Stevenson and Ozgur First Edition Introduction to Management Science with Spreadsheets McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter 2 Forecasting Part 2 Introduction to Management Science and Forecasting

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–2 Learning Objectives 1.Explain the importance of forecasting in organizations. 2.Describe the three major approaches to forecasting. 3.Use a variety of techniques to make forecasts. 4.Measure the accuracy of a forecast over time using various methods. 5.Determine when a forecast can be improved. 6.Discuss the main considerations in selecting a forecasting technique. 7.Utilize Excel to solve various forecasting problems. After completing this chapter, you should be able to:

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–3 The Importance of Forecasting Forecasting –is important because it helps reduce uncertainty. –provides decision makers with an improved picture of probable future events and, thereby, enable decision makers to plan accordingly. –is used for planning the system itself. –is used for planning the use of the system –as a process has an inherent tendency for inaccuracy.

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–4 The Importance of Forecasting The Forecasting Process 1.Determine the purpose of the forecast. 2.Determine the time horizon. 3.Select an appropriate technique. 4.Identify the necessary data, and gather it if necessary. 5.Make the forecast. 6.Monitor forecast errors in order to determine if the forecast is performing adequately. If it is not, take appropriate corrective action.

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–5 Approaches to Forecasting Qualitative Forecasts –are based on judgment and/or opinion rather than on the analysis of “hard” data. Forecasts That Use Time Series Data –involve the assumption that past experience reflects probable future experience (i.e., the past movements or patterns in the data will persist into the future). Explanatory Models – incorporate one or more variables that are related to the variable of interest and, therefore, they can be used to predict future values of that variable.

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–6 Selecting the Forecasting Technique Factors affecting the choice of the forecasting technique to be used: –the importance (purpose) of the forecast –the desired accuracy of the forecast –the cost of developing the forecast –resources available to support and conduct the forecasting process –the planning horizon (long- or short-term) –the sophistication of the users of the forecast –A good rule is to choose the simplest technique that gives acceptable results.

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–7 Table 2–7 Forecasting Approaches

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–8 Table 2–7 Forecasting Approaches (cont’d)

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–9 Figure 2–1Examples of Simple Patterns Sometimes Found in Time Series Data

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–10 Figure 2–2Data with Trend and Seasonal Variations Source: E. Turban, Jay Aronson, and Ting-Peng Liang, Decision Support Systems and Intelligence Systems, 7th ed. (Upper Saddle River, NJ: Prentice Hall, 2005), p. 109.

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–11 Figure 2–3Averaging Applied to Three Possible Patterns

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–12 Example 2-1

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–13 Figure 2–4A Moving Average Forecast Tends to Smooth and Lag Changes in the Data

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–14 Figure 2–5The More Periods in a Moving Average, the Greater the Forecast Will Lag Changes in the Data

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–15 Example 2-2

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–16 Exhibit 2-1Moving Average Input and Output

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–17 Exhibit 2-2Moving Average Preparation Screen

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–18 Figure 2–6Relative Weights in Exponential Smoothing

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–19 Figure 2–7A Small Value of α Will Smooth More Than a Larger Value

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–20 Exhibit 2-3Exponential Smoothing Input, Output, and Chart

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–21 Exhibit 2-4Exponential Smoothing Preparation Wizard

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–22 Table 2–1Values of Σt, t2, and Σt2

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–23 Example 2-3 Monthly demand for Dan’s Doughnuts over the past nine months for trays (six dozen per tray) of sugar doughnuts was Mar 112 Apr 125 May 120 Jun 133 Jul 136 Aug 146 Sept 140 Oct 155 Nov Plot the data to determine if a linear trend equation is appropriate. 2.Obtain a trend equation. 3.Forecast demand for the next two months. Solution 1.The data seem to show an upward, roughly linear trend:

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–24 Example 2-3 (cont’d)

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–25 Exhibit 2–5Data for Linear Trend/Regression Analysis

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–26 Exhibit 2–6Scatter Plot Development

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–27 Exhibit 2–7Scatter Plot

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–28 Exhibit 2–8Scatter Plot Titles, Axes, and Labels

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–29 Exhibit 2–9Scatter Diagram

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–30 Exhibit 2–10Scatter Diagram

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–31 Exhibit 2–11Regression Output

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–32 Example 2-4

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–33 Example 2-4 cont’d A plot of the actual data and predicted values is shown below.

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–34 Exhibit 2–12Trend-Adjusted Exponential Smoothing

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–35 Figure 2–8Naive Approaches with Seasonality

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–36 Example 2-5 The manager of a parking lot has computed daily relatives for the number of cars per day for his lot. The computations are repeated here (about three weeks are shown for illustration). A seven-period centered moving average is used because there are seven days (seasons) per week. The estimated Friday relative is Relative for other days can be computed in a similar manner. For example, the estimated Monday relative is /3 = 0.73

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–37 Figure 2–9A Centered Moving Average Closely Tracks the Data

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–38 Example 2-6

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–39 Exhibit 2–13Seasonal Relative Computations

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–40 Explanatory Models Simple Linear Regression –A model of two variables thought to be related. Dependent variable: the variable to be forecasted. Independent variable is used to “explain” or predict the value of the dependent variable. Using the regression approach –Identify an independent variable or variables. –Obtain a sample of at least 10 observations. –Develop an equation. –Identify any restrictions on predictions. –Measure accuracy in a given forecast.

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–41 Table 2–2 Data for Regression Problem

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–42 Figure 2–10 A Linear Relationship Appears to Exist

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–43 Table 2–2 Calculations for Regression Coefficients

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–44 Figure 2–11 Graph of Regression Line

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–45 Table 2–4 Selected Values of t. 025 for n-2 Degrees of Freedom (df)

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–46 Figure 2–12 The Conditional Distributions of y’s Are Assumed to be Normal

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–47 Regression Assumptions Normality –For any given value of x, there is a distribution of possible y values that has a mean equal to the expected value (i.e., y = a + bx) and the distribution is normal. Homoscedasticity –The conditional distributions for all values of x have the same dispersion. Linearity. –The requirement of uniform scatter also means that there should not be any patterns around the line. Independence. –Values of y should not be correlated over time. If they are, it may be more appropriate to use a time series model.

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–48 Figure 2–13 The Scatter around the Line Is Not Uniform

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–49 Figure 2–14 There Should Not Be Any Patterns around the Line

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–50 Exhibit 2–14 Linear Regression-Explanatory Model Output

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–51 Table 2–5 Expansion of Data Used in Simple Regression Section

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–52 Exhibit 2–15 Input Box for Multiple Regression

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–53 Exhibit 2–16 Multiple Regression Output with Excel

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–54 Summarizing Forecast Accuracy The mean absolute deviation (MAD) –measures the average forecast error over a number of periods, without regard to the sign of the error: The mean squared error (MSE) –is the average squared error experienced over a number of periods.

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–55 Example 2-7

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–56 Figure 2–15 Monitoring Forecast Errors

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–57 Relative Measures of Forecast Accuracy Percentage error (PE) –for a given time series data measures the percentage point deviation of the forecasted value from the actual value. Mean percentage error (MPE) –measures the forecast bias Mean absolute percentage error (MAPE) –measures overall forecast accuracy.

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–58 Example 2-8

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–59 Example 2-8 cont’d

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–60 Example 2-8 cont’d

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–61 Tracking Signal The tracking signal –Is the ratio of cumulative forecast error at any point in time to the corresponding MAD at that point in time. –A value of a tracking signal that is beyond the action limits suggests the need for corrective action.

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–62 Example 2-9

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–63 Exhibit 2–17Measuring Forecast Accuracy Using MAD, MSE, MPE, and MAPE

Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 2–64 Table 2–6 Comparison of Types of Forecasts