3-1 Forecasting

CHAPTER3

Forecasting

Homework Problems: # 2,3,4,8(a),22(a)(b),23,25,27 on pp. 125-131.

3-2 Forecasting

• Forecast – astatementaboutthefuturevalueofavariableofinterest• Wemakeforecastsaboutsuchthingsasweather,demand,andresourceavailability,profits,costs,productivity,etc.

• Forecastsareanimportantelementinmakinginformeddecisions

Forecast

3-3 Forecasting

Accounting Cost/profitestimates

Finance Cashflowandfunding

HumanResources Hiring/recruiting/training

Marketing Pricing,promotion,strategy

MIS IT/ISsystems,services

Operations Demand,Schedules,MRP,workloads

Product/servicedesign Newproductsandservices

Uses of Forecasts3-4 Forecasting

Two Important Aspects of Forecasts

• Expectedlevelofdemand• Thelevelofdemandmaybeafunctionofsomestructuralvariation (vs.randomvariation)suchastrendorseasonalvariation

• Accuracy• Relatedtothepotentialsizeofforecasterror

3-5 Forecasting

Features Common to All Forecasts1. Techniquesassumesomeunderlyingcausal system

thatexistedinthepastwillpersistintothefuture=>

2. Forecastsarerarelyperfect3. Forecastsforgroups ofitemsaremoreaccurate

thanthoseforindividualitems4. Forecastaccuracydecreasesastheforecasting

horizonincreasese.g.,

!

3-6 Forecasting

Elements of a Good Forecast

Theforecast• shouldbetimely• shouldbeaccurate• shouldbereliable• shouldbeexpressedinmeaningfulunits(e.g.,• shouldbeinwriting• techniqueshouldbesimpletounderstandanduse• shouldbecosteffective

3-7 Forecasting

Steps in the Forecasting Process

1. Determinethepurposeoftheforecast2. Establishatimehorizon3. Selectaforecastingtechnique4. Obtain,clean,andanalyzeappropriatedata5. Maketheforecast6. Monitortheforecast

3-8 Forecasting

Forecast Accuracy and Control

• Forecasterswanttominimizeforecasterrors• Itisnearlyimpossibletocorrectlyforecastreal-worldvariablevaluesonaregularbasis

• So,itisimportanttoprovideanindicationoftheextenttowhichtheforecastmightdeviatefromthevalueofthevariablethatactuallyoccurs

• Forecastaccuracyshouldbeanimportantforecastingtechniqueselection criterion

3-9 Forecasting

Types of Forecasts

• Judgmental - usessubjectiveinputs(e.g.,)

• Timeseries- useshistorical dataassumingthefuturewillbelikethepast

• Associativemodels- usesexplanatory variablestopredictthefuture

(e.g.,ISM/NAPMpurchasingmanagerindex,)

3-10 Forecasting

Forecast Accuracy and Control (contd.)

• Forecasterrorsshouldbemonitored• Error=Actual– Forecast• Iferrorsfallbeyondacceptablebounds,correctiveactionmaybenecessary

• UCL&LCL=?

3-11 Forecasting

ForecastAccuracyMetrics

MADmeasuresthemagnitudeofforecasterror

MSEweightserrorsaccordingtotheirsquaredvalues

MAPEweightserrorsrelativeto actualvalues

Bias(meanerror)measuresconsistentlyhighorlowforecast

3-12 Forecasting

Forecast Error CalculationPeriod

Actual(A)

Forecast(F)

(A-F)Error |Error| Error2 [|Error|/Actual]x100

1 107 110 -3 3 9 2.80%

2 125 121 4 4 16 3.20%

3 115 112 3 3 9 2.61%

4 118 120 -2 2 4 1.69%

5 108 109 1 1 1 0.93%

Sum 13 39 11.23%

n=5 n-1=4 n=5

MAD MSE MAPE

= = =2.25%

Q. Are these numbers small or large?

3-13 Forecasting

Forecasting Approaches• QualitativeForecasting

• Qualitativetechniquespermittheinclusionofsoft informationsuchas:• Humanfactors• Personalopinions• Hunches

• Thesefactorsaredifficult,orimpossible,toquantify

• QuantitativeForecasting• Quantitativetechniquesinvolveeithertheprojectionofhistoricaldataorthedevelopmentofassociativemethodsthatattempttousecausalvariables tomakeaforecast

• Thesetechniquesrelyonhard data

3-14 Forecasting

Judgmental Forecasts

• Forecaststhatusesubjectiveinputssuchasopinionsfromconsumersurveys,salesstaff,managers,executives,andexperts• Executiveopinions• Salesforceopinions• Consumersurveys• Delphimethod

3-15 Forecasting

Time Series Forecasts

• Forecaststhatprojectpatterns identifiedinrecenttime-seriesobservations• Time-series:atime-orderedsequenceofobservationstakenatregular timeintervals

• Assumethatfuturevaluesofthetime-seriescanbeestimatedfrompastvaluesofthetime-series

3-16 Forecasting

Time Series Forecasts

• Trend - long-termmovementindata• Seasonality - short-termregularvariationsindatae.g.,inayear,

• Cycle – wavelikevariationsofmorethanoneyear’sduration

• Irregularvariations- causedbyunusualcircumstances

• Randomvariations- causedbychance

3-17 Forecasting

Forecast Variations3-18 Forecasting

Naive Forecasts

• NaïveForecast• Usesasinglepreviousvalueofatimeseriesasthebasisforaforecast• Theforecastforatimeperiodisequaltotheprevioustimeperiod’sactual value

• Canbeusedwhen• Thetimeseriesisstable• Thereisatrend• Thereisseasonality

3-19 Forecasting

Time-Series Forecasting-- Averaging• TheseTechniquesworkbestwhenaseriestendstovaryaboutanaverage• Averagingtechniquessmoothvariationsinthedata• Theycanhandlestepchangesorgradualchangesinthelevelofaseries

• Techniques• Movingaverage• Weightedmovingaverage• Exponentialsmoothing

3-20 Forecasting

Moving Averages

• Techniquethataveragesanumberofthemostrecent actualvaluesingeneratingaforecast

3-21 Forecasting

Moving Averages

• Asnewdatabecomeavailable,theforecastisupdatedbyaddingthenewestvalueanddroppingtheoldestandthenre-computingtheaverage

• Thenumberofdatapointsincludedintheaveragedeterminesthemodel’ssensitivity• Fewerdatapoints(smalln)used-- moreresponsive• Moredatapointsused-- lessresponsive

3-22 Forecasting

Weighted Moving Averages

• Themostrecent valuesinatimeseriesaregivenmoreweightincomputingaforecast• Thechoiceofweights,w,issomewhatarbitraryandinvolvessometrialanderror

3-23 Forecasting

Moving Averages ExampleGiventhefollowingdata: Period # of complaints

1 60

2 65

3 55

4 585 64

A).Preparetheforecastsforperiod6usinga3-period,5-periodmovingaverage.

B).Prepareaweightedmovingaverageforecastforperiod6usingweightsof0.5,0.3,0.2

C).Prepareaweightedmovingaverageforecastforperiod6usingweightsof0.3,0.2,and0.1.

D).Exponentialsmoothingusingα=0.4

3-24 Forecasting

Simple Moving Average

Q.Whatn (largevs.small)touse?

3-25 Forecasting

Exponential Smoothing

Ft = Ft-1 + α (At-1 - Ft-1)

Ft = α At-1 + (1- α) Ft-1

where Ft = Forecast for period tFt-1 = Forecast for the previous periodα = Smoothing constant, between 0 and 1At-1 = Actual demand or sales from previous period

3-26 Forecasting

Exponential Smoothing

•Premise--Themostrecentobservationsmighthavethehighestpredictivevalue.

• Therefore,weshouldgivemoreweighttothemorerecenttimeperiodswhenforecasting.

Ft = Ft-1 + α (At-1 - Ft-1)

• Exponentialsmoothingisakindofweightedmovingaverage.

3-27 Forecasting

Exponential smoothing ExamplePeriod # of complaints1 602 653 554 585 646 ?

D).Given F2 =60andα=0.4

3-28 Forecasting

Picking a Smoothing Constant

35

40

45

50

1 2 3 4 5 6 7 8 9 10 11 12

Period

Demand α=0.1

α=0.4

Actual

Q. Small or large α value to use? Ft = Ft-1 + α (At-1 - Ft-1)

3-29 Forecasting

Selecting a value3-30 Forecasting

Exponential Smoothing• Simple(single)exponentialsmoothingisappropriateonlywhendatavaryaroundanaverageorhavesteporgradualchanges(i.e.,datawithouttrend orseasonalcomponents).ØIfatimeseriesexhibitstrend,andsimpleexponentialsmoothingisusedonit,theforecastswillalllagthetrend.

• Doubleexponentialsmoothingortrend-adjusted exponentialsmoothingorHolt’sMethodsmoothesbothrandomerrorsandtrends.

• TripleSmoothingortrend- andseasonal-adjustedexponentialsmoothingorHolt-Winters Methodincorporatesrandomerror,trend,andseasonalcomponents.

3-31 Forecasting

Other Forecasting Methods - Focus

• FocusForecasting• Somecompaniesuseforecastsbasedona“bestcurrentperformance”basis• Applyseveralforecastingmethodstothelastseveralperiodsofhistoricaldata

• Themethodwiththehighestaccuracyisusedtomaketheforecastforthefollowingperiod

• Thisprocessisrepeatedeachmonth

3-32 Forecasting

Other Forecasting Methods - Diffusion

• DiffusionModels• Historicaldataonwhichtobaseaforecastarenot availablefornewproducts• Predictionsarebasedonratesofproductadoptionandusagespreadfromotherestablishedproducts

• Takeintoaccountfactssuchas• Marketpotential• Attentionfrommassmedia• Word-of-mouth

3-33 Forecasting

Technique for Trend

• Lineartrendequation• Non-lineartrends

• Parabolictrend• Exponentialtrend• Growthcurvetrend

3-34 Forecasting

Linear Trend Equation• Asimpledataplot canrevealtheexistenceandnatureofatrend

• Lineartrendequation

0

0

===

===

+==

ttb

tFatF

btaFY

t

t

t

from periods time of number Specified line the of Slope at of Value

period for Forecast where

3-35 Forecasting

Estimating slope and intercept• Slopeandinterceptcanbeestimatedfromhistoricaldata

btay +=

tbay +=

tbya -= -

3-36 Forecasting

Linear Trend Equation Exampleweek sales

t y ty1 1 150 1502 4 157 3143 9 162 4864 16 166 6645 25 177 885

3-37 Forecasting

Linear Trend Calculation3-38 Forecasting

Associative Forecasting Techniques• Homevaluesmayberelatedtosuchfactorsashomeandpropertysize,location,numberofbedrooms,andnumberofbathrooms• Associativetechniquesarebasedonthedevelopmentofanequationthatsummarizestheeffectsofpredictor variables

• Predictorvariables - variablesthatcanbeusedtopredictvaluesofthevariableofinterest

3-39 Forecasting

Simple Linear Regression

• Regression:atechniqueforfittingalinetoasetofdatapoints• Simplelinearregression- thesimplestformofregressionthatinvolvesalinearrelationshipbetweentwo variables• Theobjectofsimplelinearregressionistoobtainanequationofastraightlinethatminimizesthesumofsquaredverticaldeviationsfromtheline(i.e.,theleastsquarescriterion)

Example?

3-40 Forecasting

Least Squares Line

Predictor

3-41 Forecasting

Standard Error• Standarderrorofestimate

• Ameasureofthescatterofpointsaroundaregressionline

• Ifthestandarderrorisrelativelysmall,thepredictionsusingthelinearequationwilltendtobemoreaccuratethanifthestandarderrorislarger

3-42 Forecasting

Linear Model Seems Reasonable

A straight line is fitted to a set of sample points.

0

10

20

30

40

50

0 5 10 15 20 25

Computedrelationship

3-43 Forecasting

Correlation Coefficient• Correlation=r

• Ameasureofthestrength anddirection ofrelationshipbetweentwovariables

• Rangesbetween-1.00and+1.00• whenr≈0?• Whenr→0,itindicates

• r2,squareofthecorrelationcoefficient• Ameasureofthepercentageofvariabilityinthevaluesofythatis“explained”bytheindependentvariable

• Rangesbetween0and1.00

3-44 Forecasting

Regression and Correlation ExampleGiventhefollowingvaluesofXandY,(1)obtainalinearregressionlineforthedata,and(2)whatpercentageofthevariationisexplainedbytheregressionline?x y

15.00 74.0025.00 80.0040.00 84.0032.00 81.0051.00 96.0047.00 95.0030.00 83.0018.00 78.0014.00 70.0015.00 72.0022.00 85.0024.00 88.0033.00 90.00

3-45 Forecasting

Regression and Correlation Examplex y xy x2 y2

15.00 74.0025.00 80.0040.00 84.0032.00 81.0051.00 96.0047.00 95.0030.00 83.0018.00 78.0014.00 70.0015.00 72.0022.00 85.0024.00 88.0033.00 90.00 2970.0 1089.0 8100.0366.00 1076.0 31329.0 12078.0 89860.0

1110.0 225.0 5476.02000.0 625.0 6400.0

3-46 Forecasting

Regression and Correlation Example

Whatcanwesayaboutxandy?

3-47 Forecasting

Simple Linear Regression Assumptions

1. Variationsaroundthelinearerandom2. Deviationsaroundtheaveragevalue(the

line)shouldbenormallydistributed3. Predictionsaremadeonlywithintherange

ofobservedvalues

3-48 Forecasting

Issues to consider• Alwaysplot thelinetoverifythatalinearrelationshipsisappropriate

• Thedatamaybetime-dependent.• Ifthey

• useanalysisoftimeseries• usetimeasanindependentvariableinamultipleregressionanalysis

• Asmallcorrelation(whenrissmall)mayindicatethatothervariablesareimportant

3-49 Forecasting

Controlling the Forecast

• Controlchart• Avisualtoolformonitoringforecasterrors• Usedtodetectnon-randomnessinerrors

• Forecastingerrorsareincontrolif1. Allerrorsarewithinthecontrollimits,and2. Nopatterns,suchastrendsorcycles,are

present

3-50 Forecasting

Sources of Forecast errors• Modelmaybeinadequatee.g.,

• Irregularvariationse.g.,

• Incorrectuseofforecastingtechniquee.g.,

• Randomvariation:theinherentvariationthatremainsinthedataafterallcausesofvariationhavebeenaccountedfor.

3-51 Forecasting

Control Charts for forecast errors

MSEUCL += 0

MSELCL -= 0

MSEwhere is used in practice as an estimate of the standard deviation of the forecast errors

-

3-52 Forecasting

Control Charts for forecast errors

3-53 Forecasting

Choosing a Forecasting Technique• Nosingletechniqueworksineverysituation• Twomostimportantfactors

• Cost• Accuracy

• Otherfactorsincludetheavailabilityof:• Historicaldata• Computers• Timeneededtogatherandanalyzethedata• Forecasthorizon

3-54 Forecasting

Using Forecast Information• Reactiveapproach

• Viewforecastsasprobablefuturedemand• Reacttomeetthatdemand

• Proactiveapproach• Seekstoactivelyinfluence demand

• Advertising• Pricing• Product/servicemodifications

• Seekstoactivelyknow thedemandbyworkingcloselywithsupplychainpartners