1. DAVIS AQUILANO CHASE PowerPoint Presentation by Charlie Cook F O U R T H E D I T I O N Forecasting © The McGraw-Hill Companies, Inc., 2003 chapter 9

2. Fundamentals of Operations Management 4e© The McGraw-Hill Companies, Inc., 20039–2 Chapter Objectives Introduce the basic concepts of forecasting and its importance within an organization. Identify several of the more common forecasting methods and how they can improve the performance of both manufacturing and service operations. Provide a framework for understanding how forecasts are developed Demonstrate that errors exist in all forecasts and show how to measure and assess these errors. Discuss some of the software programs that are available for developing forecasting models.

3. Fundamentals of Operations Management 4e© The McGraw-Hill Companies, Inc., 20039–3 Managerial Issues Recognizing the increased importance of forecasting in both manufacturing and services. How to go about implementing forecasting at all levels in the organization. Understanding how managers can use the various forecasting methods to decide when to add manufacturing capacity and where to locate retail service outlets for maximum sales.

4. Fundamentals of Operations Management 4e© The McGraw-Hill Companies, Inc., 20039–4 Types of Forecasting Qualitative Techniques –Nonquantitative forecasting techniques based on expert opinions and intuition. Typically used when there are no data available. Time Series Analysis –Analyzing data by time periods to determine if trends or patterns occur. Causal Relationship Forecasting –Relating demand to an underlying factor other than time.

5. Fundamentals of Operations Management 4e© The McGraw-Hill Companies, Inc., 20039–5 Comparing the Costs and Benefits of Forecasting Exhibit 9.1

6. Fundamentals of Operations Management 4e© The McGraw-Hill Companies, Inc., 20039–6 Forecasting Techniques and Common Models Exhibit 9.2a

7. Fundamentals of Operations Management 4e© The McGraw-Hill Companies, Inc., 20039–7 Forecasting Techniques and Common Models Exhibit 9.2b

8. Fundamentals of Operations Management 4e© The McGraw-Hill Companies, Inc., 20039–8 Comparison of Forecasting Techniques Exhibit 9.3

9. Fundamentals of Operations Management 4e© The McGraw-Hill Companies, Inc., 20039–9 Components of Demand Average Demand for the Period Trends Seasonal Influence Cyclical Elements Random Variation

10. Fundamentals of Operations Management 4e© The McGraw-Hill Companies, Inc., 20039–10 Historical Monthly Product Demand Consisting of a Growth Trend, Cyclical Factor, and Seasonal Demand Exhibit 9.4

11. Fundamentals of Operations Management 4e© The McGraw-Hill Companies, Inc., 20039–11 Common Types of Trends Exhibit 9.5a

12. Fundamentals of Operations Management 4e© The McGraw-Hill Companies, Inc., 20039–12 Common Types of Trends (cont’d) Exhibit 9.5b

13. Fundamentals of Operations Management 4e© The McGraw-Hill Companies, Inc., 20039–13 Time Series Analysis Simple Moving Average –Average over a given number of time periods that is updated by replacing the data in the oldest period with that in the most recent period. F t =Forecasted sales for the period A t-1 =Actual sales in period t-1 n=Number of periods in the moving average

14. Fundamentals of Operations Management 4e© The McGraw-Hill Companies, Inc., 20039–14 Forecast Demand Based on a Three- and Nine-Week Simple Moving Average Exhibit 9.6

15. Fundamentals of Operations Management 4e© The McGraw-Hill Companies, Inc., 20039–15 Moving Average Forecast of Three- and Nine-Week Periods versus Actual Demand Exhibit 9.7

16. Fundamentals of Operations Management 4e© The McGraw-Hill Companies, Inc., 20039–16 Time Series Analysis (cont’d) Weighted Moving Average –Simple moving average where weights are assigned to each time period in the average. The sum of all of the weights must equal one. F t =Forecasted sales for the period A t-1 =Actual sales in period t-1 w t-1 =Weight assigned to period t-1 n=Number of periods in the moving average

17. Fundamentals of Operations Management 4e© The McGraw-Hill Companies, Inc., 20039–17 Time Series Analysis (cont’d) Exponential Smoothing –Times series forecasting technique that does not require large amounts of historical data. Benefits of Using Exponential Models –Models are surprisingly accurate. –Model formulation is fairly easy. –Readily understood by users. –Little computation is required. –Limited use of historical data.

18. Fundamentals of Operations Management 4e© The McGraw-Hill Companies, Inc., 20039–18 Time Series Analysis (cont’d) Exponential Smoothing Constant Alpha (  ) –A value between 0 and 1 that is used to minimize the error between historical demand and respective forecasts. –Use small values for  if demand is stable, larger values for  if demand is fluctuating. –Adaptive forecasting Two or more predetermined values of alpha Computed values of alpha

19. Fundamentals of Operations Management 4e© The McGraw-Hill Companies, Inc., 20039–19 Time Series Analysis (cont’d) Exponential Smoothing Formula F t =Exponentially smoothed forecast for period t F t-1 =Exponentially smoothed forecast for prior period A t-1 =Actual demand in the prior period  =Desired response rate, or smoothing constant

20. Fundamentals of Operations Management 4e© The McGraw-Hill Companies, Inc., 20039–20 Time Series Analysis (cont’d) Exponential Smoothing With a Trend Constant Delta (  ) to correct for lagging behind a trend: FIT t =Forecast including trend  =Trend constant

21. Fundamentals of Operations Management 4e© The McGraw-Hill Companies, Inc., 20039–21 Exponential Forecasts versus Actual Demands for Units of a Product over Time Showing the Forecast Lag Exhibit 9.8

22. Fundamentals of Operations Management 4e© The McGraw-Hill Companies, Inc., 20039–22 Forecasting Errors in Time Series Analysis Sources of Error –Projection of past trends into the future –Bias errors Consistent mistakes causing a forecast to be too high or too low: wrong relationships, wrong trend line, errors in shifting seasonal demand, undetected trends. –Random errors Unexplainable variations (noise) in a forecast that cannot be explained by the forecast model.

23. Fundamentals of Operations Management 4e© The McGraw-Hill Companies, Inc., 20039–23 Forecasting Errors in Time Series Analysis (cont’d) Measurement of Error –MAD (mean absolute deviation)—Average forecasting error based on the absolute difference between actual and forecast demands. t=Period number A t =Actual demand for period t F t =Forecast for period t n=Total number of periods | |=Absolute value

24. Fundamentals of Operations Management 4e© The McGraw-Hill Companies, Inc., 20039–24 A Normal Distribution with a Mean=0 and a MAD=1 Exhibit 9.9

25. Fundamentals of Operations Management 4e© The McGraw-Hill Companies, Inc., 20039–25 Forecasting Errors in Time Series Analysis (cont’d) Measurement of Error (cont’d) –Tracking signal—a measurement of error that indicates if the forecast is staying within specified limits of the actual demand. RSFE=Running sum of forecast errors MAD=Mean absolute deviation

26. Fundamentals of Operations Management 4e© The McGraw-Hill Companies, Inc., 20039–26 Computing the Mean Absolute Deviation (MAD), the Running Sum of Forecast Errors (RSFE), and the Tracking Signal from Forecast and Actual Data Exhibit 9.10

27. Fundamentals of Operations Management 4e© The McGraw-Hill Companies, Inc., 20039–27 A Plot of Tracking Signals Calculated in Exhibit 9.10 Exhibit 9.11

28. Fundamentals of Operations Management 4e© The McGraw-Hill Companies, Inc., 20039–28 The Percentage of Points Included within the Control Limits for a Range of 0 to 4 MADs Exhibit 9.12

29. Fundamentals of Operations Management 4e© The McGraw-Hill Companies, Inc., 20039–29 Forecasting Errors in Time Series Analysis (cont’d) Mean Absolute Percentage Error (MAPE) –Used to determine the forecasting errors as a percentage of the actual demand. A t =Actual demand F t =Forecast demand n=number of periods in forecast

30. Fundamentals of Operations Management 4e© The McGraw-Hill Companies, Inc., 20039–30 Linear Regression Analysis –A forecasting technique that assumes that the relationship between the dependent and independent variables is a straight line. Y=Dependent variable to be solved for a=Y intercept b=Slope of the XY relationship X=Independent variable (e.g., units of time)

31. Fundamentals of Operations Management 4e© The McGraw-Hill Companies, Inc., 20039–31 Least Squares Regression Line Exhibit 9.13

32. Fundamentals of Operations Management 4e© The McGraw-Hill Companies, Inc., 20039–32 Least Squares Regression Analysis Exhibit 9.14A

33. Fundamentals of Operations Management 4e© The McGraw-Hill Companies, Inc., 20039–33 Linear Regression Analysis (cont’d) Standard Error of the Estimate –A measure of the dispersion of data about a regression line. –How well (or closely) the regression line fits the data.  2 1 2 ˆ      n n i ii YX yy S

34. Fundamentals of Operations Management 4e© The McGraw-Hill Companies, Inc., 20039–34 Standard Error of the Estimate in a Spreadsheet Exhibit 9.14B

35. Fundamentals of Operations Management 4e© The McGraw-Hill Companies, Inc., 20039–35 Causal Relationship Forecasting Leading Indicator –An event whose occurrence causes, presages or influences the occurrence of another subsequent event. Warning strips on the highway Prerequisites to a college course An engagement ring

36. Fundamentals of Operations Management 4e© The McGraw-Hill Companies, Inc., 20039–36 Causal Relationship: Sales to Housing Starts Exhibit 9.15

37. Fundamentals of Operations Management 4e© The McGraw-Hill Companies, Inc., 20039–37 Causal Relationship Forecasting Reliability of Data –Coefficient of determination The proportion of variability in demand that can be attributed to an independent variable.

38. Fundamentals of Operations Management 4e© The McGraw-Hill Companies, Inc., 20039–38 Exhibit 9.16 The Relationship between Y, y i, ŷ i, in Determining r 2

39. Fundamentals of Operations Management 4e© The McGraw-Hill Companies, Inc., 20039–39 Causal Relationship Forecasting (cont’d) Reliability of Data –Mean squared error—A measure of the variability in the data about a regression line.  2 2 ˆ     n yy ii MSE

40. Fundamentals of Operations Management 4e© The McGraw-Hill Companies, Inc., 20039–40 Causal Relationship Forecasting (cont’d) Multiple Regression Analysis –Forecasting using more than one independent variable; measuring the combined effects of several independent variables on the dependent variable.

41. Fundamentals of Operations Management 4e© The McGraw-Hill Companies, Inc., 20039–41 Causal Relationship Forecasting (cont’d) Neural Networks –A forecasting technique simulating human learning that develops complex relationships between the model inputs and outputs.

42. Fundamentals of Operations Management 4e© The McGraw-Hill Companies, Inc., 20039–42 The Application of Forecasting to Service Operations Real-time data acquisition makes information immediately available to decision makers. –Point-of-Sale (POS) equipment –Yield management—attempts to maximize the revenues of a firm.