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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-1 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Chapter 5 Forecasting Prepared by Lee Revere and John Large

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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-2 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Learning Objectives Students will be able to: 1.Understand and know when to use various families of forecasting models. 2.Compare moving averages, exponential smoothing, and trend time-series models. 3.Seasonally adjust data. 4.Understand Delphi and other qualitative decision-making approaches. 5.Compute a variety of error measures.

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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-3 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Chapter Outline 5.1 Introduction 5.2 Types of Forecasts 5.3 Scatter Diagrams and Time Series 5.4 Measures of Forecast Accuracy 5.5 Time-Series Forecasting Models 5.6 Monitoring and Controlling Forecasts 5.7 Using the Computer to Forecast

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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-4 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Introduction Eight steps to forecasting: 1.Determine the use of the forecast. 2.Select the items or quantities to be forecasted. 3.Determine the time horizon of the forecast. 4.Select the forecasting model or models. 5.Gather the data needed to make the forecast. 6.Validate the forecasting model. 7.Make the forecast. 8.Implement the results. These steps provide a systematic way of initiating, designing, and implementing a forecasting system.

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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-5 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Types of Forecasts Moving Average Exponential Smoothing Trend Projections Time-Series Methods: include historical data over a time interval Forecasting Techniques No single method is superior Delphi Methods Jury of Executive Opinion Sales Force Composite Consumer Market Survey Qualitative Models : attempt to include subjective factors Causal Methods: include a variety of factors Regression Analysis Multiple Regression Decomposition

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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-6 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Qualitative Methods Delphi Method interactive group process consisting of obtaining information from a group of respondents through questionnaires and surveys Jury of Executive Opinion obtains opinions of a small group of high- level managers in combination with statistical models Sales Force Composite allows each sales person to estimate the sales for his/her region and then compiles the data at a district or national level Consumer Market Survey solicits input from customers or potential customers regarding their future purchasing plans

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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-7 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Scatter Diagrams Radios Televisions Compact Discs Scatter diagrams are helpful when forecasting time-series data because they depict the relationship between variables.

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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-8 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Measures of Forecast Accuracy Forecast errors allow one to see how well the forecast model works and compare that model with other forecast models. Forecast error = actual value – forecast value

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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-9 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Measures of Forecast Accuracy (continued) Measures of forecast accuracy include: Mean Absolute Deviation (MAD) Mean Squared Error (MSE) Mean Absolute Percent Error (MAPE) = |forecast errors| n = (errors) n = actual n 100% error 2

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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-10 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Hospital Days – Forecast Error Example Ms. Smith forecasted total hospital inpatient days last year. Now that the actual data are known, she is reevaluating her forecasting model. Compute the MAD, MSE, and MAPE for her forecast. MonthForecastActual JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC380396

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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-11 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Hospital Days – Forecast Error Example ForecastActual|error|error^2|error/actual| JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC AVERAGE MAD =MSE =MAPE =.0368*100 =

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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-12 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Decomposition of a Time- Series Time series can be decomposed into: Trend (T): gradual up or down movement over time Seasonality (S): pattern of fluctuations above or below trend line that occurs every year Cycles(C): patterns in data that occur every several years Random variations (R): “blips”in the data caused by chance and unusual situations

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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-13 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Components of Decomposition Trend Actual Data Cyclic Random

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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-14 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Decomposition of Time- Series: Two Models Multiplicative model assumes demand is the product of the four components. demand = T * S * C * R Additive model assumes demand is the summation of the four components. demand = T + S + C + R

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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-15 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Moving Averages n Simple moving average = demand in previous n periods Moving average methods consist of computing an average of the most recent n data values for the time series and using this average for the forecast of the next period.

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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-16 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Wallace Garden Supply’s Three-Month Moving Average MonthActual Shed Sales Three-Month Moving Average January10 February12 March13 April16 May19 June23 July26 ( )/3 = 11 2 / 3 ( )/3 = 13 2 / 3 ( )/3 = 16 ( )/3 = 19 1 / 3

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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-17 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Weighted Moving Averages Weighted moving averages use weights to put more emphasis on recent periods. (weight for period n) (demand in period n) ∑ weights Weighted moving average =

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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-18 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Calculating Weighted Moving Averages Weights Applied Period 3 Last month 2 Two months ago 1 Three months ago 3*Sales last month + 2*Sales two months ago + 1*Sales three months ago 6 Sum of weights

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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-19 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Wallace Garden’s Weighted Three-Month Moving Average MonthActual Shed Sales Three-Month Weighted Moving Average January February March April May June July26 [3*13+2*12+1*10]/6 = 12 1 / 6 [3*16+2*13+1*12]/6 =14 1 / 3 [3*19+2*16+1*13]/6 = 17 [3*23+2*19+1*16]/6 = 20 1 / 2

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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-20 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Exponential Smoothing Exponential smoothing is a type of moving average technique that involves little record keeping of past data. New forecast = previous forecast + (previous actual –previous forecast) Mathematically this is expressed as: F t = F t-1 + (Y t-1 - F t-1 ) F t-1 = previous forecast = smoothing constant F t = new forecast Y t-1 = previous period actual

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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-21 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Port of Baltimore Exponential Smoothing Example QtrActual Tonnage Unloaded Rounded Forecast using = = ( ) = ( ) = ( ) = ( ) = ( ) = ( ) = ( ) 9? 179= ( )

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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-22 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Port of Baltimore Exponential Smoothing Example QtrActual Tonnage Unloaded Rounded Forecast using = = ( ) = ( ) = ( ) = ( ) = ( ) = ( ) = ( ) 9? 184 = ( )

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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-23 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Selecting a Smoothing Constant Actual Forecast with a = 0.10 Absolute Deviations Forecast with a = 0.50 Absolute Deviations MAD To select the best smoothing constant, evaluate the accuracy of each forecasting model. The lowest MAD results from = 0.10

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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-24 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ PM Computer: Moving Average Example PM Computer assembles customized personal computers from generic parts. The owners purchase generic computer parts in volume at a discount from a variety of sources whenever they see a good deal. It is important that they develop a good forecast of demand for their computers so they can purchase component parts efficiently.

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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-25 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ PM Computers: Data Periodmonthactual demand 1Jan37 2Feb40 3Mar41 4Apr37 5May45 6June50 7July43 8Aug47 9Sept56 Compute a 2-month moving average Compute a 3-month weighted average using weights of 4,2,1 for the past three months of data Compute an exponential smoothing forecast using = 0.7 Using MAD, what forecast is most accurate?

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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-26 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ PM Computers: Moving Average Solution MAD Exponential smoothing resulted in the lowest MAD.

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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-27 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Exponential Smoothing with Trend Adjustment Simple exponential smoothing - first-order smoothing Trend adjusted smoothing - second- order smoothing Low gives less weight to more recent trends, while high gives higher weight to more recent trends. Simple exponential smoothing fails to respond to trends, so a more complex model is necessary with trend adjustment.

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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-28 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Exponential Smoothing with Trend Adjustment Forecast including trend (FIT t+1 ) = new forecast (F t ) + trend correction(T t ) where T t = (1 - )T t-1 + (F t – F t-1 ) T i = smoothed trend for period 1 T i-1 = smoothed trend for the preceding period = trend smoothing constant F t = simple exponential smoothed forecast for period t F t-1 = forecast for period t-1

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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-29 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Trend Projection Trend projections are used to forecast time-series data that exhibit a linear trend. Least squares may be used to determine a trend projection for future forecasts. Least squares determines the trend line forecast by minimizing the mean squared error between the trend line forecasts and the actual observed values. The independent variable is the time period and the dependent variable is the actual observed value in the time series.

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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-30 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Trend Projection (continued) The formula for the trend projection is: Y = b + b X where: Y = predicted value b1 = slope of the trend line b0 = intercept X = time period (1,2,3…n) 0 1

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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-31 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Midwestern Manufacturing Trend Projection Example Midwestern Manufacturing Company’s demand for electrical generators over the period of 1996 – 2000 is given below. YearTimeSales

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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-32 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Midwestern Manufacturing Company Trend Solution Sales = (time)

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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-33 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Midwestern Manufacturing’s Trend Forecast points Trend Line Actual demand line

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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-34 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Seasonal Variations Seasonal indices can be used to make adjustments in the forecast for seasonality. A seasonal index indicates how a particular season compares with an average season. The seasonal index can be found by dividing the average value for a particular season by the average of all the data.

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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-35 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Eichler Supplies: Seasonal Index Example MonthSales Demand Average Two-Year Demand Average Monthly Demand Seasonal Index Year 1 Year Jan Feb Mar Apr May … …………… Total Average Demand 1,128 Seasonal Index: = Average 2 -year demand/Average monthly demand

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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-36 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Seasonal Variations with Trend Steps of Multiplicative Time-Series Model 1. Compute the CMA for each observation. 2.Compute seasonal ratio (observation/CMA). 3. Average seasonal ratios to get seasonal indices. 4. If seasonal indices do not add to the number of seasons, multiply each index by (number of seasons)/(sum of the indices). Centered Moving Average (CMA) is an approach that prevents a variation due to trend from being incorrectly interpreted as a variation due to the season.

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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-37 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Turner IndustriesSeasonal Variations with Trend Turner Industries Seasonal Variations with Trend Turner Industries’ sales figures are shown below with the CMA and seasonal ratio. CMA (qtr 3 / yr 1 ) =.5(108) (116) 4 Seasonal Ratio = Sales Qtr 3 = 150 CMA 132

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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-38 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Decomposition Method with Trend and Seasonal Components Decomposition is the process of isolating linear trend and seasonal factors to develop more accurate forecasts. There are five steps to decomposition: 1. Compute the seasonal index for each season. 2. Deseasonalize the data by dividing each number by its seasonal index. 3. Compute a trend line with the deseasonalized data. 4. Use the trend line to forecast. 5. Multiply the forecasts by the seasonal index.

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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-39 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Turner Industries: Decomposition Method Turner Industries has noticed a trend in quarterly sales figures. There is also a seasonal component. Below is the seasonal index and deseasonalized sales data. * This value is derived by averaging the season rations for each quarter. Refer to slide Seasonal Index for Qtr 1 = = =

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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-40 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Turner Industries: Decomposition Method Using the deseasonalized data, the following trend line was computed: Sales = X

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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-41 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Turner Industries: Decomposition Method Using the trend line, the following forecast was computed: Sales = X For period 13 (quarter 1/ year 4): Sales = (13) = (before seasonality adjustment) After seasonality adjustment: Sales = (0.85) = Seasonal index for quarter 1

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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-42 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Multiple Regression with Trend and Seasonal Components Multiple regression can be used to develop an additive decomposition model. One independent variable is time. Seasons are represented by dummy independent variables. Y = a + b X + b X + b X + b X Where X = time period X = 1 if quarter 2 = 0 otherwise X = 1 if quarter 3 = 0 otherwise X = 1 if quarter 4 = 0 otherwise

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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-43 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Monitoring and Controlling Forecasts Tracking signals measure how well predictions fit actual data.

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To accompany Quantitative Analysis for Management, 9e by Render/Stair/Hanna 5-44 © 2006 by Prentice Hall, Inc. Upper Saddle River, NJ Monitoring and Controlling Forecasts

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