02 demand forecasting

8/8/2019 02 Demand Forecasting

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MODULEMODULE--22MODULEMODULE--22

DemandDemand ForecastingForecasting


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OverviewOverview

IntroductionIntroduction

Qualitative Forecasting MethodsQualitative Forecasting Methods

Quantitative Forecasting ModelsQuantitative Forecasting Models

How to Have a Successful Forecasting SystemHow to Have a Successful Forecasting System

Computer Software for ForecastingComputer Software for Forecasting

Forecasting in Small Businesses and StartForecasting in Small Businesses and Start--UpUp

VenturesVentures

WrapWrap--Up: What WorldUp: What World--Class Producers DoClass Producers Do


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IntroductionIntroductionIntroductionIntroduction

Demand estimatesDemand estimates for products and servicesfor products and services

are the starting point for all the other planningare the starting point for all the other planning

in operations management.in operations management.

Management teams developManagement teams develop sales forecastssales forecastsbased in part on demand estimates.based in part on demand estimates.

The sales forecasts become inputs to bothThe sales forecasts become inputs to both

business strategy andbusiness strategy and production resourceproduction resourceforecastsforecasts..


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Forecasting is an Integral PartForecasting is an Integral Part

of Business Planningof Business Planning

Forecasting is an Integral PartForecasting is an Integral Part

of Business Planningof Business Planning

ForecastForecast

Method(s)Method(s)

DemandDemand

EstimatesEstimates

SalesSales

ForecastForecast

ManagementManagement

TeamTeam

Inputs:Inputs:

Market,Market,

Economic,Economic,

OtherOther

BusinessBusiness

StrategyStrategy

Production ResourceProduction Resource

ForecastsForecasts


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Some Reasons WhySome Reasons Why

Forecasting is Essential in OMForecasting is Essential in OM

Some Reasons WhySome Reasons Why

Forecasting is Essential in OMForecasting is Essential in OM

New Facility PlanningNew Facility Planning It can take 5 years to designIt can take 5 years to design

and build a new factory or design and implement aand build a new factory or design and implement a

new production process.new production process.

Production PlanningProduction Planning Demand for products varyDemand for products varyfrom month to month and it can take several monthsfrom month to month and it can take several months

to change the capacities of production processes.to change the capacities of production processes.

Workforce SchedulingWorkforce Scheduling Demand for services (andDemand for services (and

the necessary staffing) can vary from hour to hourthe necessary staffing) can vary from hour to hourand employees weekly work schedules must beand employees weekly work schedules must be

developed in advance.developed in advance.


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LongLong--Range ForecastsRange ForecastsLongLong--Range ForecastsRange Forecasts

Time spans usually greaterTime spans usually greater

than one yearthan one year

Necessary to support strategicNecessary to support strategic

decisions about planningdecisions about planning

products, processes, andproducts, processes, andfacilitiesfacilities


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Examples of Production Resource ForecastsExamples of Production Resource ForecastsExamples of Production Resource ForecastsExamples of Production Resource Forecasts

LongLong

RangeRange

MediumMedium

RangeRange

ShortShortRangeRange

YearsYears

MonthsMonths

Days,Days,WeeksWeeks

Product Lines,Product Lines,

Factory CapacitiesFactory Capacities

ForecastForecast

HorizonHorizon

TimeTime

SpanSpan

Item BeingItem Being

ForecastedForecasted

Unit ofUnit of

MeasureMeasure

Product Groups,Product Groups,

Depart. CapacitiesDepart. Capacities

Specific Products,Specific Products,Machine CapacitiesMachine Capacities

Dollars,Dollars,

TonsTons

Units,Units,

PoundsPounds

Units,Units,HoursHours


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Forecasting MethodsForecasting Methods

Qualitative ApproachesQualitative Approaches

Quantitative ApproachesQuantitative Approaches


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NonNon--Statistical (Qualitative) ApproachesStatistical (Qualitative) Approaches

Usually based on judgments about causal factors thatUsually based on judgments about causal factors that

underlie the demand of particular products or servicesunderlie the demand of particular products or services

Do not require a demand history for the product orDo not require a demand history for the product or

service, therefore are useful for new products/servicesservice, therefore are useful for new products/services Approaches vary in sophistication from scientificallyApproaches vary in sophistication from scientifically

conducted surveys to intuitive hunches about futureconducted surveys to intuitive hunches about future

eventsevents

The approach/method that is appropriate depends on aThe approach/method that is appropriate depends on aproducts life cycle stageproducts life cycle stage


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Qualitative MethodsQualitative MethodsQualitative MethodsQualitative Methods

Educated guessEducated guess intuitive hunchesintuitive hunches Executive committee consensusExecutive committee consensus

Delphi methodDelphi method

Survey of sales forceSurvey of sales force

Survey of customersSurvey of customers

Historical analogyHistorical analogy Market research orMarket research or scientificallyscientifically

conducted surveysconducted surveys


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Qualitative MethodsQualitative MethodsQualitative MethodsQualitative Methods

Educated guessEducated guess intuitive hunchesintuitive hunches

Executive committee consensusExecutive committee consensus

Delphi methodDelphi method

Survey of sales forceSurvey of sales force Survey of customersSurvey of customers

Historical analogyHistorical analogy

Market researchMarket research sscientifically conducted surveyscientifically conducted surveys


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Quantitative Forecasting ApproachesQuantitative Forecasting ApproachesQuantitative Forecasting ApproachesQuantitative Forecasting Approaches

Based on the assumption that the forces thatBased on the assumption that the forces that

generated the past demand will generate thegenerated the past demand will generate the

future demand, i.e., history will tend to repeatfuture demand, i.e., history will tend to repeat

itselfitself Analysis of the past demand pattern provides aAnalysis of the past demand pattern provides a

good basis for forecasting future demandgood basis for forecasting future demand

Majority of quantitative approaches fall in theMajority of quantitative approaches fall in thecategory ofcategory oftime series analysistime series analysis


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AA time seriestime series is a set of numbersis a set of numberswhere the order or sequence of thewhere the order or sequence of the

numbers is important, e.g., historicalnumbers is important, e.g., historical

demanddemand

Analysis of the time series identifiesAnalysis of the time series identifies

patternspatterns Once the patterns are identified, theyOnce the patterns are identified, they

can be used to develop a forecastcan be used to develop a forecast

Time Series AnalysisTime Series AnalysisTime Series AnalysisTime Series Analysis


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Components of a Time SeriesComponents of a Time SeriesComponents of a Time SeriesComponents of a Time Series

TrendsTrends are noted by an upward orare noted by an upward or

downward sloping line.downward sloping line.

CycleCycle is a data pattern that may coveris a data pattern that may cover

several years before it repeats itself.several years before it repeats itself.

SeasonalitySeasonality is a data pattern that repeatsis a data pattern that repeats

itself over the period of one year or less.itself over the period of one year or less. Random fluctuation (noise)Random fluctuation (noise) results fromresults from

random variation or unexplained causes.random variation or unexplained causes.


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Seasonal PatternsSeasonal PatternsSeasonal PatternsSeasonal Patterns

Length of TimeLength of Time Number ofNumber of

Before Pattern Length ofBefore Pattern Length of SeasonsSeasons

Is RepeatedIs Repeated SeasonSeason in Patternin Pattern

YearYear Quarter Quarter 44

YearYear MonthMonth 1212

YearYear Week Week 5252

MonthMonth DayDay 2828--3131

WeekWeek DayDay 77


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Quantitative Forecasting ApproachesQuantitative Forecasting Approaches

Linear RegressionLinear Regression Simple Moving AverageSimple Moving Average

Weighted Moving AverageWeighted Moving Average Exponential SmoothingExponential Smoothing

(exponentially weighted moving(exponentially weighted moving

average)average) Exponential Smoothing with TrendExponential Smoothing with Trend

(double exponential smoothing)(double exponential smoothing)


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Simple Linear RegressionSimple Linear RegressionSimple Linear RegressionSimple Linear Regression

Linear regression analysis establishes aLinear regression analysis establishes a

relationship between a dependent variable andrelationship between a dependent variable and

one or more independent variables.one or more independent variables.

InIn simple linear regression analysissimple linear regression analysis there isthere isonly one independent variable.only one independent variable.

If the data is a time series, the independentIf the data is a time series, the independent

variable is the time period.variable is the time period. The dependent variable is whatever we wish toThe dependent variable is whatever we wish to

forecast.forecast.


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Regression EquationRegression Equation

This model is of the form:This model is of the form:

Y = a +Y = a + bXbX

Y = dependent variableY = dependent variable

X = independent variableX = independent variable

a = ya = y--axis interceptaxis intercept

b = slope of regression lineb = slope of regression line


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Constants a and bConstants a and b

The constants a and b are computed using theThe constants a and b are computed using the

following equations:following equations:

2

2 2

x y- x xya =

n x -( x)

2 2

xy- x yb = n x -( x)

n


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Once theOnce the aa and b values areand b values are

computed, a future value of Xcomputed, a future value of X

can be entered into thecan be entered into theregression equation and aregression equation and a

corresponding value of Y (thecorresponding value of Y (theforecast) can be calculated.forecast) can be calculated.


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Example: College EnrollmentExample: College EnrollmentExample: College EnrollmentExample: College Enrollment

Simple Linear RegressionSimple Linear Regression

At a small regional college enrollments have grownAt a small regional college enrollments have grown

steadily over the past six years, as evidenced below.steadily over the past six years, as evidenced below.

Use time series regression to forecast the studentUse time series regression to forecast the student

enrollments for the next three years.enrollments for the next three years.

StudentsStudents StudentsStudents

YearYear Enrolled (1000s)Enrolled (1000s) YearYear Enrolled (1000s)Enrolled (1000s)

11 2.52.5 44 3.23.2

22 2.82.8 55 3.33.3

33 2.92.9 66 3.43.4


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xx yy xx22 xyxy

11 2.52.5 11 2.52.5

22 2.82.8 44 5.65.633 2.92.9 99 8.78.7

44 3.23.2 1616 12.812.8

55 3.33.3 2525 16.516.5

66 3.43.4 3636 20.420.477x=21x=21 77y=18.1y=18.1 77xx22=91=91 77xy=66.5xy=66.5


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Y = 2.387 + 0.180XY = 2.387 + 0.180X

2

91(18.1) 21(66.5)2.387

6(91) (21)a

! !

6(66.5 21(18.10.180

105b

! !


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YY77

= 2.387 + 0.180(7) = 3.65 or3,650 students= 2.387 + 0.180(7) = 3.65 or3,650 students

YY88 = 2.387 + 0.180(8) = 3.83 or3,830 students= 2.387 + 0.180(8) = 3.83 or3,830 students

YY99 = 2.387 + 0.180(9) = 4.01 or4,010 students= 2.387 + 0.180(9) = 4.01 or4,010 students

Note: Enrollment is expected to increase by 180Note: Enrollment is expected to increase by 180

students per year.students per year.


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(CAUSAL FORECASTING METHODS)(CAUSAL FORECASTING METHODS)

SimpleSimple linear regression can also be usedlinear regression can also be used

when the independent variable X representswhen the independent variable X representsa variable other than timea variable other than time..

In this case, linear regression isIn this case, linear regression isrepresentative of a class of forecastingrepresentative of a class of forecasting

models calledmodels called causal forecasting modelscausal forecasting models..


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Example: Railroad Products Co.Example: Railroad Products Co.Example: Railroad Products Co.Example: Railroad Products Co.

Simple Linear RegressionSimple Linear Regression Causal ModelCausal ModelThe manager of RPC wants to project the firmsThe manager of RPC wants to project the firms

sales for the next 3 years. He knows that RPCs longsales for the next 3 years. He knows that RPCs long--

range sales are tied very closely to national freight carrange sales are tied very closely to national freight car

loadings. On the next slide are 7 years of relevantloadings. On the next slide are 7 years of relevanthistorical data.historical data.

Develop a simple linear regression modelDevelop a simple linear regression model

between RPC sales and national freight car loadings.between RPC sales and national freight car loadings.

Forecast RPC sales for the next 3 years, given that theForecast RPC sales for the next 3 years, given that the

rail industry estimates car loadings of 250, 270, andrail industry estimates car loadings of 250, 270, and

300 million.300 million.


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Simple Linear RegressionSimple Linear Regression Causal ModelCausal Model

RPC SalesRPC Sales Car LoadingsCarLoadings

YearYear ($millions)($millions) (millions)(millions)

11 9.59.5 12012022 11.011.0 13513533 12.012.0 13013044 12.512.5 150150

55 14.014.0 17017066 16.016.0 19019077 18.018.0 220220


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xx yy xx22 xyxy

120120 9.59.5 14,40014,400 1,1401,140

135135 11.011.0 18,22518,225 1,4851,485

130130 12.012.0 16,90016,900 1,5601,560

150150 12.512.5 22,50022,500 1,8751,875

170170 14.014.0 28,90028,900 2,3802,380

190190 16.016.0 36,10036,100 3,0403,040

220220 18.018.0 48,40048,400 3,9603,960

1,1151,115 93.093.0 185,425185,425 15,44015,440


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Y = 0.528 + 0.0801XY = 0.528 + 0.0801X

2

185,425(93 1, 115(15,440a 0.528

7(185,425 (1,115

! !

2

7(15, 440 1,115(93b 0.0801

7(185,425 (1,115

! !


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YY88 = 0.528 + 0.0801(250) = $20.55 million= 0.528 + 0.0801(250) = $20.55 million



Note: RPC sales are expected to increase byNote: RPC sales are expected to increase by$80,100 for each additional million national freight$80,100 for each additional million national freightcar loadings.car loadings.


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Multiple Regression AnalysisMultiple Regression AnalysisMultiple Regression AnalysisMultiple Regression Analysis

Multiple regression analysis is used when there areMultiple regression analysis is used when there aretwo or more independent variables.two or more independent variables.

An example of a multiple regression equation is:An example of a multiple regression equation is:

Y = 50.0 + 0.05XY = 50.0 + 0.05X11 + 0.10X+ 0.10X22 0.03X0.03X33

where: Y = firms annual sales ($millions)where: Y = firms annual sales ($millions)

XX11 = industry sales ($millions)= industry sales ($millions)

XX22 = regional per capita income ($thousands)= regional per capita income ($thousands)

XX33

= regional per capita debt ($thousands)= regional per capita debt ($thousands)


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Coefficient ofCorrelation (Coefficient ofCorrelation (rr))Coefficient ofCorrelation (Coefficient ofCorrelation (rr))

The coefficient of correlation,The coefficient of correlation, rr, explains the, explains therelative importance of the relationship betweenrelative importance of the relationship between

xx andandyy..

The sign ofThe sign ofrrshows the direction of theshows the direction of the

relationship.relationship.

The absolute value ofThe absolute value ofrrshows the strength ofshows the strength of

the relationship.the relationship.

The sign ofThe sign ofrris always the same as the sign ofis always the same as the sign of

b.b.

rrcan take on any value betweencan take on any value between 1 and +1.1 and +1.


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Meanings of several values ofMeanings of several values ofrr::

--1 a perfect negative relationship (as1 a perfect negative relationship (asxx goes up,goes up,yy

goes down by one unit, and vice versa)goes down by one unit, and vice versa)+1 a perfect positive relationship (as+1 a perfect positive relationship (asxx goes up,goes up,yy

goes up by one unit, and vice versa)goes up by one unit, and vice versa)

0 no relationship exists between0 no relationship exists betweenxx andandyy

+0.3 a weak positive relationship+0.3 a weak positive relationship

--0.8 a strong negative relationship0.8 a strong negative relationship


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rr is computed byis computed by::

2 2 2 2

( ) ( )

n xy x yr

n x x n y y

!

- -


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Coefficient of Determination (Coefficient of Determination (rr22))Coefficient of Determination (Coefficient of Determination (rr22))

The coefficient of determination,The coefficient of determination, rr22, is the square of, is the square ofthe coefficient of correlation.the coefficient of correlation.

The modification ofThe modification ofrrtoto rr22 allows us to shift fromallows us to shift from

subjective measures of relationship to a more specificsubjective measures of relationship to a more specific

measure.measure.

rr22 is determined by the ratio of explained variation tois determined by the ratio of explained variation to

total variationtotal variation::

22

2( )( )Y yry y

!


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Coefficient of CorrelationCoefficient of Correlation

xx yy xx22 xyxy yy22

120120 9.59.5 14,40014,400 1,1401,140 90.2590.25

135135 11.011.0 18,22518,225 1,4851,485 121.00121.00

130130 12.012.0 16,90016,900 1,5601,560 144.00144.00

150150 12.512.5 22,50022,500 1,8751,875 156.25156.25

170170 14.014.0 28,90028,900 2,3802,380 196.00196.00

190190 16.016.0 36,10036,100 3,0403,040 256.00256.00

220220 18.018.0 48,40048,400 3,9603,960 324.00324.00

1,1151,115 93.093.0 185,425185,425 15,44015,440 1,287.501,287.50


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Coefficient of CorrelationCoefficient of Correlation

rr = .9829= .9829

2 2

7( ) ( )

7( 25) ( 5) 7( 287.5) ( )r

!

- -


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Coefficient of DeterminationCoefficient of Determination

rr22 = (.9829)= (.9829)22 = .= .966966

96.6% of the variation in RPC sales is96.6% of the variation in RPC sales is

explained by national freight carexplained by national freight car

loadings.loadings.


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Ranging ForecastsRanging ForecastsRanging ForecastsRanging Forecasts

Forecasts for future periods are only estimatesForecasts for future periods are only estimatesand are subject to error.and are subject to error.

One way to deal with uncertainty is to developOne way to deal with uncertainty is to develop

bestbest--estimate forecasts and theestimate forecasts and the rangesranges withinwithinwhich the actual data are likely to fall.which the actual data are likely to fall.

The ranges of a forecast are defined by theThe ranges of a forecast are defined by the

upper and lower limits of a confidenceupper and lower limits of a confidenceinterval.interval.


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The ranges or limits of a forecast are estimated by:The ranges or limits of a forecast are estimated by:

Upper limit = Y + t(Upper limit = Y + t(ssyxyx))

Lower limit = YLower limit = Y -- t(t(ssyxyx))

where:where:

Y = bestY = best--estimate forecastestimate forecast

t = number of standard deviations from the meant = number of standard deviations from the mean

of the distribution to provide a givenof the distribution to provide a given probaproba--bilitybility of exceeding the limits through chanceof exceeding the limits through chance

ssyxyx = standard error of the forecast= standard error of the forecast


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TheThe standard error (deviation) of the forecaststandard error (deviation) of the forecast isiscomputed as:computed as:

2

yx

y - a y - b xys = n - 2


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Ranging ForecastsRanging Forecasts

Recall that linear regression analysisRecall that linear regression analysis

provided a forecast of annual sales forprovided a forecast of annual sales for

RPC in year8 equal to $20.55 million.RPC in year8 equal to $20.55 million.

Set the limits (ranges) of the forecastSet the limits (ranges) of the forecast

so that there is only a 5 percentso that there is only a 5 percent

probability of exceeding the limits byprobability of exceeding the limits by

chance.chance.


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Step 1: Compute the standard error of theStep 1: Compute the standard error of the

forecasts,forecasts, ssyxyx..

Step 2: Determine the appropriate value for t.Step 2: Determine the appropriate value for t.

n = 7,n = 7, soso degrees of freedom = ndegrees of freedom = n 2 = 5.2 = 5.Area in upper tail = .05/2 = .025Area in upper tail = .05/2 = .025

Appendix B, Table 2 shows t = 2.571.Appendix B, Table 2 shows t = 2.571.

1 87.5 .528(93) .0801(15, 0) .57487 2

yxs ! !


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Step 3: Compute upper and lower limits.Step 3: Compute upper and lower limits.

Upper limit = 20.55 + 2.571(.5748)Upper limit = 20.55 + 2.571(.5748)

= 20.55 + 1.478= 20.55 + 1.478= 22.028= 22.028

Lower limit = 20.55Lower limit = 20.55 -- 2.571(.5748)2.571(.5748)

= 20.55= 20.55 -- 1.4781.478

= 19.072= 19.072

WeWe are 95% confidentare 95% confident that thethat the actual sales for year8actual sales for year8will be between $19.072 and $22.028 million.will be between $19.072 and $22.028 million.


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Seasonalized Time Series Regression AnalysisSeasonalized Time Series Regression AnalysisSeasonalized Time Series Regression AnalysisSeasonalized Time Series Regression Analysis

Select a representative historical data set.Select a representative historical data set. Develop a seasonal index for each season.Develop a seasonal index for each season.

Use the seasonal indexes toUse the seasonal indexes to dede--seasonalizeseasonalize thethe

data.data. PerformPerform linear regressionlinear regression analysis on theanalysis on the dede--

seasonalizedseasonalized data.data.

Use the regression equation to compute theUse the regression equation to compute theforecasts.forecasts.

Use theUse the seasonalizedseasonalized indexes to reapply theindexes to reapply the

seasonal patterns to the forecasts.seasonal patterns to the forecasts.


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Example: Computer Products Corp.Example: Computer Products Corp.Example: Computer Products Corp.Example: Computer Products Corp.

SeasonalizedSeasonalized Times Series RegressionTimes Series RegressionAnalysisAnalysis

An analyst at CPC wants to developAn analyst at CPC wants to develop

next years quarterly forecasts of salesnext years quarterly forecasts of sales

revenue for CPCs line of Epsilonrevenue for CPCs line of Epsilon

Computers. She believes that the mostComputers. She believes that the most

recent 8 quarters of sales (shown on therecent 8 quarters of sales (shown on the

next slide) are representative of nextnext slide) are representative of next

years sales.years sales.


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SeasonalizedSeasonalized Times Series Regression AnalysisTimes Series Regression Analysis

Representative HistoricalRepresentative Historical Sales DataSales Data SetSet

YearYear Qtr.Qtr. ($mil.)($mil.) Year Year Qtr.Qtr. ($mil.)($mil.)

11 11 7.47.4 22 11 8.38.3

11 22 6.56.5 22 22 7.47.4

11 33 4.94.9 22 33 5.45.4

11 44 16.116.1 22 44 18.018.0


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Seasonalized Times Series Regression AnalysisSeasonalized Times Series Regression Analysis

Compute the Seasonal IndexesCompute the Seasonal Indexes

Quarterly SalesQuarterly Sales

YearYear Q1Q1 Q2Q2 Q3Q3 Q4Q4 TotalTotal

11 7.47.4 6.56.5 4.94.9 16.116.1 34.934.9

22 8.38.3 7.47.4 5.45.4 18.018.0 39.139.1

TotalsTotals 15

.7

15

.7

13

.913

.9 10.3

10.3 34

.134

.174

.074

.0Qtr. Avg.Qtr. Avg. 7.857.85 6.956.95 5.155.15 17.0517.05 9.259.25

Seas.Ind.Seas.Ind. .849.849 .751.751 .557.557 1.8431.843 4.0004.000


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SeasonalizedSeasonalized Times Series Regression AnalysisTimes Series Regression Analysis

DeseasonalizeDeseasonalize the Datathe Data

Quarterly SalesQuarterly Sales

YearYear Q1Q1 Q2Q2 Q3Q3 Q4Q411 8.728.72 8.668.66 8.808.80 8.748.74

22 9.789.78 9.859.85 9.699.69 9.779.77

(Quarterly Sales) / index = de(Quarterly Sales) / index = de--seasonlizedseasonlized salessales


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Perform Regression on Deseasonalized DataPerform Regression on Deseasonalized Data

Yr.Yr. Qtr.Qtr. xx yy xx22 xyxy

11 11 11 8.728.72 11 8.728.7211 22 22 8.668.66 44 17.3217.3211 33 33 8.808.80 99 26.4026.4011 44 44 8.748.74 1616 34.9634.9622 11 55 9.789.78 2525 48.9048.90

22 22 66 9.859.85 3636 59.1059.1022 33 77 9.699.69 4949 67.8367.8322 44 88 9.779.77 6464 78.1678.16

TotalsTotals 3636 74.0174.01 204204 341.39341.39


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Perform Regression on Deseasonalized DataPerform Regression on Deseasonalized Data

Y = 8.357 + 0.199XY = 8.357 + 0.199X

2

204(74.01 36(341.39a 8.357

8(204 (36

! !

2

8(341.39 36(74.01b 0.199

8(204 (36

! !


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Compute the Deseasonalized ForecastsCompute the Deseasonalized Forecasts

YY99 = 8.357 + 0.199(9) = 10.148= 8.357 + 0.199(9) = 10.148

YY1010 = 8.357 + 0.199(10) = 10.347= 8.357 + 0.199(10) = 10.347

YY1111 = 8.357 + 0.199(11) = 10.546= 8.357 + 0.199(11) = 10.546

YY1212 = 8.357 + 0.199(12) = 10.745= 8.357 + 0.199(12) = 10.745

Note: Average sales are expected to increase byNote: Average sales are expected to increase by

.199 million (about $200,000) per quarter..199 million (about $200,000) per quarter.


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Seasonalize the ForecastsSeasonalize the Forecasts

Seas.Seas. Deseas.Deseas. Seas.Seas.

Yr.Yr. Qtr.Qtr. IndexIndex ForecastForecast ForecastForecast

33 11 .849.849 10.14810.148 8.628.62

33 22 .751.751 10.34710.347 7.777.77

33 33 .557.557 10.54610.546 5.875.8733 44 1.8431.843 10.74510.745 19.8019.80


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ShortShort--Range ForecastsRange ForecastsShortShort--Range ForecastsRange Forecasts

Time spans ranging from a fewTime spans ranging from a fewdays to a few weeksdays to a few weeks

Cycles, seasonality, and trendCycles, seasonality, and trendmay have little effectmay have little effect

Random fluctuation is mainRandom fluctuation is maindata componentdata component


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Evaluating ForecastEvaluating Forecast--Model PerformanceModel PerformanceEvaluating ForecastEvaluating Forecast--Model PerformanceModel Performance

ShortShort--range forecastingrange forecastingmodels are evaluated on themodels are evaluated on the

basis of three characteristics:basis of three characteristics: Impulse responseImpulse response

NoiseNoise--dampening abilitydampening ability AccuracyAccuracy


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Evaluating ForecastEvaluating Forecast--Model PerformanceModel PerformanceEvaluating ForecastEvaluating Forecast--Model PerformanceModel Performance

Impulse Response and NoiseImpulse Response and Noise--DampeningDampeningAbilityAbility

If forecasts have little periodIf forecasts have little period--toto--period fluctuation,period fluctuation,

they are said to bethey are said to be noise dampeningnoise dampening..

Forecasts that respond quickly to changes in dataForecasts that respond quickly to changes in data

are said to have a highare said to have a high impulse responseimpulse response..

A forecast system that responds quickly to dataA forecast system that responds quickly to data

changes necessarily picks up a great deal ofchanges necessarily picks up a great deal ofrandom fluctuation (random fluctuation (noisenoise).).

Hence, there is aHence, there is a tradetrade--off between high impulseoff between high impulse

response and high noise dampening.response and high noise dampening.


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Evaluating ForecastEvaluating Forecast--Model PerformanceModel Performance

Accuracy :Accuracy :

Accuracy is the typical criterion forAccuracy is the typical criterion for

judging the performance of ajudging the performance of aforecasting approachforecasting approach

Accuracy is how well theAccuracy is how well the

forecasted values match the actualforecasted values match the actualvaluesvalues


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Monitoring AccuracyMonitoring AccuracyMonitoring AccuracyMonitoring Accuracy

Accuracy of a forecasting approach needs toAccuracy of a forecasting approach needs tobe monitored to assess the confidence you canbe monitored to assess the confidence you can

have in its forecasts and changes in the markethave in its forecasts and changes in the market

may require reevaluation of the approachmay require reevaluation of the approach Accuracy can be measured in several waysAccuracy can be measured in several ways

Standard error of the forecast (coveredStandard error of the forecast (covered

earlier in slide4

1)earlier in slide4

1) Mean absolute deviation (MAD)Mean absolute deviation (MAD)

Mean squared error (Mean squared error (MSEMSE))


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Monitoring AccuracyMonitoring AccuracyMonitoring AccuracyMonitoring Accuracy

Mean Absolute Deviation (MAD)Mean Absolute Deviation (MAD)

n

e io snoeviationabsoluteouMAD

n

i i

i=1

Actual demand -Forecast demand

MAD =n


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Mean Squared Error (Mean Squared Error (MSEMSE))

MSEMSE = (= (SSyxyx))22

A small value forA small value for SSyxyx

(standard error of the(standard error of the

forecast) meansforecast) means data points are tightly groupeddata points are tightly grouped

around the line and error range is small.around the line and error range is small.

When the forecast errors are normallyWhen the forecast errors are normally

distributed, the values of MAD anddistributed, the values of MAD and ssyxyx are related:are related:

MSEMSE = 1.25(MAD)= 1.25(MAD)

Monitoring AccuracyMonitoring Accuracy


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ShortShort--Range Forecasting MethodsRange Forecasting MethodsShortShort--Range Forecasting MethodsRange Forecasting Methods

(Simple) Moving Average(Simple) Moving Average

Weighted Moving AverageWeighted Moving Average

Exponential SmoothingExponential Smoothing

Exponential SmoothingExponential Smoothingwith Trendwith Trend


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Simple Moving AverageSimple Moving Average

AnAn averaging period (APaveraging period (AP) is given or) is given orselectedselected

The forecast for the next period is theThe forecast for the next period is the

arithmetic average of the AP most recentarithmetic average of the AP most recentactual demandsactual demands

It is called a simple average because eachIt is called a simple average because each

period used to compute the average isperiod used to compute the average isequally weightedequally weighted

. . . more. . . more


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Simple Moving AverageSimple Moving AverageSimple Moving AverageSimple Moving Average

It is called moving because as new demandIt is called moving because as new demanddata becomes available, the oldest data is notdata becomes available, the oldest data is not

usedused

By increasing the AP, the forecast is lessBy increasing the AP, the forecast is lessresponsive to fluctuations in demand (lowresponsive to fluctuations in demand (low

impulse response and high noise dampening)impulse response and high noise dampening)

By decreasing the AP, the forecast is moreBy decreasing the AP, the forecast is moreresponsive to fluctuations in demand (highresponsive to fluctuations in demand (high

impulse response and low noise dampening)impulse response and low noise dampening)


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Weighted Moving AverageWeighted Moving Average

This is a variation on the simpleThis is a variation on the simplemoving average where the weightsmoving average where the weights

used to compute the average are notused to compute the average are not

equal.equal.

This allows more recent demand dataThis allows more recent demand data

to have a greater effect on the movingto have a greater effect on the moving

average, therefore the forecast.average, therefore the forecast.



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Weighted Moving AverageWeighted Moving AverageWeighted Moving AverageWeighted Moving Average

The weights must add to 1.0The weights must add to 1.0and generally decrease in valueand generally decrease in value

with the age of the data.with the age of the data. The distribution of the weightsThe distribution of the weights

determine the impulse responsedetermine the impulse responseof the forecast.of the forecast.


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The weights used to compute the forecast (movingThe weights used to compute the forecast (movingaverage) are exponentially distributed.average) are exponentially distributed.

The forecast is the sum of the old forecast and aThe forecast is the sum of the old forecast and a

portion (portion (EE) of the forecast error (A) of the forecast error (A tt--11 -- FFtt--11).).

FFtt = F= Ftt--11 ++ EE(A(A tt--11 -- FFtt--11))


Exponential SmoothingExponential Smoothing


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Exponential SmoothingExponential SmoothingExponential SmoothingExponential Smoothing

The smoothing constant,The smoothing constant, EE,,must be between 0.0 and 1.0.must be between 0.0 and 1.0.

A largeA large EEprovides a highprovides a highimpulse response forecast.impulse response forecast.

A smallA small EEprovides a lowprovides a lowimpulse response forecast.impulse response forecast.


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Example: Central Call CenterExample: Central Call CenterExample: Central Call CenterExample: Central Call Center

Moving AverageMoving AverageCCCCCC wishes to forecast the number ofwishes to forecast the number of

incoming calls it receives in a day from theincoming calls it receives in a day from the

customers of one of its clients, BMI.customers of one of its clients, BMI. CCCCCC

schedules the appropriate number of telephoneschedules the appropriate number of telephone

operators based on projected call volumes.operators based on projected call volumes.

CCCCCC believes that the most recent 12 daysbelieves that the most recent 12 daysof call volumes (shown on the next slide) areof call volumes (shown on the next slide) are

representative of the near future call volumes.representative of the near future call volumes.


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Moving AverageMoving Average Representative Historical DataRepresentative Historical Data

DayDay CallsCalls DayDay CallsCalls

11 159159 77 20320322 217217 88 195195

33 186186 99 188188

44 161161 1010 168168

55 173173 1111 19819866 157157 1212 159159


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Moving AverageMoving Average

Use the moving average methodUse the moving average method

with an AP =3

days to develop awith an AP =3

days to develop aforecast of the call volume in Day 13.forecast of the call volume in Day 13.

FF1313 = (168 + 198 + 159)/3 = 175.0 calls= (168 + 198 + 159)/3 = 175.0 calls

C C CC C CC C CC C C


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Weighted Moving AverageWeighted Moving AverageUse the weighted moving average method with anUse the weighted moving average method with an

AP = 3 days and weights of .1 (for oldest datum), .3,AP = 3 days and weights of .1 (for oldest datum), .3,

and .6 to develop a forecast of the call volume in Dayand .6 to develop a forecast of the call volume in Day13.13.

FF1313 = .1(168) + .3(198) + .6(159) = 171.6 calls= .1(168) + .3(198) + .6(159) = 171.6 calls

Note: The WMA forecast is lower than the MA

Note: The WMA forecast is lower than the MAforecast because Dayforecast because Day 12s12s relatively low call volumerelatively low call volume

carries almost twice as much weight in the WMAcarries almost twice as much weight in the WMA

(.60) as it does in the MA (.33).(.60) as it does in the MA (.33).


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EXPONENTIAL SMOOTHINGEXPONENTIAL SMOOTHINGEXPONENTIAL SMOOTHINGEXPONENTIAL SMOOTHING

It takes the forecast for the prior period andIt takes the forecast for the prior period andadds an adjustment to obtain the forecast for theadds an adjustment to obtain the forecast for the

next period.next period.

This adjustment is a proportion of the forecastThis adjustment is a proportion of the forecasterror in the prior period and computed byerror in the prior period and computed by

multiplying the forecast error in the prior periodmultiplying the forecast error in the prior period

by a constant that is between zero and one.by a constant that is between zero and one.

This constant (This constant () is called the smoothing) is called the smoothing

constant. Its value is estimated or derived.constant. Its value is estimated or derived.

E l C l C ll CE l C l C ll CE l C l C ll CE l C l C ll C


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Exponential SmoothingExponential SmoothingIf a smoothing constant value of .25 isIf a smoothing constant value of .25 is

used and the exponential smoothingused and the exponential smoothing

forecast for Day 11 was 180.76 calls, whatforecast for Day 11 was 180.76 calls, what

is the exponential smoothing forecast foris the exponential smoothing forecast for

Day 13?Day 13?

FF1212 = 180.76 + .25(198= 180.76 + .25(198 180.76) = 185.07180.76) = 185.07

FF1313 = 185.07 + .25(159= 185.07 + .25(159 185.07) = 178.55185.07) = 178.55

E l C l C ll CE l C l C ll CE l C l C ll CE l C l C ll C


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Forecast AccuracyForecast Accuracy based on MADbased on MAD(mean absolute deviation) :(mean absolute deviation) :

Which forecasting method (Which forecasting method (the AP = 3the AP = 3

moving averagemoving average oror thethe EE = .= .2525(smoothing constant),(smoothing constant), exponential smoothingexponential smoothing))

is preferred, based on the MAD over the mostis preferred, based on the MAD over the most

recent 9 days? (Assume that the exponentialrecent 9 days? (Assume that the exponential

smoothing forecast for Day 3 is the same assmoothing forecast for Day 3 is the same as

the actual call volume.)the actual call volume.)

E l C t l C ll C tE l C t l C ll C tE l C t l C ll C tE l C t l C ll C t


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AP = 3AP = 3 EE = .25= .25DayDay CallsCalls Forec.Forec. |Error||Error| Forec.Forec. |Error||Error|

44 161161 187.3187.3 26.326.3 186.0186.0 25.025.055 173173 188.0188.0 15.015.0 179.8179.8 6.86.8

66 157157 173.3173.3 16.316.3 178.1178.1 21.121.177 203203 163.7163.7 39.339.3 172.8172.8 30.230.288 195195 177.7177.7 17.317.3 180.4180.4 14.614.699 188188 185.0185.0 3.03.0 184.0184.0 4.04.01010 168168 195.3195.3 27.327.3 185.0185.0 17.017.01111 198198 183.7183.7 14.314.3 180.8180.8 17.217.21212 159159 184.7184.7 25.725.7 185.1185.1 26.126.1

MADMAD 20.520.5 18.018.0

E i l S hi i h T dE i l S hi i h T dE i l S hi i h T dE i l S hi i h T d


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Exponential Smoothing with TrendExponential Smoothing with TrendExponential Smoothing with TrendExponential Smoothing with Trend

As we move towardAs we move toward mediummedium--rangerangeforecastsforecasts, trend becomes more important., trend becomes more important.

Incorporating a trend component intoIncorporating a trend component into

exponentially smoothed forecasts isexponentially smoothed forecasts is

calledcalled double exponential smoothingdouble exponential smoothing..

The estimate for the average and theThe estimate for the average and the

estimate for the trend are both smoothed.estimate for the trend are both smoothed.

E ti l S thi ith T dE ti l S thi ith T dE ti l S thi ith T dE ti l S thi ith T d


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Model FormModel Form

FTFTtt = S= Stt--11 + T+ Ttt--11

where:where:

FTFTtt = forecast with trend in period t= forecast with trend in period t

SStt--11 = smoothed forecast (average) in period t= smoothed forecast (average) in period t--11

TTtt--11 = smoothed trend estimate in period t= smoothed trend estimate in period t--11

E ti l S thi ith T dE ti l S thi ith T dE ti l S thi ith T dE ti l S thi ith T d


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Smoothing the AverageSmoothing the Average

SStt == FTFTtt ++ EE(A(Att FTFTtt))

Smoothing the TrendSmoothing the Trend

TTtt = T= Ttt--11 ++ FF((FTFTtt FTFTtt--11 -- TTtt--11))

where:where: AAtt = actual data in period t= actual data in period t

EE = smoothing constant for the average= smoothing constant for the averageFF = smoothing constant for the= smoothing constant for the trendtrend

Note :Note : Values forValues for andand are estimated orare estimated or

experimentally derived.experimentally derived.

C it i fC it i f S l tiS l ti F ti M th dF ti M th d


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Criteria forCriteria for Selecting aSelecting a Forecasting MethodForecasting Method

CostCost

AccuracyAccuracy

Data availableData available Time spanTime span

Nature of products and servicesNature of products and services

Impulse response and noiseImpulse response and noise

dampeningdampening

C it i fC it i f S l tiS l ti F ti M th dF ti M th dC it i fC it i f S l tiS l ti F ti M th dF ti M th d


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Criteria forCriteria for SelectingSelecting Forecasting MethodForecasting MethodCriteria forCriteria for SelectingSelecting Forecasting MethodForecasting Method

Cost and AccuracyCost and Accuracy There is aThere is a tradetrade--off between cost and accuracyoff between cost and accuracy;;

generally, more forecast accuracy can be obtainedgenerally, more forecast accuracy can be obtained

at a cost.at a cost. HighHigh--accuracy approaches have disadvantages:accuracy approaches have disadvantages:

Use more dataUse more data

Data are ordinarily more difficult to obtainData are ordinarily more difficult to obtain

The models are more costly to design,The models are more costly to design,implement, and operateimplement, and operate

Take longer to useTake longer to use



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Criteria forCriteria for Selecting aSelecting a Forecasting MethodForecasting MethodCriteria forCriteria for Selecting aSelecting a Forecasting MethodForecasting Method

Cost and AccuracyCost and Accuracy Low/ModerateLow/Moderate--Cost ApproachesCost Approaches

statistical models, historicalstatistical models, historical

analogies, executiveanalogies, executive--committeecommittee

consensusconsensus

HighHigh--Cost ApproachesCost Approaches complexcomplexeconometric models, Delphi, andeconometric models, Delphi, and

market researchmarket research



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Data AvailableData Available Is the necessary data available or can itIs the necessary data available or can it

be economically obtained?be economically obtained?

If the need is to forecast sales of aIf the need is to forecast sales of a newnew

product, then a customer survey mayproduct, then a customer survey may

not be practical; instead,not be practical; instead, historicalhistoricalanalogyanalogy or market research may haveor market research may have

to be used.to be used.



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Time SpanTime Span What operations resource is being forecastWhat operations resource is being forecast

and for what purpose?and for what purpose?

ShortShort--term staffing needsterm staffing needs might best bemight best beforecast with moving average or exponentialforecast with moving average or exponential

smoothing models.smoothing models.

LongLong--term factory capacityterm factory capacity needs mightneeds mightbest be predicted with regression orbest be predicted with regression or

executiveexecutive--committee consensus methods.committee consensus methods.



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Nature of Products and ServicesNature of Products and Services

Is the product/service high cost orIs the product/service high cost or

high volume?

high volume?

Where is the product/service in itsWhere is the product/service in its

life cycle?life cycle?

Does the product/service haveDoes the product/service haveseasonal demand fluctuations?seasonal demand fluctuations?



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Impulse Response andN

oise DampeningImpulse Response andN

oise Dampening An appropriate balance must beAn appropriate balance must be

achieved between:achieved between:

HowHow responsiveresponsive we want thewe want theforecasting model to be to changes inforecasting model to be to changes in

the actual demand datathe actual demand data

Our desire to suppressOur desire to suppress undesirableundesirablechance variation or noisechance variation or noise in thein the

demand datademand data

Reasons for Ineffective ForecastingReasons for Ineffective ForecastingReasons for Ineffective ForecastingReasons for Ineffective Forecasting


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Reasons for Ineffective ForecastingReasons for Ineffective ForecastingReasons for Ineffective ForecastingReasons for Ineffective Forecasting

N

ot involving a broad cross section of peopleN

ot involving a broad cross section of people Not recognizing that forecasting is integral toNot recognizing that forecasting is integral to

business planningbusiness planning

Not recognizing that forecasts will always beNot recognizing that forecasts will always be

wrongwrong

Not forecasting the right thingsNot forecasting the right things

Not selecting an appropriate forecastingNot selecting an appropriate forecasting

methodmethod

Not tracking the accuracy of the forecastingNot tracking the accuracy of the forecasting

modelsmodels

Monitoring and ControllingMonitoring and ControllingMonitoring and ControllingMonitoring and Controlling


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g gg g

a Forecasting Modela Forecasting Model

g gg g


Tracking Signal (TSTracking Signal (TS)) :: The TS measures the cumulative forecast errorThe TS measures the cumulative forecast error

over n periods in terms of MADover n periods in terms of MAD

If the forecasting model is performing well, the TSIf the forecasting model is performing well, the TS

should be around zeroshould be around zero The TS indicates the direction of the forecastingThe TS indicates the direction of the forecasting

error; if the TS iserror; if the TS is positive,positive, increase the forecasts,increase the forecasts,if the TS is negativeif the TS is negative ,, decrease the forecasts.decrease the forecasts.

n

i i1

(Actual demand - Forecast demand )

TS =MAD

i!

Monitoring and ControllingMonitoring and ControllingMonitoring and ControllingMonitoring and Controlling


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g gg g


g gg g


Tracking SignalTracking Signal The value of the TS can be used toThe value of the TS can be used to

automatically trigger newautomatically trigger new parameter valuesparameter values

of a model, thereby correcting modelof a model, thereby correcting model

performance.performance.

If the limits are set too narrow, theIf the limits are set too narrow, the

parameter values will be changed too often.parameter values will be changed too often.

If the limits are set too wide, the parameterIf the limits are set too wide, the parameter

values will not be changed often enough andvalues will not be changed often enough and

accuracy will suffer.accuracy will suffer.

Computer Software for ForecastingComputer Software for ForecastingComputer Software for ForecastingComputer Software for Forecasting


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Computer Software for ForecastingComputer Software for ForecastingComputer Software for ForecastingComputer Software for Forecasting

Examples of computer software with forecastingExamples of computer software with forecastingcapabilitiescapabilities

Forecast ProForecast Pro

AutoboxAutobox

SmartForecastsSmartForecasts for Windowsfor Windows

SASSAS

SPSSSPSS

SAPSAP

POMPOM SoftwareSoftware LibaryLibary

Primarily forPrimarily for

forecastingforecasting

HaveHave

ForecastingForecastingmodulesmodules

Forecasting in Small BusinessesForecasting in Small BusinessesForecasting in Small BusinessesForecasting in Small Businesses


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gg

and Startand Start--Up VenturesUp Ventures

gg

and Startand Start--Up VenturesUp Ventures

Forecasting for these businesses canForecasting for these businesses can

be difficult for the following reasons:be difficult for the following reasons: Not enough personnel with the time to forecastNot enough personnel with the time to forecast

Personnel lack the necessary skills to develop goodPersonnel lack the necessary skills to develop good

forecastsforecasts

Such businesses are not dataSuch businesses are not data--rich environmentsrich environments

Forecasting for new products/services is alwaysForecasting for new products/services is alwaysdifficult, even for the experienced forecasterdifficult, even for the experienced forecaster

Sources of Forecasting Data and HelpSources of Forecasting Data and HelpSources of Forecasting Data and HelpSources of Forecasting Data and Help


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Sources of Forecasting Data and HelpSources of Forecasting Data and HelpSources of Forecasting Data and HelpSources of Forecasting Data and Help

Government agencies at theGovernment agencies at thelocal, regional, state, andlocal, regional, state, and

federal levelsfederal levels Industry associationsIndustry associations

Consulting companiesConsulting companies

Some Specific Forecasting DataSome Specific Forecasting DataSome Specific Forecasting DataSome Specific Forecasting Data


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Some Specific Forecasting DataSome Specific Forecasting DataSome Specific Forecasting DataSome Specific Forecasting Data

Consumer Confidence IndexConsumer Confidence Index Consumer Price Index (CPI)Consumer Price Index (CPI)

Gross Domestic Product (GDP)Gross Domestic Product (GDP)

Housing StartsHousing Starts Index ofLeading Economic IndicatorsIndex ofLeading Economic Indicators

Personal Income and ConsumptionPersonal Income and Consumption

Producer Price Index (PPI)Producer Price Index (PPI)

PurchasingPurchasing ManagersManagers IndexIndex

Retail SalesRetail Sales

WrapWrap Up: WorldUp: World Class PracticeClass Practice


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WrapWrap--Up: WorldUp: World--Class PracticeClass Practice

Predisposed to have effective methods ofPredisposed to have effective methods offorecasting because they have exceptionalforecasting because they have exceptional

longlong--range business planningrange business planning

Formal forecasting effortFormal forecasting effort

Develop methods to monitor theDevelop methods to monitor the

performance of their forecasting modelsperformance of their forecasting models

Do not overlook the short run.... excellentDo not overlook the short run.... excellent

short range forecasts as wellshort range forecasts as well

End of Module 2End of Module 2


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02 demand forecasting

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