Forecasting

Chapter 2ForecastingPart 2 Introduction to Management Science and ForecastingLearning ObjectivesExplain the importance of forecasting in organizations.Describe the three major approaches to forecasting.Use a variety of techniques to make forecasts.Measure the accuracy of a forecast over time using various methods.Determine when a forecast can be improved.Discuss the main considerations in selecting a forecasting technique.Utilize Excel to solve various forecasting problems.After completing this chapter, you should be able to:2Copyright © 2007 The McGraw-Hill Companies. All rights reserved. The Importance of ForecastingForecastingis 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 systemas a process has an inherent tendency for inaccuracy.3Copyright © 2007 The McGraw-Hill Companies. All rights reserved. The Importance of ForecastingThe Forecasting ProcessDetermine the purpose of the forecast. Determine the time horizon. Select an appropriate technique.Identify the necessary data, and gather it if necessary. Make the forecast.Monitor forecast errors in order to determine if the forecast is performing adequately. If it is not, take appropriate corrective action.4Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Approaches to ForecastingQualitative Forecastsare based on judgment and/or opinion rather than on the analysis of “hard” data.Forecasts That Use Time Series Datainvolve 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.5Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Selecting the Forecasting Technique Factors affecting the choice of the forecasting technique to be used:the importance (purpose) of the forecastthe desired accuracy of the forecastthe cost of developing the forecastresources available to support and conduct the forecasting processthe planning horizon (long- or short-term)the sophistication of the users of the forecastA good rule is to choose the simplest technique that gives acceptable results.6Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Table 2–7 Forecasting Approaches7Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Table 2–7 Forecasting Approaches (cont’d)8Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Figure 2–1 Examples of Simple Patterns Sometimes Found in Time Series Data9Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Figure 2–2 Data with Trend and Seasonal VariationsSource: E. Turban, Jay Aronson, and Ting-Peng Liang, Decision Support Systems and Intelligence Systems, 7th ed. (Upper Saddle River, NJ: Prentice Hall, 2005), p. 109.10Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Figure 2–3 Averaging Applied to Three Possible Patterns11Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Example 2-1 12Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Figure 2–4 A Moving Average Forecast Tends to Smooth and LagChanges in the Data13Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Figure 2–5 The More Periods in a Moving Average, the Greater theForecast Will Lag Changes in the Data14Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Example 2-2 15Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 2-1 Moving Average Input and Output16Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 2-2 Moving Average Preparation Screen17Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Figure 2–6 Relative Weights in Exponential Smoothing18Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Figure 2–7 A Small Value of α Will Smooth More Than a Larger Value19Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 2-3 Exponential Smoothing Input, Output, and Chart20Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 2-4 Exponential Smoothing Preparation Wizard21Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Table 2–1 Values of Σt, t2, and Σt222Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Example 2-3Monthly demand for Dan’s Doughnuts over the past nine months for trays (six dozen per tray) of sugar doughnuts wasMar 112Apr 125May 120Jun 133Jul 136Aug 146Sept 140Oct 155Nov 1521. 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.Solution1. The data seem to show an upward, roughly linear trend:23Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Example 2-3 (cont’d)24Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 2–5 Data for Linear Trend/Regression Analysis25Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 2–6 Scatter Plot Development26Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 2–7 Scatter Plot27Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 2–8 Scatter Plot Titles, Axes, and Labels28Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 2–9 Scatter Diagram29Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 2–10 Scatter Diagram30Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 2–11 Regression Output31Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Example 2-432Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Example 2-4 cont’dA plot of the actual data and predicted values is shown below.33Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 2–12 Trend-Adjusted Exponential Smoothing34Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Figure 2–8 Naive Approaches with Seasonality35Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Example 2-5The 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 136 + 140 + 133 + 3 + 136. Relative for other days can be computed in a similar manner. For example, the estimated Monday relative is 0.77 + 0.72 + 0.69/3 = 0.7336Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Figure 2–9 A Centered Moving Average Closely Tracks the Data37Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Example 2-638Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 2–13 Seasonal Relative Computations39Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Explanatory ModelsSimple Linear RegressionA 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 approachIdentify 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.40Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Table 2–2 Data for Regression Problem41Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Figure 2–10 A Linear Relationship Appears to Exist42Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Table 2–2 Calculations for Regression Coefficients43Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Figure 2–11 Graph of Regression Line44Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Table 2–4 Selected Values of t.025 for n-2 Degrees of Freedom (df)45Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Figure 2–12 The Conditional Distributions of y’s Are Assumed to be Normal46Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Regression AssumptionsNormality 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.HomoscedasticityThe 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.47Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Figure 2–13 The Scatter around the Line Is Not Uniform48Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Figure 2–14 There Should Not Be Any Patterns around the Line49Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 2–14 Linear Regression-Explanatory Model Output50Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Table 2–5 Expansion of Data Used in Simple Regression Section51Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 2–15 Input Box for Multiple Regression52Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 2–16 Multiple Regression Output with Excel53Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Summarizing Forecast AccuracyThe 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. 54Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Example 2-755Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Figure 2–15 Monitoring Forecast Errors56Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Relative Measures of Forecast AccuracyPercentage 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 biasMean absolute percentage error (MAPE)measures overall forecast accuracy.57Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Example 2-858Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Example 2-8 cont’d59Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Example 2-8 cont’d60Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Tracking SignalThe tracking signalIs 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.61Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Example 2-962Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Exhibit 2–17 Measuring Forecast Accuracy Using MAD, MSE, MPE, and MAPE63Copyright © 2007 The McGraw-Hill Companies. All rights reserved. Table 2–6 Comparison of Types of Forecasts64Copyright © 2007 The McGraw-Hill Companies. All rights reserved.