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    360_ch04 360_ch04 Presentation Transcript

    • © 2011 Pearson4 - 14 ForecastingPowerPoint presentation to accompanyPowerPoint presentation to accompanyHeizer and RenderHeizer and RenderOperations Management, 10eOperations Management, 10ePrinciples of Operations Management, 8ePrinciples of Operations Management, 8ePowerPoint slides by Jeff Heyl
    • © 2011 Pearson4 - 2OutlineOutline Global Company Profile: DisneyWorld What Is Forecasting? Forecasting Time Horizons The Influence of Product Life Cycle Types Of Forecasts
    • © 2011 Pearson4 - 3Outline – ContinuedOutline – Continued The Strategic Importance ofForecasting Human Resources Capacity Supply Chain Management Seven Steps in the ForecastingSystem
    • © 2011 Pearson4 - 4Outline – ContinuedOutline – Continued Forecasting Approaches Overview of Qualitative Methods Overview of Quantitative Methods Time-Series Forecasting Decomposition of a Time Series Naive Approach
    • © 2011 Pearson4 - 5Outline – ContinuedOutline – Continued Time-Series Forecasting (cont.) Moving Averages Exponential Smoothing Exponential Smoothing with TrendAdjustment Trend Projections Seasonal Variations in Data Cyclical Variations in Data
    • © 2011 Pearson4 - 6Outline – ContinuedOutline – Continued Associative Forecasting Methods:Regression and CorrelationAnalysis Using Regression Analysis forForecasting Standard Error of the Estimate Correlation Coefficients forRegression Lines Multiple-Regression Analysis
    • © 2011 Pearson4 - 7Outline – ContinuedOutline – Continued Monitoring and ControllingForecasts Adaptive Smoothing Focus Forecasting Forecasting in the Service Sector
    • © 2011 Pearson4 - 8Learning ObjectivesLearning ObjectivesWhen you complete this chapter youWhen you complete this chapter youshould be able to :should be able to :1. Understand the three time horizonsand which models apply for each use2. Explain when to use each of the fourqualitative models3. Apply the naive, moving average,exponential smoothing, and trendmethods
    • © 2011 Pearson4 - 9Learning ObjectivesLearning ObjectivesWhen you complete this chapter youWhen you complete this chapter youshould be able to :should be able to :4. Compute three measures of forecastaccuracy5. Develop seasonal indexes6. Conduct a regression and correlationanalysis7. Use a tracking signal
    • © 2011 Pearson4 - 10Forecasting at Disney WorldForecasting at Disney World Global portfolio includes parks in HongKong, Paris, Tokyo, Orlando, andAnaheim Revenues are derived from people – howmany visitors and how they spend theirmoney Daily management report contains onlythe forecast and actual attendance ateach park
    • © 2011 Pearson4 - 11Forecasting at Disney WorldForecasting at Disney World Disney generates daily, weekly, monthly,annual, and 5-year forecasts Forecast used by labor management,maintenance, operations, finance, andpark scheduling Forecast used to adjust opening times,rides, shows, staffing levels, and guestsadmitted
    • © 2011 Pearson4 - 12Forecasting at Disney WorldForecasting at Disney World 20% of customers come from outside theUSA Economic model includes grossdomestic product, cross-exchange rates,arrivals into the USA A staff of 35 analysts and 70 field peoplesurvey 1 million park guests, employees,and travel professionals each year
    • © 2011 Pearson4 - 13Forecasting at Disney WorldForecasting at Disney World Inputs to the forecasting model includeairline specials, Federal Reservepolicies, Wall Street trends,vacation/holiday schedules for 3,000school districts around the world Average forecast error for the 5-yearforecast is 5% Average forecast error for annualforecasts is between 0% and 3%
    • © 2011 Pearson4 - 14What is Forecasting?What is Forecasting? Process of predictinga future event Underlying basisof all businessdecisions Production Inventory Personnel Facilities??
    • © 2011 Pearson4 - 15 Short-range forecast Up to 1 year, generally less than 3 months Purchasing, job scheduling, workforcelevels, job assignments, production levels Medium-range forecast 3 months to 3 years Sales and production planning, budgeting Long-range forecast 3+years New product planning, facility location,research and developmentForecasting Time HorizonsForecasting Time Horizons
    • © 2011 Pearson4 - 16Distinguishing DifferencesDistinguishing Differences Medium/long rangeMedium/long range forecasts deal withmore comprehensive issues and supportmanagement decisions regardingplanning and products, plants andprocesses Short-termShort-term forecasting usually employsdifferent methodologies than longer-termforecasting Short-termShort-term forecasts tend to be moreaccurate than longer-term forecasts
    • © 2011 Pearson4 - 17Influence of Product LifeInfluence of Product LifeCycleCycle Introduction and growth require longerforecasts than maturity and decline As product passes through life cycle,forecasts are useful in projecting Staffing levels Inventory levels Factory capacityIntroduction – Growth – Maturity – DeclineIntroduction – Growth – Maturity – Decline
    • © 2011 Pearson4 - 18Product Life CycleProduct Life CycleBest period toincrease marketshareR&D engineering iscriticalPractical to changeprice or qualityimageStrengthen nichePoor time tochange image,price, or qualityCompetitive costsbecome criticalDefend marketpositionCost controlcriticalIntroduction Growth Maturity DeclineCompanyStrategy/IssuesFigure 2.5Internet search enginesSalesDrive-throughrestaurantsCD-ROMsAnalogTVsiPodsBoeing 787LCD &plasma TVsTwitterAvatarsXbox 360
    • © 2011 Pearson4 - 19Product Life CycleProduct Life CycleProduct designand developmentcriticalFrequentproduct andprocess designchangesShort productionrunsHigh productioncostsLimited modelsAttention toqualityIntroduction Growth Maturity DeclineOMStrategy/IssuesForecastingcriticalProduct andprocessreliabilityCompetitiveproductimprovementsand optionsIncrease capacityShift towardproduct focusEnhancedistributionStandardizationFewer productchanges, moreminor changesOptimumcapacityIncreasingstability ofprocessLong productionrunsProductimprovement andcost cuttingLittle productdifferentiationCostminimizationOvercapacityin theindustryPrune line toeliminateitems notreturninggood marginReducecapacityFigure 2.5
    • © 2011 Pearson4 - 20Types of ForecastsTypes of Forecasts Economic forecasts Address business cycle – inflation rate,money supply, housing starts, etc. Technological forecasts Predict rate of technological progress Impacts development of new products Demand forecasts Predict sales of existing products andservices
    • © 2011 Pearson4 - 21Strategic Importance ofStrategic Importance ofForecastingForecasting Human Resources – Hiring, training,laying off workers Capacity – Capacity shortages canresult in undependable delivery, lossof customers, loss of market share Supply Chain Management – Goodsupplier relations and priceadvantages
    • © 2011 Pearson4 - 22Seven Steps in ForecastingSeven Steps in Forecasting1. Determine the use of the forecast2. Select the items to be forecasted3. Determine the time horizon of theforecast4. Select the forecasting model(s)5. Gather the data6. Make the forecast7. Validate and implement results
    • © 2011 Pearson4 - 23The Realities!The Realities! Forecasts are seldom perfect Most techniques assume anunderlying stability in the system Product family and aggregatedforecasts are more accurate thanindividual product forecasts
    • © 2011 Pearson4 - 24Forecasting ApproachesForecasting Approaches Used when situation is vague andlittle data exist New products New technology Involves intuition, experience e.g., forecasting sales on InternetQualitative MethodsQualitative Methods
    • © 2011 Pearson4 - 25Forecasting ApproachesForecasting Approaches Used when situation is ‘stable’ andhistorical data exist Existing products Current technology Involves mathematical techniques e.g., forecasting sales of colortelevisionsQuantitative MethodsQuantitative Methods
    • © 2011 Pearson4 - 26Overview of QualitativeOverview of QualitativeMethodsMethods1. Jury of executive opinion Pool opinions of high-level experts,sometimes augment by statisticalmodels2. Delphi method Panel of experts, queried iteratively
    • © 2011 Pearson4 - 27Overview of QualitativeOverview of QualitativeMethodsMethods3. Sales force composite Estimates from individualsalespersons are reviewed forreasonableness, then aggregated4. Consumer Market Survey Ask the customer
    • © 2011 Pearson4 - 28 Involves small group of high-levelexperts and managers Group estimates demand by workingtogether Combines managerial experience withstatistical models Relatively quick ‘Group-think’disadvantageJury of Executive OpinionJury of Executive Opinion
    • © 2011 Pearson4 - 29Sales Force CompositeSales Force Composite Each salesperson projects his orher sales Combined at district and nationallevels Sales reps know customers’ wants Tends to be overly optimistic
    • © 2011 Pearson4 - 30Delphi MethodDelphi Method Iterative groupprocess,continues untilconsensus isreached 3 types ofparticipants Decision makers Staff RespondentsStaff(Administeringsurvey)Decision Makers(Evaluateresponses andmake decisions)Respondents(People who canmake valuablejudgments)
    • © 2011 Pearson4 - 31Consumer Market SurveyConsumer Market Survey Ask customers about purchasingplans What consumers say, and whatthey actually do are often different Sometimes difficult to answer
    • © 2011 Pearson4 - 32Overview of QuantitativeOverview of QuantitativeApproachesApproaches1. Naive approach2. Moving averages3. Exponentialsmoothing4. Trend projection5. Linear regressiontime-seriesmodelsassociativemodel
    • © 2011 Pearson4 - 33 Set of evenly spaced numericaldata Obtained by observing responsevariable at regular time periods Forecast based only on pastvalues, no other variablesimportant Assumes that factors influencingpast and present will continueinfluence in futureTime Series ForecastingTime Series Forecasting
    • © 2011 Pearson4 - 34TrendSeasonalCyclicalRandomTime Series ComponentsTime Series Components
    • © 2011 Pearson4 - 35Components of DemandComponents of DemandDemandforproductorservice| | | |1 2 3 4Time (years)Average demandover 4 yearsTrendcomponentActual demandlineRandom variationFigure 4.1Seasonal peaks
    • © 2011 Pearson4 - 36 Persistent, overall upward ordownward pattern Changes due to population,technology, age, culture, etc. Typically several yearsdurationTrend ComponentTrend Component
    • © 2011 Pearson4 - 37 Regular pattern of up anddown fluctuations Due to weather, customs, etc. Occurs within a single yearSeasonal ComponentSeasonal ComponentNumber ofPeriod Length SeasonsWeek Day 7Month Week 4-4.5Month Day 28-31Year Quarter 4Year Month 12Year Week 52
    • © 2011 Pearson4 - 38 Repeating up and down movements Affected by business cycle,political, and economic factors Multiple years duration Often causal orassociativerelationshipsCyclical ComponentCyclical Component0 5 10 15 20
    • © 2011 Pearson4 - 39 Erratic, unsystematic, ‘residual’fluctuations Due to random variation or unforeseenevents Short durationand nonrepeatingRandom ComponentRandom ComponentM T W T F
    • © 2011 Pearson4 - 40Naive ApproachNaive Approach Assumes demand in nextperiod is the same asdemand in most recent period e.g., If January sales were 68, thenFebruary sales will be 68 Sometimes cost effective andefficient Can be good starting point
    • © 2011 Pearson4 - 41 MA is a series of arithmetic means Used if little or no trend Used often for smoothing Provides overall impression of dataover timeMoving Average MethodMoving Average MethodMoving average =∑ demand in previous n periodsn
    • © 2011 Pearson4 - 42January 10February 12March 13April 16May 19June 23July 26Actual 3-MonthMonth Shed Sales Moving Average(12 + 13 + 16)/3 = 13 2/3(13 + 16 + 19)/3 = 16(16 + 19 + 23)/3 = 19 1/3Moving Average ExampleMoving Average Example101012121313(1010 + 1212 + 1313)/3 = 11 2/3
    • © 2011 Pearson4 - 43Graph of Moving AverageGraph of Moving Average| | | | | | | | | | | |J F M A M J J A S O N DShedSales30 –28 –26 –24 –22 –20 –18 –16 –14 –12 –10 –ActualSalesMovingAverageForecast
    • © 2011 Pearson4 - 44 Used when some trend might bepresent Older data usually less important Weights based on experience andintuitionWeighted Moving AverageWeighted Moving AverageWeightedmoving average =∑ (weight for period n)x (demand in period n)∑ weights
    • © 2011 Pearson4 - 45January 10February 12March 13April 16May 19June 23July 26Actual 3-Month WeightedMonth Shed Sales Moving Average[(3 x 16) + (2 x 13) + (12)]/6 = 141/3[(3 x 19) + (2 x 16) + (13)]/6 = 17[(3 x 23) + (2 x 19) + (16)]/6 = 201/2Weighted Moving AverageWeighted Moving Average101012121313[(3 x 1313) + (2 x 1212) + (1010)]/6 = 121/6Weights Applied Period33 Last month22 Two months ago11 Three months ago6 Sum of weights
    • © 2011 Pearson4 - 46 Increasing n smooths the forecastbut makes it less sensitive tochanges Do not forecast trends well Require extensive historical dataPotential Problems WithPotential Problems WithMoving AverageMoving Average
    • © 2011 Pearson4 - 47Moving Average AndMoving Average AndWeighted Moving AverageWeighted Moving Average30 –25 –20 –15 –10 –5 –Salesdemand| | | | | | | | | | | |J F M A M J J A S O N DActualsalesMovingaverageWeightedmovingaverageFigure 4.2
    • © 2011 Pearson4 - 48 Form of weighted moving average Weights decline exponentially Most recent data weighted most Requires smoothing constant (α) Ranges from 0 to 1 Subjectively chosen Involves little record keeping ofpast dataExponential SmoothingExponential Smoothing
    • © 2011 Pearson4 - 49Exponential SmoothingExponential Smoothingt = Last period’s forecast+ α (Last period’s actual demand– Last period’s forecast)Ft = Ft – 1 + α(At – 1 - Ft – 1)where Ft = new forecastFt – 1 = previous forecastα = smoothing (or weighting)constant (0 ≤ α ≤ 1)
    • © 2011 Pearson4 - 50Exponential SmoothingExponential SmoothingExampleExamplePredicted demand = 142 Ford MustangsActual demand = 153Smoothing constant α = .20
    • © 2011 Pearson4 - 51Exponential SmoothingExponential SmoothingExampleExamplePredicted demand = 142 Ford MustangsActual demand = 153Smoothing constant α = .20New forecast = 142 + .2(153 – 142)
    • © 2011 Pearson4 - 52Exponential SmoothingExponential SmoothingExampleExamplePredicted demand = 142 Ford MustangsActual demand = 153Smoothing constant α = .20New forecast = 142 + .2(153 – 142)= 142 + 2.2= 144.2 ≈ 144 cars
    • © 2011 Pearson4 - 53Effect ofEffect ofSmoothing ConstantsSmoothing ConstantsWeight Assigned toMost 2nd Most 3rd Most 4th Most 5th MostRecent Recent Recent Recent RecentSmoothing Period Period Period Period PeriodConstant (α) α(1 - α) α(1 - α)2α(1 - α)3α(1 - α)4α = .1 .1 .09 .081 .073 .066α = .5 .5 .25 .125 .063 .031
    • © 2011 Pearson4 - 54Impact of DifferentImpact of Different αα225 –200 –175 –150 –| | | | | | | | |1 2 3 4 5 6 7 8 9QuarterDemandα = .1Actualdemandα = .5
    • © 2011 Pearson4 - 55Impact of DifferentImpact of Different αα225 –200 –175 –150 –| | | | | | | | |1 2 3 4 5 6 7 8 9QuarterDemandα = .1Actualdemandα = .5 Chose high values of αwhen underlying averageis likely to change Choose low values of αwhen underlying averageis stable
    • © 2011 Pearson4 - 56ChoosingChoosing ααThe objective is to obtain the mostaccurate forecast no matter thetechniqueWe generally do this by selecting theWe generally do this by selecting themodel that gives us the lowest forecastmodel that gives us the lowest forecasterrorerrorForecast error = Actual demand - Forecast value= At - Ft
    • © 2011 Pearson4 - 57Common Measures of ErrorCommon Measures of ErrorMean Absolute Deviation (MAD)MAD =∑ |Actual - Forecast|nMean Squared Error (MSE)MSE =∑ (Forecast Errors)2n
    • © 2011 Pearson4 - 58Common Measures of ErrorCommon Measures of ErrorMean Absolute Percent Error (MAPE)MAPE =∑100|Actuali - Forecasti|/Actualinni = 1
    • © 2011 Pearson4 - 59Comparison of ForecastComparison of ForecastErrorErrorRounded Absolute Rounded AbsoluteActual Forecast Deviation Forecast DeviationTonnage with for with forQuarter Unloaded α = .10 α = .10 α = .50 α = .501 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.503 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.3082.45 98.62
    • © 2011 Pearson4 - 60Comparison of ForecastComparison of ForecastErrorErrorRounded Absolute Rounded AbsoluteActual Forecast Deviation Forecast DeviationTonnage with for with forQuarter Unloaded α = .10 α = .10 α = .50 α = .501 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.503 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.3082.45 98.62MAD =∑ |deviations|n= 82.45/8 = 10.31For α = .10= 98.62/8 = 12.33For α = .50
    • © 2011 Pearson4 - 61Comparison of ForecastComparison of ForecastErrorErrorRounded Absolute Rounded AbsoluteActual Forecast Deviation Forecast DeviationTonnage with for with forQuarter Unloaded α = .10 α = .10 α = .50 α = .501 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.503 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.3082.45 98.62MAD 10.31 12.33= 1,526.54/8 = 190.82For α = .10= 1,561.91/8 = 195.24For α = .50MSE =∑ (forecast errors)2n
    • © 2011 Pearson4 - 62Comparison of ForecastComparison of ForecastErrorErrorRounded Absolute Rounded AbsoluteActual Forecast Deviation Forecast DeviationTonnage with for with forQuarter Unloaded α = .10 α = .10 α = .50 α = .501 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.503 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.3082.45 98.62MAD 10.31 12.33MSE 190.82 195.24= 44.75/8 = 5.59%For α = .10= 54.05/8 = 6.76%For α = .50MAPE =∑100|deviationi|/actualinni = 1
    • © 2011 Pearson4 - 63Comparison of ForecastComparison of ForecastErrorErrorRounded Absolute Rounded AbsoluteActual Forecast Deviation Forecast DeviationTonnage with for with forQuarter Unloaded α = .10 α = .10 α = .50 α = .501 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.503 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.3082.45 98.62MAD 10.31 12.33MSE 190.82 195.24MAPE 5.59% 6.76%
    • © 2011 Pearson4 - 64Exponential Smoothing withExponential Smoothing withTrend AdjustmentTrend AdjustmentWhen a trend is present, exponentialsmoothing must be modifiedForecastincluding (FITt) =trendExponentially Exponentiallysmoothed (Ft) + smoothed (Tt)forecast trend
    • © 2011 Pearson4 - 65Exponential Smoothing withExponential Smoothing withTrend AdjustmentTrend AdjustmentFt = α(At - 1) + (1 - α)(Ft - 1 + Tt - 1)Tt = β(Ft - Ft - 1) + (1 - β)Tt - 1Step 1: Compute FtStep 2: Compute TtStep 3: Calculate the forecast FITt = Ft + Tt
    • © 2011 Pearson4 - 66Exponential Smoothing withExponential Smoothing withTrend Adjustment ExampleTrend Adjustment ExampleForecastActual Smoothed Smoothed IncludingMonth(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt1 12 11 2 13.002 173 204 195 246 217 318 289 3610Table 4.1
    • © 2011 Pearson4 - 67Exponential Smoothing withExponential Smoothing withTrend Adjustment ExampleTrend Adjustment ExampleForecastActual Smoothed Smoothed IncludingMonth(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt1 12 11 2 13.002 173 204 195 246 217 318 289 3610Table 4.1F2 = αA1 + (1 - α)(F1 + T1)F2 = (.2)(12) + (1 - .2)(11 + 2)= 2.4 + 10.4 = 12.8 unitsStep 1: Forecast for Month 2
    • © 2011 Pearson4 - 68Exponential Smoothing withExponential Smoothing withTrend Adjustment ExampleTrend Adjustment ExampleForecastActual Smoothed Smoothed IncludingMonth(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt1 12 11 2 13.002 17 12.803 204 195 246 217 318 289 3610Table 4.1T2 = β(F2 - F1) + (1 - β)T1T2 = (.4)(12.8 - 11) + (1 - .4)(2)= .72 + 1.2 = 1.92 unitsStep 2: Trend for Month 2
    • © 2011 Pearson4 - 69Exponential Smoothing withExponential Smoothing withTrend Adjustment ExampleTrend Adjustment ExampleForecastActual Smoothed Smoothed IncludingMonth(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt1 12 11 2 13.002 17 12.80 1.923 204 195 246 217 318 289 3610Table 4.1FIT2 = F2 + T2FIT2 = 12.8 + 1.92= 14.72 unitsStep 3: Calculate FIT for Month 2
    • © 2011 Pearson4 - 70Exponential Smoothing withExponential Smoothing withTrend Adjustment ExampleTrend Adjustment ExampleForecastActual Smoothed Smoothed IncludingMonth(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt1 12 11 2 13.002 17 12.80 1.92 14.723 204 195 246 217 318 289 3610Table 4.115.18 2.10 17.2817.82 2.32 20.1419.91 2.23 22.1422.51 2.38 24.8924.11 2.07 26.1827.14 2.45 29.5929.28 2.32 31.6032.48 2.68 35.16
    • © 2011 Pearson4 - 71Exponential Smoothing withExponential Smoothing withTrend Adjustment ExampleTrend Adjustment ExampleFigure 4.3| | | | | | | | |1 2 3 4 5 6 7 8 9Time (month)Productdemand35 –30 –25 –20 –15 –10 –5 –0 –Actual demand (At)Forecast including trend (FITt)with α = .2 and β = .4
    • © 2011 Pearson4 - 72Trend ProjectionsTrend ProjectionsFitting a trend line to historical data pointsto project into the medium to long-rangeLinear trends can be found using the leastsquares techniquey = a + bx^where y = computed value ofthe variable to be predicted(dependent variable)a = y-axis interceptb = slope of the regression linex = the independent variable^
    • © 2011 Pearson4 - 73Least Squares MethodLeast Squares MethodTime periodValuesofDependentVariableFigure 4.4Deviation1(error)Deviation5Deviation7Deviation2Deviation6Deviation4Deviation3Actual observation(y-value)Trend line, y = a + bx^
    • © 2011 Pearson4 - 74Least Squares MethodLeast Squares MethodTime periodValuesofDependentVariableFigure 4.4Deviation1(error)Deviation5Deviation7Deviation2Deviation6Deviation4Deviation3Actual observation(y-value)Trend line, y = a + bx^Least squares methodminimizes the sum of thesquared errors (deviations)
    • © 2011 Pearson4 - 75Least Squares MethodLeast Squares MethodEquations to calculate the regression variablesb =Σxy - nxyΣx2- nx2y = a + bx^a = y - bx
    • © 2011 Pearson4 - 76Least Squares ExampleLeast Squares Exampleb = = = 10.54∑xy - nxy∑x2- nx23,063 - (7)(4)(98.86)140 - (7)(42)a = y - bx = 98.86 - 10.54(4) = 56.70Time Electrical PowerYear Period (x) Demand x2xy2003 1 74 1 742004 2 79 4 1582005 3 80 9 2402006 4 90 16 3602007 5 105 25 5252008 6 142 36 8522009 7 122 49 854∑x = 28 ∑y = 692 ∑x2= 140 ∑xy = 3,063x = 4 y = 98.86
    • © 2011 Pearson4 - 77b = = = 10.54∑xy - nxy∑x2- nx23,063 - (7)(4)(98.86)140 - (7)(42)a = y - bx = 98.86 - 10.54(4) = 56.70Time Electrical PowerYear Period (x) Demand x2xy2003 1 74 1 742004 2 79 4 1582005 3 80 9 2402006 4 90 16 3602007 5 105 25 5252008 6 142 36 8522009 7 122 49 854∑x = 28 ∑y = 692 ∑x2= 140 ∑xy = 3,063x = 4 y = 98.86Least Squares ExampleLeast Squares ExampleThe trend line isy = 56.70 + 10.54x^
    • © 2011 Pearson4 - 78Least Squares ExampleLeast Squares Example| | | | | | | | |2003 2004 2005 2006 2007 2008 2009 2010 2011160 –150 –140 –130 –120 –110 –100 –90 –80 –70 –60 –50 –YearPowerdemandTrend line,y = 56.70 + 10.54x^
    • © 2011 Pearson4 - 80Seasonal Variations In DataSeasonal Variations In DataThe multiplicativeseasonal modelcan adjust trenddata for seasonalvariations indemand
    • © 2011 Pearson4 - 81Seasonal Variations In DataSeasonal Variations In Data1. Find average historical demand for each season2. Compute the average demand over all seasons3. Compute a seasonal index for each season4. Estimate next year’s total demand5. Divide this estimate of total demand by thenumber of seasons, then multiply it by theseasonal index for that seasonSteps in the process:Steps in the process:
    • © 2011 Pearson4 - 82Seasonal Index ExampleSeasonal Index ExampleJan 80 85 105 90 94Feb 70 85 85 80 94Mar 80 93 82 85 94Apr 90 95 115 100 94May 113 125 131 123 94Jun 110 115 120 115 94Jul 100 102 113 105 94Aug 88 102 110 100 94Sept 85 90 95 90 94Oct 77 78 85 80 94Nov 75 72 83 80 94Dec 82 78 80 80 94Demand Average Average SeasonalMonth 2007 2008 2009 2007-2009 Monthly Index
    • © 2011 Pearson4 - 83Seasonal Index ExampleSeasonal Index ExampleJan 80 85 105 90 94Feb 70 85 85 80 94Mar 80 93 82 85 94Apr 90 95 115 100 94May 113 125 131 123 94Jun 110 115 120 115 94Jul 100 102 113 105 94Aug 88 102 110 100 94Sept 85 90 95 90 94Oct 77 78 85 80 94Nov 75 72 83 80 94Dec 82 78 80 80 94Demand Average Average SeasonalMonth 2007 2008 2009 2007-2009 Monthly Index0.957Seasonal index =Average 2007-2009 monthly demandAverage monthly demand= 90/94 = .957
    • © 2011 Pearson4 - 84Seasonal Index ExampleSeasonal Index ExampleJan 80 85 105 90 94 0.957Feb 70 85 85 80 94 0.851Mar 80 93 82 85 94 0.904Apr 90 95 115 100 94 1.064May 113 125 131 123 94 1.309Jun 110 115 120 115 94 1.223Jul 100 102 113 105 94 1.117Aug 88 102 110 100 94 1.064Sept 85 90 95 90 94 0.957Oct 77 78 85 80 94 0.851Nov 75 72 83 80 94 0.851Dec 82 78 80 80 94 0.851Demand Average Average SeasonalMonth 2007 2008 2009 2007-2009 Monthly Index
    • © 2011 Pearson4 - 85Seasonal Index ExampleSeasonal Index ExampleJan 80 85 105 90 94 0.957Feb 70 85 85 80 94 0.851Mar 80 93 82 85 94 0.904Apr 90 95 115 100 94 1.064May 113 125 131 123 94 1.309Jun 110 115 120 115 94 1.223Jul 100 102 113 105 94 1.117Aug 88 102 110 100 94 1.064Sept 85 90 95 90 94 0.957Oct 77 78 85 80 94 0.851Nov 75 72 83 80 94 0.851Dec 82 78 80 80 94 0.851Demand Average Average SeasonalMonth 2007 2008 2009 2007-2009 Monthly IndexExpected annual demand = 1,200Jan x .957 = 961,20012Feb x .851 = 851,20012Forecast for 2010
    • © 2011 Pearson4 - 86Seasonal Index ExampleSeasonal Index Example140 –130 –120 –110 –100 –90 –80 –70 –| | | | | | | | | | | |J F M A M J J A S O N DTimeDemand2010 Forecast2009 Demand2008 Demand2007 Demand
    • © 2011 Pearson4 - 87San Diego HospitalSan Diego Hospital10,200 –10,000 –9,800 –9,600 –9,400 –9,200 –9,000 –| | | | | | | | | | | |Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec67 68 69 70 71 72 73 74 75 76 77 78MonthInpatientDays953095519573959496169637965996809702972497459766Figure 4.6Trend Data
    • © 2011 Pearson4 - 88San Diego HospitalSan Diego Hospital1.06 –1.04 –1.02 –1.00 –0.98 –0.96 –0.94 –0.92 –| | | | | | | | | | | |Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec67 68 69 70 71 72 73 74 75 76 77 78MonthIndexforInpatientDays1.041.021.010.991.031.041.000.980.970.990.970.96Figure 4.7Seasonal Indices
    • © 2011 Pearson4 - 89San Diego HospitalSan Diego Hospital10,200 –10,000 –9,800 –9,600 –9,400 –9,200 –9,000 –| | | | | | | | | | | |Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec67 68 69 70 71 72 73 74 75 76 77 78MonthInpatientDaysFigure 4.89911926597649520969194119949972495429355100689572Combined Trend and Seasonal Forecast
    • © 2011 Pearson4 - 90Associative ForecastingAssociative ForecastingUsed when changes in one or moreindependent variables can be used to predictthe changes in the dependent variableMost common technique is linearregression analysisWe apply this technique just as we didWe apply this technique just as we didin the time series examplein the time series example
    • © 2011 Pearson4 - 91Associative ForecastingAssociative ForecastingForecasting an outcome based on predictorvariables using the least squares techniquey = a + bx^where y = computed value ofthe variable to be predicted(dependent variable)a = y-axis interceptb = slope of the regression linex = the independent variablethough to predict the value of thedependent variable^
    • © 2011 Pearson4 - 92Associative ForecastingAssociative ForecastingExampleExampleSales Area Payroll($ millions), y ($ billions), x2.0 13.0 32.5 42.0 22.0 13.5 74.0 –3.0 –2.0 –1.0 –| | | | | | |0 1 2 3 4 5 6 7SalesArea payroll
    • © 2011 Pearson4 - 93Associative ForecastingAssociative ForecastingExampleExampleSales, y Payroll, x x2xy2.0 1 1 2.03.0 3 9 9.02.5 4 16 10.02.0 2 4 4.02.0 1 1 2.03.5 7 49 24.5∑y = 15.0 ∑x = 18 ∑x2= 80 ∑xy = 51.5x = ∑x/6 = 18/6 = 3y = ∑y/6 = 15/6 = 2.5b = = = .25∑xy - nxy∑x2- nx251.5 - (6)(3)(2.5)80 - (6)(32)a = y - bx = 2.5 - (.25)(3) = 1.75
    • © 2011 Pearson4 - 94Associative ForecastingAssociative ForecastingExampleExampley = 1.75 + .25x^ Sales = 1.75 + .25(payroll)If payroll next yearis estimated to be$6 billion, then:Sales = 1.75 + .25(6)Sales = $3,250,0004.0 –3.0 –2.0 –1.0 –| | | | | | |0 1 2 3 4 5 6 7Nodel’ssalesArea payroll3.25
    • © 2011 Pearson4 - 95Standard Error of theStandard Error of theEstimateEstimate A forecast is just a point estimate of afuture value This point isactually themean of aprobabilitydistributionFigure 4.94.0 –3.0 –2.0 –1.0 –| | | | | | |0 1 2 3 4 5 6 7Nodel’ssalesArea payroll3.25
    • © 2011 Pearson4 - 96Standard Error of theStandard Error of theEstimateEstimatewhere y = y-value of each datapointyc = computed value ofthe dependent variable, from theregression equationn = number of datapointsSy,x =∑(y - yc)2n - 2
    • © 2011 Pearson4 - 97Standard Error of theStandard Error of theEstimateEstimateComputationally, this equation isconsiderably easier to useWe use the standard error to set upprediction intervals around thepoint estimateSy,x =∑y2- a∑y - b∑xyn - 2
    • © 2011 Pearson4 - 98Standard Error of theStandard Error of theEstimateEstimate4.0 –3.0 –2.0 –1.0 –| | | | | | |0 1 2 3 4 5 6 7Nodel’ssalesArea payroll3.25Sy,x = =∑y2- a∑y - b∑xyn - 239.5 - 1.75(15) - .25(51.5)6 - 2Sy,x = .306The standard errorof the estimate is$306,000 in sales
    • © 2011 Pearson4 - 99 How strong is the linearrelationship between the variables? Correlation does not necessarilyimply causality! Coefficient of correlation, r,measures degree of association Values range from -1 to +1CorrelationCorrelation
    • © 2011 Pearson4 - 100Correlation CoefficientCorrelation Coefficientr =nΣxy - ΣxΣy[nΣx2- (Σx)2][nΣy2- (Σy)2]
    • © 2011 Pearson4 - 101Correlation CoefficientCorrelation Coefficientr =nΣxy - ΣxΣy[nΣx2- (Σx)2][nΣy2- (Σy)2]yx(a) Perfect positivecorrelation:r = +1yx(b) Positivecorrelation:0 < r < 1yx(c) No correlation:r = 0yx(d) Perfect negativecorrelation:r = -1
    • © 2011 Pearson4 - 102 Coefficient of Determination, r2,measures the percent of change iny predicted by the change in x Values range from 0 to 1 Easy to interpretCorrelationCorrelationFor the Nodel Construction example:r = .901r2= .81
    • © 2011 Pearson4 - 103Multiple RegressionMultiple RegressionAnalysisAnalysisIf more than one independent variable is to beused in the model, linear regression can beextended to multiple regression toaccommodate several independent variablesy = a + b1x1 + b2x2 …^Computationally, this is quiteComputationally, this is quitecomplex and generally done on thecomplex and generally done on thecomputercomputer
    • © 2011 Pearson4 - 104Multiple RegressionMultiple RegressionAnalysisAnalysisy = 1.80 + .30x1 - 5.0x2^In the Nodel example, including interest rates inthe model gives the new equation:An improved correlation coefficient of r = .96means this model does a better job of predictingthe change in construction salesSales = 1.80 + .30(6) - 5.0(.12) = 3.00Sales = $3,000,000
    • © 2011 Pearson4 - 105 Measures how well the forecast ispredicting actual values Ratio of cumulative forecast errors tomean absolute deviation (MAD) Good tracking signal has low values If forecasts are continually high or low, theforecast has a bias errorMonitoring and ControllingMonitoring and ControllingForecastsForecastsTracking SignalTracking Signal
    • © 2011 Pearson4 - 106Monitoring and ControllingMonitoring and ControllingForecastsForecastsTrackingsignalCumulative errorMAD=Trackingsignal =∑(Actual demand inperiod i -Forecast demandin period i)(∑|Actual - Forecast|/n)
    • © 2011 Pearson4 - 107Tracking SignalTracking SignalTracking signal+0 MADs–Upper control limitLower control limitTimeSignal exceeding limitAcceptablerange
    • © 2011 Pearson4 - 108Tracking Signal ExampleTracking Signal ExampleCumulativeAbsolute AbsoluteActual Forecast Cumm Forecast ForecastQtr Demand Demand Error Error Error Error MAD1 90 100 -10 -10 10 10 10.02 95 100 -5 -15 5 15 7.53 115 100 +15 0 15 30 10.04 100 110 -10 -10 10 40 10.05 125 110 +15 +5 15 55 11.06 140 110 +30 +35 30 85 14.2
    • © 2011 Pearson4 - 109CumulativeAbsolute AbsoluteActual Forecast Cumm Forecast ForecastQtr Demand Demand Error Error Error Error MAD1 90 100 -10 -10 10 10 10.02 95 100 -5 -15 5 15 7.53 115 100 +15 0 15 30 10.04 100 110 -10 -10 10 40 10.05 125 110 +15 +5 15 55 11.06 140 110 +30 +35 30 85 14.2Tracking Signal ExampleTracking Signal ExampleTrackingSignal(Cumm Error/MAD)-10/10 = -1-15/7.5 = -20/10 = 0-10/10 = -1+5/11 = +0.5+35/14.2 = +2.5The variation of the tracking signalbetween -2.0 and +2.5 is within acceptablelimits
    • © 2011 Pearson4 - 110Adaptive ForecastingAdaptive Forecasting It’s possible to use the computer tocontinually monitor forecast errorand adjust the values of the α andβ coefficients used in exponentialsmoothing to continually minimizeforecast error This technique is called adaptivesmoothing
    • © 2011 Pearson4 - 111Focus ForecastingFocus Forecasting Developed at American Hardware Supply,based on two principles:1. Sophisticated forecasting models are notalways better than simple ones2. There is no single technique that shouldbe used for all products or services This approach uses historical data to testmultiple forecasting models for individualitems The forecasting model with the lowesterror is then used to forecast the nextdemand
    • © 2011 Pearson4 - 112Forecasting in the ServiceForecasting in the ServiceSectorSector Presents unusual challenges Special need for short term records Needs differ greatly as function ofindustry and product Holidays and other calendar events Unusual events
    • © 2011 Pearson4 - 113Fast Food RestaurantFast Food RestaurantForecastForecast20% –15% –10% –5% –11-12 1-2 3-4 5-6 7-8 9-1012-1 2-3 4-5 6-7 8-9 10-11(Lunchtime) (Dinnertime)Hour of dayPercentageofsalesFigure 4.12
    • © 2011 Pearson4 - 114FedEx Call Center ForecastFedEx Call Center ForecastFigure 4.1212% –10% –8% –6% –4% –2% –0% –Hour of dayA.M. P.M.2 4 6 8 10 12 2 4 6 8 10 12
    • © 2011 Pearson4 - 115All rights reserved. No part of this publication may be reproduced, stored in a retrievalsystem, or transmitted, in any form or by any means, electronic, mechanical, photocopying,recording, or otherwise, without the prior written permission of the publisher.Printed in the United States of America.