW problem.

    25. © The McGraw-Hill Companies, Inc., 2008 10.25 The Exponential Smoothing Forecasting Method The exponential smoothing forecasting method places the greatest weight on the last value in the time series and then progressively smaller weights on the older values. Forecast = a (Last value) + (1 – a) (Last forecast) a is the smoothing constant between 0 and 1. This method places a weight of a on the last value, a(1–a) on the next-to-last value, a(1–a)2 on the next prior value, etc. For example, when a = 0.5, the method places a weight of 0.5 on the last value, 0.25 on the next-to-last, 0.125 on the next prior, etc. A larger value of a places more emphasis on the more recent values, a smaller value places more emphasis on the older values. The choice of the value of the smoothing constant a has a substantial effect on the forecast. A small value (say, a = 0.1) is appropriate if conditions are relatively stable. A larger value (say, a = 0.5) is appropriate if significant changes occur frequently.

    26. © The McGraw-Hill Companies, Inc., 2008 10.26 The Exponential Smoothing Method Applied to CCW Figure 10.8 The Excel template in your MS Courseware for the exponential smoothing method with seasonal adjustments is applied here to the CCW problem.Figure 10.8 The Excel template in your MS Courseware for the exponential smoothing method with seasonal adjustments is applied here to the CCW problem.

    27. © The McGraw-Hill Companies, Inc., 2008 10.27 A Time Series with Trend (Population of a State over Time) Figure 10.9 A time series that gives the estimated population of a certain state over a series of years. The trend line shows the basic upward trend of the population.Figure 10.9 A time series that gives the estimated population of a certain state over a series of years. The trend line shows the basic upward trend of the population.

    28. © The McGraw-Hill Companies, Inc., 2008 10.28 Exponential Smoothing with Trend Forecasting Method The exponential smoothing with trend forecasting method uses the recent values in the time series to estimate any current upward or downward trend in these values. Trend = Average change from one time-series value to the next The formula for forecasting the next value in the time series adds the estimated trend. Forecast = a (Last value) + (1 – a) (Last forecast) + Estimated trend a is the smoothing constant between 0 and 1. Exponential smoothing also is used to obtain and update the estimated trend. Estimated trend = b (Latest trend) + (1 – b) (Last estimate of trend) b is the trend smoothing constant. The formula for forecasting n periods from now is Forecast = a (Last value) + (1 – a) (Last forecast) + n (Estimated trend)

    29. © The McGraw-Hill Companies, Inc., 2008 10.29 Exponential Smoothing with Trend Applied to CCW Figure 10.10 The Excel template in your MS Courseware for the exponential smoothing method with trend with seasonal adjustments is applied here to the CCW problem.Figure 10.10 The Excel template in your MS Courseware for the exponential smoothing method with trend with seasonal adjustments is applied here to the CCW problem.

    30. © The McGraw-Hill Companies, Inc., 2008 10.30 MAD and MSE for the Various Forecasting Method Table 10.2 The Average Forecasting Error (MAD) and Mean Square Error (MSE) for the various time-series forecasting methods when forecasting CCW call volumes.Table 10.2 The Average Forecasting Error (MAD) and Mean Square Error (MSE) for the various time-series forecasting methods when forecasting CCW call volumes.

    31. © The McGraw-Hill Companies, Inc., 2008 10.31 Typical Probability Distribution of Call Volume (Assumes Mean = 7,500) Figure 10.11 A typical probability distribution of what the average daily call volume will be for CCW in a quarter when the mean is 7,500.Figure 10.11 A typical probability distribution of what the average daily call volume will be for CCW in a quarter when the mean is 7,500.

    32. © The McGraw-Hill Companies, Inc., 2008 10.32 Typically Probability Distributions of Call Volume in the Four Quarters (Assumes Annual Mean = 7,500) Figure 10.12 Typical probability distributions of CCW’s average daily call volumes in the four quarters of a year in which the overall average is 7,500.Figure 10.12 Typical probability distributions of CCW’s average daily call volumes in the four quarters of a year in which the overall average is 7,500.

    33. © The McGraw-Hill Companies, Inc., 2008 10.33 Comparison of Typical Probability Distributions of Seasonally-Adjusted Call Volumes in Years 1 and 2 Figure 10.13 Comparison of typical probability distributions of CCW’s average daily call volumes (seasonally adjusted) in years 1 and 2.Figure 10.13 Comparison of typical probability distributions of CCW’s average daily call volumes (seasonally adjusted) in years 1 and 2.

    34. © The McGraw-Hill Companies, Inc., 2008 10.34 Comparison of the Forecasting Methods Last value method: Suitable for a time series that is so unstable that even the next-to-last value is not considered relevant for forecasting the next value. Averaging method: Suitable for a very stable time series where even its first few values are considered relevant for forecasting the next value. Moving-average method: Suitable for a moderately stable time series where the last few values are considered relevant for forecasting the next value. Exponential smoothing method: Suitable for a time series in the range from somewhat unstable to rather stable, where the value of the smoothing constant needs to be adjusted to fit the anticipated degree of stability. Exponential smoothing with trend: Suitable for a time series where the mean of the distribution tends to follow a trend either up or down, provided that changes in the trend occur only occasionally and gradually.

    35. © The McGraw-Hill Companies, Inc., 2008 10.35 The Consultant’s Recommendations Forecasting should be done monthly rather than quarterly. Hiring and training of new agents also should be done monthly. Recently retired agents should be offered the opportunity to work part time on an on-call basis. Since sales drive call volume, the forecasting process should begin by forecasting sales. For forecasting purposes, total sales should be broken down into the major components: The relatively stable market base of numerous small-niche products. Each of the few (perhaps three or four) major new products. Exponential smoothing with a relatively small smoothing constant is suggested for forecasting sales of the marketing base of numerous small-niche products. Exponential smoothing with trend, with relatively large smoothing constants, is suggested for forecasting sales of each major new product. Seasonally adjusted time series should be used for each application of the methods. The forecasts in recommendation 5 should be summed to obtain a forecast of total sales. Causal forecasting with linear regression should be used to obtain a forecast of call volume from this forecast of total sales.

    36. © The McGraw-Hill Companies, Inc., 2008 10.36 Causal Forecasting Causal forecasting obtains a forecast of the quantity of interest (the dependent variable) by relating it directly to one or more other quantities (the independent variables) that drive the quantity of interest. Table 10.3 Possible examples of causal forecasting.Table 10.3 Possible examples of causal forecasting.

    37. © The McGraw-Hill Companies, Inc., 2008 10.37 Sales and Call Volume Data for CCW Figure 10.14 The data needed to do causal forecasting for the CCW problem by relating call volume to sales.Figure 10.14 The data needed to do causal forecasting for the CCW problem by relating call volume to sales.

    38. © The McGraw-Hill Companies, Inc., 2008 10.38 Adding a Trendline to the Graph Figure 10.15 Figure 10.14 has been modified here by adding a trend line to the graph.Figure 10.15 Figure 10.14 has been modified here by adding a trend line to the graph.

    39. © The McGraw-Hill Companies, Inc., 2008 10.39 Linear Regression When doing causal forecasting with a single independent variable, linear regression involves approximating the relationship between the dependent variable (call volume for CCW) and the independent variable (sales for CCW) by a straight line. This linear regression line is drawn on a graph with the independent variable on the horizontal axis and the dependent variable on the vertical axis. The line is constructed after plotting a number of points showing each observed value of the independent variable and the corresponding value for the dependent variable. The linear regression line has the form y = a + bx where y = Estimated value of the dependent variable a = Intercept of the linear regression line with the y-axis b = Slope of the linear regression line x = Value of the independent variable

    40. © The McGraw-Hill Companies, Inc., 2008 10.40 Excel Template for Linear Regression Figure 10.16 The Excel template in your MS Courseware for doing causal forecasting with linear regression, as illustrated here for the CCW problem.Figure 10.16 The Excel template in your MS Courseware for doing causal forecasting with linear regression, as illustrated here for the CCW problem.

    41. © The McGraw-Hill Companies, Inc., 2008 10.41 Judgmental Forecasting Methods Manager’s Opinion: A single manager uses his or her best judgment. Jury of Executive Opinion: A small group of high-level managers pool their best judgment to collectively make the forecast. Salesforce Composite: A bottom-up approach where each salesperson provides an estimate of what sales will be in his or her region. These estimates are then aggregated into a corporate sales forecast. Consumer Market Survey: A grass-roots approach that surveys customers and potential customers regarding their future purchasing plans and how they would respond to various new features in products. Delphi Method: A panel of experts in different locations who independently fill out a series of questionnaires. The results from each questionnaire are provided with the next one, so each expert can evaluate the group information in adjusting his or her responses next time.

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