1. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.1 Table of Contents Chapter 13 (Forecasting) Some Applications of Forecasting (Section 13.1)13.2–13.4 A Case Study: The Computer Club Warehouse Problem (Section 13.2)13.5–13.9 Applying Time-Series Forecasting to the Case Study (Section 13.3)13.10–13.26 Time-Series Forecasting with CB Predictor (Section 13.4)13.27–13.34 The Time-Series Forecasting Methods in Perspective (Section 13.5)13.35–13.39 Causal Forecasting with Linear Regression (Section 13.6)13.40–13.44 Judgmental Forecasting Methods (Section 13.7)13.45 Forecasting in Practice (Section 13.8)13.46–13.47

2. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.2 Some Applications of Forecasting Sales Forecasting –Any company engaged in selling goods needs to forecast demand for those goods. –Underestimating demand leads to shortages, lost sales, unhappy customers, etc. –Overestimating demand is costly due to inventory costs, forced price reductions, unneeded production, etc. –Examples: Merit Brass Company (1993), Hidroeléctrica Español (1990), American Airlines (1992). Forecasting Economic Trends –How much will the nation’s gross domestic product grow next quarter? Next year? What is the forecast for the rate of inflation? Unemployment? –Statistical models to forecast economic trends (econometric models) have been developed by government agencies, universities, consulting firms, etc. –Models can be very influential in determining govermental policies. –Example: U.S. Department of Labor (1988). All articles can be downloaded at www.mhhe.com/hillier2e/articles

3. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.3 Some Applications of Forecasting Forecasting Production Yields –The yield of a production process refers to the percentage of completed items that meet quality standards and do not need to be discarded. –If an expensive setup is required, or there is only one production run, an accurate forecast is necessary to provide a good chance of fulfilling an order with acceptable items without excessive production costs. –Example: Albuquerque Microelectronics Operation (1994) Forecasting the Need for Spare Parts –Many companies need to maintain an inventory of spare parts to enable them to repair either their equipment or their products leased or sold to customers. –Example: American Airlines (1989). Forecasting Staffing Needs –For a service company, forecasting “sales” becomes forecasting demand for services, which translates into forecasting staffing needs. –Too few staff leads to long lines, unhappy customers, perhaps lost business. Too many increases personnel cost. –Examples: United Airlines (1986), Taco Bell (1998), L. L Bean (1995). All articles can be downloaded at www.mhhe.com/hillier2e/articles

4. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.4 Applications of Statistical Forecasting Methods OrganizationQuantity Being ForecastedIssue of Interfaces Merit Brass Co.Sales of finished goodsJan-Feb 1993 Hidroelétrica EspañolEnergy demandJan-Feb 1990 American AirlinesDemand for different fare classesJan-Feb 1992 American Airlines Need for spare parts to repair airplanes July-Aug 1989 Albuquerque Microelectronics Production yield in wafer fabricationMar-Apr 1994 U.S. Department of LaborUnemployment insurance paymentsMar-Apr 1988 United Airlines Demand at reservations offices and airports Jan-Feb 1986 Taco BellNumber of customer arrivalsJan-Feb 1988 L.L. BeanStaffing needs at call centerNov-Dec 1995 All references available for download at www.mhhe.com/hillier2e/articles

5. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.5 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?

6. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.6 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

7. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.7 Average Daily Call Volume (3 Years of Data)

8. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.8 Applying the 25-Percent Rule

9. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.9 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.

10. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.10 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)

11. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.11 Calculation of Seasonal Factors for CCW Quarter Three-Year Average Seasonal Factor 17,0197,019 / 7,529 = 0.93 26,7846,784 / 7,529 = 0.90 37,4347,434 / 7,529 = 0.99 48,8808,880 / 7,529 = 1.18 Total = 30,117 Average = 30,117 / 4 = 7,529

12. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.12 Excel Template for Calculating Seasonal Factors

13. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.13 Seasonally Adjusted Time Series for CCW

14. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.14 Outline for Forecasting Call Volume 1.Select a time-series forecasting method. 2.Apply this method to the seasonally adjusted time series to obtain a forecast of the seasonally adjusted call volume for the next time period. 3.Multiply this forecast by the corresponding seasonal factor to obtain a forecast of the actual call volume (without seasonal adjustment).

15. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.15 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 naïve method, because statisticians consider it naïve 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.

16. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.16 The Last-Value Method Applied to CCW’s Problem

17. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.17 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.

18. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.18 The Averaging Method Applied to CCW’s Problem

19. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.19 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.

20. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.20 The Moving-Average Method Applied to CCW

21. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.21 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 =  (Last value) + (1 –  ) (Last forecast)  is the smoothing constant between 0 and 1. This method places a weight of a on the last value,  (1–  ) on the next-to-last value,  (1–  ) 2 on the next prior value, etc. –For example, when  = 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  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,  = 0.1) is appropriate if conditions are relatively stable. –A larger value (say,  = 0.5) is appropriate if significant changes occur frequently.

22. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.22 The Exponential Smoothing Method Applied to CCW

23. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.23 A Time Series with Trend (Population of a State over Time)

24. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.24 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 =  (Last value) + (1 –  ) (Last forecast) + Estimated trend  is the smoothing constant between 0 and 1. Exponential smoothing also is used to obtain and update the estimated trend. Estimated trend =  (Latest trend) + (1 –  ) (Last estimate of trend)  is the trend smoothing constant. The formula for forecasting n periods from now is Forecast =  (Last value) + (1 –  ) (Last forecast) + n (Estimated trend)

25. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.25 Exponential Smoothing with Trend Applied to CCW

26. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.26 MAD and MSE for the Various Forecasting Method Forecasting MethodMADMSE CCW’s 25 percent rule424317,815 Last-value method295145,909 Averaging method400242,876 Moving-average method437238,816 Exponential smoothing324157,836 Exponential smoothing with trend345180,796

27. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.27 Using CB Predictor: Enter the Data on a Spreadsheet

28. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.28 Using CB Predictor: Input Data Pane

29. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.29 Using CB Predictor: Data Attributes Pane

30. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.30 Using CB Predictor: Method Gallery Pane

31. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.31 Using CB Predictor: Results Pane

32. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.32 CB Predictor Preview Graph

33. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.33 CB Predictor Results

34. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.34 Relationship Between CB Predictor Techniques and the Forecasting Techniques in the Textbook CB Predictor TechniqueRelated Technique in Section 13.3 Single moving averageMoving average Double moving averageNot covered Single exponential smoothingExponential smoothing Double exponential smoothingExponential smoothing with trend Seasonal additiveNot covered Holt-Winters additiveNot covered Seasonal multiplicativeExponential smoothing with seasonality Holt-Winters multiplicativeExponential smoothing with seasonality and trend

35. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.35 Typical Probability Distribution of Call Volume (Assumes Mean = 7,500)

36. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.36 Typically Probability Distributions of Call Volume in the Four Quarters (Assumes Annual Mean = 7,500)

37. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.37 Comparison of Typical Probability Distributions of Seasonally-Adjusted Call Volumes in Years 1 and 2

38. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.38 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.

39. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.39 The Consultant’s Recommendations 1.Forecasting should be done monthly rather than quarterly. 2.Hiring and training of new agents also should be done monthly. 3.Recently retired agents should be offered the opportunity to work part time on an on-call basis. 4.Since sales drive call volume, the forecasting process should begin by forecasting sales. 5.For forecasting purposes, total sales should be broken down into the major components: a)The relatively stable market base of numerous small-niche products. b)Each of the few (perhaps three or four) major new products. 6.Exponential smoothing with a relatively small smoothing constant is suggested for forecasting sales of the marketing base of numerous small-niche products. 7.Exponential smoothing with trend, with relatively large smoothing constants, is suggested for forecasting sales of each major new product. 8.Seasonally adjusted time series should be used for each application of the methods. 9.The forecasts in recommendation 5 should be summed to obtain a forecast of total sales. 10.Causal forecasting with linear regression should be used to obtain a forecast of call volume from this forecast of total sales.

40. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.40 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. Type of Forecasting Possible Dependent Variable Possible Independent Variable SalesSales of a productAmount of advertising Spare partsDemand for spare partsUsage of equipment Economic trendsGross domestic productVarious economic factors CCW call volumeCall volumeTotal sales Any quantityThis same quantityTime

41. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.41 Sales and Call Volume Data for CCW

42. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.42 Adding a Trendline to the Graph

43. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.43 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

44. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.44 Excel Template for Linear Regression

45. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.45 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.

46. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.46 Forecasting in Practice A survey of forecasting practices at 500 U.S. corporations indicates that judgmental forecasting methods are somewhat more widely used than statistical methods. Among judgmental methods, the most popular is a jury of executive opinion. When forecasting sales, manager’s opinion is a close second. Statistical forecasting methods also are fairly widely used, especially in companies with high sales. Among statistical methods, the moving-average method and linear regression are the most widely used. Both exponential smoothing and the last-value method also receive considerable use.

47. McGraw-Hill/Irwin © The McGraw-Hill Companies, Inc., 2003 13.47 The Forecasting Method Used in Actual Applications OrganizationQuantity Being ForecastedForecasting Method Merit Brass Co.Sales of finished goodsExponential smoothing Hidroelétrica EspañolEnergy demandARIMA (Box-Jenkins), etc. American Airlines Demand for different fare classes Exponential smoothing American Airlines Need for spare parts to repair airplanes Causal forecasting with linear regression Albuquerque Microelectronics Production yield in wafer fabrication Exponential smoothing with trend U.S. Department of Labor Unemployment insurance payments Causal forecasting with linear regression United Airlines Demand at reservations offices and airports ARIMA (Box-Jenkins) Taco BellNumber of customer arrivalsMoving average L.L. BeanStaffing needs at call centerARIMA (Box-Jenkins) All references available for download at www.mhhe.com/hillier2e/articles