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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 07458 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 07458 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 07458 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 07458 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 07458 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 07458 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 07458 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 07458 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 07458 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 07458 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 JAN250243 FEB320315 MAR275286 APR260256 MAY250241 JUN275298 JUL300292 AUG325333 SEP320326 OCT350378 NOV365382 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 07458 Hospital Days – Forecast Error Example ForecastActual|error|error^2|error/actual| JAN250243 7490.03 FEB320315 5250.02 MAR275286 111210.04 APR260256 4160.02 MAY250241 9810.04 JUN275298 235290.08 JUL300292 8640.03 AUG325333 8640.02 SEP320326 6360.02 OCT350378 287840.07 NOV365382 172890.04 DEC380396 162560.04 AVERAGE 11.83192.833.68 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 07458 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 07458 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 07458 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 07458 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 07458 Wallace Garden Supply’s Three-Month Moving Average MonthActual Shed Sales Three-Month Moving Average January10 February12 March13 April16 May19 June23 July26 (10+12+13)/3 = 11 2 / 3 (12+13+16)/3 = 13 2 / 3 (13+16+19)/3 = 16 (16+19+23)/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 07458 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 07458 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 07458 Wallace Garden’s Weighted Three-Month Moving Average MonthActual Shed Sales Three-Month Weighted Moving Average 10 12 13 16 19 23 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 07458 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 07458 Port of Baltimore Exponential Smoothing Example QtrActual Tonnage Unloaded Rounded Forecast using =0.10 1180175 2168176= 175.00+0.10(180-175) 3159175 =175.50+0.10(168-175.50) 4175173 =174.75+0.10(159-174.75) 5190173 =173.18+0.10(175-173.18) 6205175 =173.36+0.10(190-173.36) 7180178 =175.02+0.10(205-175.02) 8182178 =178.02+0.10(180-178.02) 9? 179= 178.22+0.10(182-178.22)

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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 07458 Port of Baltimore Exponential Smoothing Example QtrActual Tonnage Unloaded Rounded Forecast using =0.50 1180175 2168178 =175.00+0.50(180-175) 3159173 =177.50+0.50(168-177.50) 4175166 =172.75+0.50(159-172.75) 5190170 =165.88+0.50(175-165.88) 6205180 =170.44+0.50(190-170.44) 7180193 =180.22+0.50(205-180.22) 8182186 =192.61+0.50(180-192.61) 9? 184 =186.30+0.50(182-186.30)

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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 07458 Selecting a Smoothing Constant Actual Forecast with a = 0.10 Absolute Deviations Forecast with a = 0.50 Absolute Deviations 1801755 5 168176817810 1591751617314 17517321669 1901731717020 2051753018025 180178219313 18217841864 MAD10.012 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 07458 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 07458 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 07458 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 07458 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 07458 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 07458 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 07458 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 07458 Midwestern Manufacturing Trend Projection Example Midwestern Manufacturing Company’s demand for electrical generators over the period of 1996 – 2000 is given below. YearTimeSales 1996174 1997279 1998380 1999490 20005105 20016142 20027122

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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 07458 Midwestern Manufacturing Company Trend Solution Sales = 56.71 + 10.54 (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 07458 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 07458 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 07458 Eichler Supplies: Seasonal Index Example MonthSales Demand Average Two-Year Demand Average Monthly Demand Seasonal Index Year 1 Year 2 80100 90940.957 758580940.851 809085940.904 90110100941.064 Jan Feb Mar Apr May115131123941.309 … …………… 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 07458 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 07458 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) + 125 + 150 + 141+.5(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 07458 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 07458 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 5-37. Seasonal Index for Qtr 1 = 0.851+0.848 = 0.85 2 108 0.85 =

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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 07458 Turner Industries: Decomposition Method Using the deseasonalized data, the following trend line was computed: Sales = 124.78 + 2.34X

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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 07458 Turner Industries: Decomposition Method Using the trend line, the following forecast was computed: Sales = 124.78 + 2.34X For period 13 (quarter 1/ year 4): Sales = 124.78 + 2.34 (13) = 155.2 (before seasonality adjustment) After seasonality adjustment: Sales = 155.2 (0.85) = 131.92 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 07458 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 1 1 2 2 3 3 4 4 12341234

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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 07458 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 07458 Monitoring and Controlling Forecasts

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