《物流系统分析与优化》课程教学课件（PPT讲稿）Data-based Forecasting

ForecastingForecastingQuantitativeQualitativeCausal ModelExpertJudgmentTrendDelphi MethodTime seriesGrassrootsStationaryTrendTrend+Seasonality

Forecasting Forecasting Quantitative Qualitative Causal Model Time series Expert Judgment Trend Stationary Trend Trend + Seasonality Delphi Method Grassroots 1

Quantitative ForecastingCasualModels:PriceCausalYear 2000PopulationModelSalesAdvertisingTime Series Models:SaleS1999Time SeriesYear 2000SaleS1998SalesModelSaleS19972

Quantitative Forecasting • Casual Models: 2 Causal Model Year 2000 Sales Price Population Advertising . • Time Series Models: Time Series Model Year 2000 Sales Sales1999 Sales1998 Sales . 1997

Causal forecasting·Regression>Find a straight line that fits the data best.Best line!12108620InterceptInterce1011121314151617181920>Slope=changeiny/ changeinx3

Causal forecasting • Regression ➢Find a straight line that fits the data best. ➢y = Intercept + slope * x (= b0 + b1 x) ➢Slope = change in y / change in x 0 2 4 6 8 10 12 10 11 12 13 14 15 16 17 18 19 20 3 Best line! Intercept

Causal Forecasting Models? Curve Fitting: Simple Linear Regression: One Independent Variable (X)is used to predict oneDependent Variable (Y): Y= a + b X: Given n observations (Xi, Y), we can fit a line to the overallpattern of these data points. The Least Squares Method instatisticscan give us the best a and b in the sense ofminimizing Z(Y;- a - bx,)2:XOXEx?ZXYib=nnZxiZYiannRegression formula is an optional learning objective4

Causal Forecasting Models • Curve Fitting: Simple Linear Regression • One Independent Variable (X) is used to predict one Dependent Variable (Y): Y = a + b X • Given n observations (Xi , Yi ), we can fit a line to the overall pattern of these data points. The Least Squares Method in statistics can give us the best a and b in the sense of minimizing (Yi - a - bXi ) 2 : 4 n X b n Y a n X X n X Y b X Y i i i i i i i i        = −         −         = − 2 2 ( ) / Regression formula is an optional learning objective

· Curve Fitting: Simple Linear Regression? Find the regression line with Excel.UseFunction:a= INTERCEPT(Yrange; Xrange)b = SLOPE(Yrange; X range)·UseSolver·Use Excel's ToolsIData Analysis I Regression? Curve Fitting: Multiple Regression. Two or more independent variables are used to predictthe dependent variable:Y= bo + biX1 + b2X2 + ... + b,X,· Use Excel's Tools I Data Analysis I Regression5

• Curve Fitting: Simple Linear Regression • Find the regression line with Excel • Use Function: a = INTERCEPT(Y range; X range) b = SLOPE(Y range; X range) • Use Solver • Use Excel’s Tools | Data Analysis | Regression • Curve Fitting: Multiple Regression • Two or more independent variables are used to predict the dependent variable: Y = b0 + b1X1 + b2X2 + . + bpXp • Use Excel’s Tools | Data Analysis | Regression 5

Time Series Forecasting ProcessLook at the dataForecast using one orEvaluatethe technique(Scatter Plot)more techniquesandpickthebestoneObservations fromtheWays to evaluateTechniques to tryscatterPlot·MADHeuristics-Averaging methodsData is reasonably·MAPE.Naivestationary·Moving Averages·StandardError(notrendorseasonality)·BIAS·SimpleExponential Smoothing·MADRegression·MAPEData shows a consistent?Linear·StandardErrortrend·Non-linear Regressions (not·BIAScoveredinthis course).R-Squared·MADClassical decomposition·MAPEData shows both a trend and·Find SeasonalIndex·Standard Error.Use regression analyses to finda seasonalpattern·BIASthe trend component.R-Squared6

Time Series Forecasting Process Observations from the scatter Plot Techniques to try Ways to evaluate Data is reasonably stationary (no trend or seasonality) Heuristics - Averaging methods • Naive • Moving Averages • Simple Exponential Smoothing • MAD • MAPE • Standard Error • BIAS Data shows a consistent trend Regression • Linear • Non-linear Regressions (not covered in this course) • MAD • MAPE • Standard Error • BIAS • R-Squared Data shows both a trend and a seasonal pattern Classical decomposition • Find Seasonal Index • Use regression analyses to find the trend component • MAD • MAPE • Standard Error • BIAS • R-Squared 6 Look at the data (Scatter Plot) Forecast using one or more techniques Evaluate the technique and pick the best one

Evaluation of Forecasting ModelBIAS-Thearithmeticaverageof theerrorsBIAS_Z(Actual-Forecast)_Errornn.n is the number of forecast errors.Excel:=AVERAGE(errorrange)MeanAbsoluteDeviation-MADMAD_Z/Actual-Forecast_[Error]nn.NodirectExcelfunctionto calculateMAD

Evaluation of Forecasting Model • BIAS - The arithmetic average of the errors • n is the number of forecast errors • Excel: =AVERAGE(error range) • Mean Absolute Deviation - MAD • No direct Excel function to calculate MAD 7 n Error n (Actual - Forecast) BIAS =  =  n |Error | n | Actual - Forecast MAD =  | = 

Evaluation of Forecasting Model? Mean Square Error - MSEMSE_Z(Actual-Forecast)"_Z(Error)?nnExcel:=SUMSQ(errorrange)/COUNT(errorrange).StandarderrorissguarerootofMSE·Mean Absolute Percentage Error-MAPE≥/Actual:Forecastl-100%ActualMAPE:n·R2 - onlyfor curve fitting model such as regression·In general, the lower the error measure (BIAS, MAD, MSE) orthe higher the R2, the better the forecasting model8

Evaluation of Forecasting Model • Mean Square Error - MSE • Excel: =SUMSQ(error range)/COUNT(error range) • Standard error is square root of MSE • Mean Absolute Percentage Error - MAPE • R2 - only for curve fitting model such as regression • In general, the lower the error measure (BIAS, MAD, MSE) or the higher the R2 , the better the forecasting model 8 n (Error) n (Actual - Forecast) MSE 2 2 =  =  n Actual | Actual - Forecast | MAPE  = *100%

Stationary data forecasting.Naive>/ sold 10 units yesterday so I think / will sell 10 unitstoday.·n-periodmovingaverage>For the past n days, I sold 12 units on average. Therefore,I think /'will sell 12 units today·Exponential smoothing>l predicted to sell 10units at thebeginningof yesterdayAt the end of yesterday,Ifound out / sold in fact 8 units.So,/willadjusttheforecastof1o(yesterday'sforecast)by adding adjusted error(α*error).This willcompensateover (under)forecastofyesterday9

Stationary data forecasting • Naïve ➢I sold 10 units yesterday, so I think I will sell 10 units today. • n-period moving average ➢For the past n days, I sold 12 units on average. Therefore, I think I will sell 12 units today. • Exponential smoothing ➢I predicted to sell 10 units at the beginning of yesterday; At the end of yesterday, I found out I sold in fact 8 units. So, I will adjust the forecast of 10 (yesterday’s forecast) by adding adjusted error (α * error). This will compensate over (under) forecast of yesterday. 9

Naive Model: The simplest time series forecasting model: Idea: "what happened last time (last year, lastmonth, yesterday) will happen again this time"NaiveModel:. Algebraic: F, =Yt-1.Yt- : actual value in period t-1Ft :forecast for periodtSpreadsheet:B3:=A2;Copydown10

Naïve Model • The simplest time series forecasting model • Idea: “what happened last time (last year, last month, yesterday) will happen again this time” • Naïve Model: • Algebraic: Ft = Yt-1 • Yt-1 : actual value in period t-1 • Ft : forecast for period t • Spreadsheet: B3: = A2; Copy down 10