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© 2008 Prentice Hall, Inc. 4 – 1

Operations ManagementOperations ManagementChapter 4 Chapter 4 ––ForecastingForecasting

PowerPoint presentation to accompanyPowerPoint presentation to accompanyHeizer/Render Heizer/Render Principles of Operations Management, 7ePrinciples of Operations Management, 7eOperations Management, 9e Operations Management, 9e


OutlineOutline

Global Company Profile: Disney Global Company Profile: Disney WorldWorldWhat Is Forecasting?What Is Forecasting?

Forecasting Time HorizonsForecasting Time HorizonsThe Influence of Product Life CycleThe Influence of Product Life Cycle

Types Of ForecastsTypes Of Forecasts


Outline Outline –– ContinuedContinuedThe Strategic Importance of The Strategic Importance of ForecastingForecasting

Human ResourcesHuman ResourcesCapacityCapacitySupply Chain ManagementSupply Chain Management

Seven Steps in the Forecasting Seven Steps in the Forecasting SystemSystem


Outline Outline –– ContinuedContinuedForecasting ApproachesForecasting Approaches

Overview of Qualitative MethodsOverview of Qualitative MethodsOverview of Quantitative MethodsOverview of Quantitative Methods


Outline Outline –– ContinuedContinuedTimeTime--Series ForecastingSeries Forecasting

Decomposition of a Time SeriesDecomposition of a Time SeriesNaive ApproachNaive ApproachMoving AveragesMoving AveragesExponential SmoothingExponential SmoothingExponential Smoothing with Trend Exponential Smoothing with Trend AdjustmentAdjustmentTrend ProjectionsTrend ProjectionsSeasonal Variations in DataSeasonal Variations in DataCyclical Variations in DataCyclical Variations in Data


Outline Outline –– ContinuedContinuedAssociative Forecasting Methods: Associative Forecasting Methods: Regression and Correlation Regression and Correlation AnalysisAnalysis

Using Regression Analysis for Using Regression Analysis for ForecastingForecastingStandard Error of the EstimateStandard Error of the EstimateCorrelation Coefficients for Correlation Coefficients for Regression LinesRegression LinesMultipleMultiple--Regression AnalysisRegression Analysis


Outline Outline –– ContinuedContinuedMonitoring and Controlling Monitoring and Controlling ForecastsForecasts

Adaptive SmoothingAdaptive SmoothingFocus ForecastingFocus Forecasting

Forecasting In The Service SectorForecasting In The Service Sector


Learning ObjectivesLearning ObjectivesWhen you complete this chapter you When you complete this chapter you should be able to :should be able to :

Understand the three time horizons and Understand the three time horizons and which models apply for each usewhich models apply for each useExplain when to use each of the four Explain when to use each of the four qualitative modelsqualitative modelsApply the naive, moving average, Apply the naive, moving average, exponential smoothing, and trend exponential smoothing, and trend methodsmethods


Learning ObjectivesLearning ObjectivesWhen you complete this chapter you When you complete this chapter you should be able to :should be able to :

Compute three measures of forecast Compute three measures of forecast accuracyaccuracyDevelop seasonal indexesDevelop seasonal indexesConduct a regression and correlation Conduct a regression and correlation analysisanalysisUse a tracking signalUse a tracking signal


Forecasting at Disney WorldForecasting at Disney World

Global portfolio includes parks in Hong Global portfolio includes parks in Hong Kong, Paris, Tokyo, Orlando, and Kong, Paris, Tokyo, Orlando, and AnaheimAnaheimRevenues are derived from people Revenues are derived from people –– how how many visitors and how they spend their many visitors and how they spend their moneymoneyDaily management report contains only Daily management report contains only the forecast and actual attendance at the forecast and actual attendance at each parkeach park



Disney generates daily, weekly, monthly, Disney generates daily, weekly, monthly, annual, and 5annual, and 5--year forecastsyear forecastsForecast used by labor management, Forecast used by labor management, maintenance, operations, finance, and maintenance, operations, finance, and park schedulingpark schedulingForecast used to adjust opening times, Forecast used to adjust opening times, rides, shows, staffing levels, and guests rides, shows, staffing levels, and guests admittedadmitted



20% of customers come from outside the 20% of customers come from outside the USAUSAEconomic model includes gross Economic model includes gross domestic product, crossdomestic product, cross--exchange rates, exchange rates, arrivals into the USAarrivals into the USAA staff of 35 analysts and 70 field people A staff of 35 analysts and 70 field people survey 1 million park guests, employees, survey 1 million park guests, employees, and travel professionals each yearand travel professionals each year



Inputs to the forecasting model include Inputs to the forecasting model include airline specials, Federal Reserve airline specials, Federal Reserve policies, Wall Street trends, policies, Wall Street trends, vacation/holiday schedules for 3,000 vacation/holiday schedules for 3,000 school districts around the worldschool districts around the worldAverage forecast error for the 5Average forecast error for the 5--year year forecast is 5%forecast is 5%Average forecast error for annual Average forecast error for annual forecasts is between 0% and 3%forecasts is between 0% and 3%


What is Forecasting?What is Forecasting?

Process of Process of predicting a future predicting a future eventeventUnderlying basis of Underlying basis of all business all business decisionsdecisions

ProductionProductionInventoryInventoryPersonnelPersonnelFacilitiesFacilities

??


ShortShort--range forecastrange forecastUp to 1 year, generally less than 3 monthsUp to 1 year, generally less than 3 monthsPurchasing, job scheduling, workforce Purchasing, job scheduling, workforce levels, job assignments, production levelslevels, job assignments, production levels

MediumMedium--range forecastrange forecast3 months to 3 years3 months to 3 yearsSales and production planning, budgetingSales and production planning, budgeting

LongLong--range forecastrange forecast33++ yearsyearsNew product planning, facility location, New product planning, facility location, research and developmentresearch and development

Forecasting Time HorizonsForecasting Time Horizons


Distinguishing DifferencesDistinguishing Differences

Medium/long rangeMedium/long range forecasts deal with forecasts deal with more comprehensive issues and support more comprehensive issues and support management decisions regarding management decisions regarding planning and products, plants and planning and products, plants and processesprocessesShortShort--termterm forecasting usually employs forecasting usually employs different methodologies than longerdifferent methodologies than longer--term term forecastingforecastingShortShort--termterm forecasts tend to be more forecasts tend to be more accurate than longeraccurate than longer--term forecaststerm forecasts


Influence of Product Life Influence of Product Life CycleCycle

Introduction and growth require longer Introduction and growth require longer forecasts than maturity and declineforecasts than maturity and declineAs product passes through life cycle, As product passes through life cycle, forecasts are useful in projectingforecasts are useful in projecting

Staffing levelsStaffing levelsInventory levelsInventory levelsFactory capacityFactory capacity

Introduction – Growth – Maturity – Decline


Product Life CycleProduct Life Cycle

Best period to Best period to increase market increase market shareshare

R&D engineering is R&D engineering is criticalcritical

Practical to change Practical to change price or quality price or quality imageimage

Strengthen nicheStrengthen niche

Poor time to Poor time to change image, change image, price, or qualityprice, or quality

Competitive costs Competitive costs become criticalbecome criticalDefend market Defend market positionposition

Cost control Cost control criticalcritical

Introduction Growth Maturity Decline

Com

pany

Str

ateg

y/Is

sues

Com

pany

Str

ateg

y/Is

sues

Figure 2.5Figure 2.5

Internet search enginesInternet search engines

SalesSales

Xbox 360Xbox 360

DriveDrive--through through restaurantsrestaurants

CDCD--ROMsROMs

3 1/23 1/2””Floppy Floppy disksdisks

LCD & plasma TVsLCD & plasma TVsAnalog TVsAnalog TVs

iPodsiPods


Product Life CycleProduct Life Cycle

Product design Product design and and development development criticalcriticalFrequent Frequent product and product and process design process design changeschangesShort production Short production runsrunsHigh production High production costscostsLimited modelsLimited modelsAttention to Attention to qualityquality

Introduction Growth Maturity Decline

OM

Str

ateg

y/Is

sues

OM

Str

ateg

y/Is

sues

Forecasting Forecasting criticalcriticalProduct and Product and process process reliabilityreliabilityCompetitive Competitive product product improvements improvements and optionsand optionsIncrease capacityIncrease capacityShift toward Shift toward product focusproduct focusEnhance Enhance distributiondistribution

StandardizationStandardizationLess rapid Less rapid product changes product changes –– more minor more minor changeschangesOptimum Optimum capacitycapacityIncreasing Increasing stability of stability of processprocessLong production Long production runsrunsProduct Product improvement improvement and cost cuttingand cost cutting

Little product Little product differentiationdifferentiationCost Cost minimizationminimizationOvercapacity Overcapacity in the in the industryindustryPrune line to Prune line to eliminate eliminate items not items not returning returning good margingood marginReduce Reduce capacitycapacity



Types of ForecastsTypes of Forecasts

Economic forecastsEconomic forecastsAddress business cycle Address business cycle –– inflation rate, inflation rate, money supply, housing starts, etc.money supply, housing starts, etc.

Technological forecastsTechnological forecastsPredict rate of technological progressPredict rate of technological progressImpacts development of new productsImpacts development of new products

Demand forecastsDemand forecastsPredict sales of existing products and Predict sales of existing products and servicesservices


Strategic Importance of Strategic Importance of ForecastingForecasting

Human Resources Human Resources –– Hiring, training, Hiring, training, laying off workerslaying off workersCapacity Capacity –– Capacity shortages can Capacity shortages can result in undependable delivery, loss result in undependable delivery, loss of customers, loss of market shareof customers, loss of market shareSupply Chain Management Supply Chain Management –– Good Good supplier relations and price supplier relations and price advantagesadvantages


Seven Steps in ForecastingSeven Steps in ForecastingDetermine the use of the forecastDetermine the use of the forecastSelect the items to be forecastedSelect the items to be forecastedDetermine the time horizon of the Determine the time horizon of the forecastforecastSelect the forecasting model(s)Select the forecasting model(s)Gather the dataGather the dataMake the forecastMake the forecastValidate and implement resultsValidate and implement results


The Realities!The Realities!

Forecasts are seldom perfectForecasts are seldom perfectMost techniques assume an Most techniques assume an underlying stability in the systemunderlying stability in the systemProduct family and aggregated Product family and aggregated forecasts are more accurate than forecasts are more accurate than individual product forecastsindividual product forecasts


Forecasting ApproachesForecasting Approaches

Used when situation is vague Used when situation is vague and little data existand little data exist

New productsNew productsNew technologyNew technology

Involves intuition, experienceInvolves intuition, experiencee.g., forecasting sales on Internete.g., forecasting sales on Internet

Qualitative MethodsQualitative Methods


Forecasting ApproachesForecasting Approaches

Used when situation is Used when situation is ‘‘stablestable’’ and and historical data existhistorical data exist

Existing productsExisting productsCurrent technologyCurrent technology

Involves mathematical techniquesInvolves mathematical techniquese.g., forecasting sales of color e.g., forecasting sales of color televisionstelevisions

Quantitative MethodsQuantitative Methods


Overview of Qualitative Overview of Qualitative MethodsMethods

Jury of executive opinionJury of executive opinionPool opinions of highPool opinions of high--level experts, level experts, sometimes augment by statistical sometimes augment by statistical modelsmodels

Delphi methodDelphi methodPanel of experts, queried iterativelyPanel of experts, queried iteratively


Overview of Qualitative Overview of Qualitative MethodsMethods

Sales force compositeSales force compositeEstimates from individual Estimates from individual salespersons are reviewed for salespersons are reviewed for reasonableness, then aggregated reasonableness, then aggregated

Consumer Market SurveyConsumer Market SurveyAsk the customerAsk the customer


Involves small group of highInvolves small group of high--level experts level experts and managersand managersGroup estimates demand by working Group estimates demand by working togethertogetherCombines managerial experience with Combines managerial experience with statistical modelsstatistical modelsRelatively quickRelatively quick‘‘GroupGroup--thinkthink’’disadvantagedisadvantage

Jury of Executive OpinionJury of Executive Opinion


Sales Force CompositeSales Force Composite

Each salesperson projects his or Each salesperson projects his or her salesher salesCombined at district and national Combined at district and national levelslevelsSales reps know customersSales reps know customers’’ wantswantsTends to be overly optimisticTends to be overly optimistic


Delphi MethodDelphi MethodIterative group Iterative group process, process, continues until continues until consensus is consensus is reachedreached3 types of 3 types of participantsparticipants

Decision makersDecision makersStaffStaffRespondentsRespondents

Staff(Administering

survey)

Decision Makers(Evaluate

responses and make decisions)

Respondents(People who can make valuable

judgments)


Consumer Market SurveyConsumer Market Survey

Ask customers about purchasing Ask customers about purchasing plansplansWhat consumers say, and what What consumers say, and what they actually do are often differentthey actually do are often differentSometimes difficult to answerSometimes difficult to answer


Overview of Quantitative Overview of Quantitative ApproachesApproaches

1.1. Naive approachNaive approach2.2. Moving averagesMoving averages3.3. Exponential Exponential

smoothingsmoothing4.4. Trend projectionTrend projection5.5. Linear regressionLinear regression

TimeTime--Series Series ModelsModels

Associative Associative ModelModel


Set of evenly spaced numerical dataSet of evenly spaced numerical dataObtained by observing response Obtained by observing response variable at regular time periodsvariable at regular time periods

Forecast based only on past values, Forecast based only on past values, no other variables importantno other variables important

Assumes that factors influencing Assumes that factors influencing past and present will continue past and present will continue influence in futureinfluence in future

Time Series ForecastingTime Series Forecasting


Trend

Seasonal

Cyclical

Random

Time Series ComponentsTime Series Components


Components of DemandComponents of DemandD

eman

d fo

r pro

duct

or s

ervi

ce

| | | |1 2 3 4

Year

Average demand over four years

Seasonal peaks

Trend component

Actual demand

Random variation



Persistent, overall upward or Persistent, overall upward or downward patterndownward patternChanges due to population, Changes due to population, technology, age, culture, etc.technology, age, culture, etc.Typically several years Typically several years duration duration

Trend ComponentTrend Component


Regular pattern of up and Regular pattern of up and down fluctuationsdown fluctuationsDue to weather, customs, etc.Due to weather, customs, etc.Occurs within a single year Occurs within a single year

Seasonal ComponentSeasonal Component

Number ofPeriod Length SeasonsWeek Day 7Month Week 4-4.5Month Day 28-31Year Quarter 4Year Month 12Year Week 52


Repeating up and down movementsRepeating up and down movementsAffected by business cycle, political, Affected by business cycle, political, and economic factorsand economic factorsMultiple years durationMultiple years durationOften causal or Often causal or associative associative relationshipsrelationships

Cyclical ComponentCyclical Component

00 55 1010 1515 2020


Erratic, unsystematic, Erratic, unsystematic, ‘‘residualresidual’’fluctuationsfluctuationsDue to random variation or Due to random variation or unforeseen eventsunforeseen eventsShort duration and Short duration and nonrepeating nonrepeating

Random ComponentRandom Component

MM TT WW TT FF


Naive ApproachNaive Approach

Assumes demand in next Assumes demand in next period is the same as period is the same as demand in most recent perioddemand in most recent period

e.g., If January sales were 68, then e.g., If January sales were 68, then February sales will be 68February sales will be 68

Sometimes cost effective and Sometimes cost effective and efficientefficientCan be good starting pointCan be good starting point


MA is a series of arithmetic means MA is a series of arithmetic means Used if little or no trendUsed if little or no trendUsed often for smoothingUsed often for smoothing

Provides overall impression of data Provides overall impression of data over timeover time

Moving Average MethodMoving Average Method

Moving average =Moving average = ∑∑ demand in previous n periodsdemand in previous n periodsnn


JanuaryJanuary 1010FebruaryFebruary 1212MarchMarch 1313AprilApril 1616MayMay 1919JuneJune 2323JulyJuly 2626

ActualActual 33--MonthMonthMonthMonth Shed SalesShed Sales Moving AverageMoving Average

(12 + 13 + 16)/3 = 13 (12 + 13 + 16)/3 = 13 22//33(13 + 16 + 19)/3 = 16(13 + 16 + 19)/3 = 16(16 + 19 + 23)/3 = 19 (16 + 19 + 23)/3 = 19 11//33

Moving Average ExampleMoving Average Example

101012121313

((1010 + + 1212 + + 1313)/3 = 11 )/3 = 11 22//33


Graph of Moving AverageGraph of Moving Average

| | | | | | | | | | | |JJ FF MM AA MM JJ JJ AA SS OO NN DD

Shed

Sal

esSh

ed S

ales

30 30 –28 28 –26 26 –24 24 –22 22 –20 20 –18 18 –16 16 –14 14 –12 12 –10 10 –

Actual Actual SalesSales

Moving Moving Average Average ForecastForecast


Used when trend is present Used when trend is present Older data usually less importantOlder data usually less important

Weights based on experience and Weights based on experience and intuitionintuition

Weighted Moving AverageWeighted Moving Average

WeightedWeightedmoving averagemoving average ==

∑∑ ((weight for period nweight for period n))x x ((demand in period ndemand in period n))

∑∑ weightsweights


JanuaryJanuary 1010FebruaryFebruary 1212MarchMarch 1313AprilApril 1616MayMay 1919JuneJune 2323JulyJuly 2626

ActualActual 33--Month WeightedMonth WeightedMonthMonth Shed SalesShed Sales Moving AverageMoving Average

[(3 x 16) + (2 x 13) + (12)]/6 = 14[(3 x 16) + (2 x 13) + (12)]/6 = 1411//33[(3 x 19) + (2 x 16) + (13)]/6 = 17[(3 x 19) + (2 x 16) + (13)]/6 = 17[(3 x 23) + (2 x 19) + (16)]/6 = 20[(3 x 23) + (2 x 19) + (16)]/6 = 2011//22

Weighted Moving AverageWeighted Moving Average

101012121313

[(3 x [(3 x 1313) + (2 x ) + (2 x 1212) + () + (1010)]/6 = 12)]/6 = 1211//66

Weights Applied Period3 Last month2 Two months ago1 Three months ago6 Sum of weights


Increasing n smooths the forecast Increasing n smooths the forecast but makes it less sensitive to but makes it less sensitive to changeschangesDo not forecast trends wellDo not forecast trends wellRequire extensive historical dataRequire extensive historical data

Potential Problems WithPotential Problems WithMoving AverageMoving Average


Moving Average And Moving Average And Weighted Moving AverageWeighted Moving Average

30 30 –

25 25 –

20 20 –

15 15 –

10 10 –

5 5 –

Sale

s de

man

dSa

les

dem

and

| | | | | | | | | | | |JJ FF MM AA MM JJ JJ AA SS OO NN DD

Actual Actual salessales

Moving Moving averageaverage

Weighted Weighted moving moving averageaverage



Form of weighted moving averageForm of weighted moving averageWeights decline exponentiallyWeights decline exponentiallyMost recent data weighted mostMost recent data weighted most

Requires smoothing constant Requires smoothing constant ((αα))Ranges from 0 to 1Ranges from 0 to 1Subjectively chosenSubjectively chosen

Involves little record keeping of past Involves little record keeping of past datadata

Exponential SmoothingExponential Smoothing


Exponential SmoothingExponential Smoothing

New forecast =New forecast = Last periodLast period’’s forecasts forecast+ + αα ((Last periodLast period’’s actual demand s actual demand

–– Last periodLast period’’s forecasts forecast))

FFtt = F= Ft t –– 11 ++ αα((AAt t –– 11 -- FFt t –– 11))

wherewhere FFtt == new forecastnew forecastFFt t –– 11 == previous forecastprevious forecast

αα == smoothing (or weighting) smoothing (or weighting) constant constant (0 (0 ≤≤ αα ≤≤ 1)1)


Exponential Smoothing Exponential Smoothing ExampleExample

Predicted demand Predicted demand = 142= 142 Ford MustangsFord MustangsActual demand Actual demand = 153= 153Smoothing constant Smoothing constant αα = .20= .20




New forecastNew forecast = 142 + .2(153 = 142 + .2(153 –– 142)142)




New forecastNew forecast = 142 + .2(153 = 142 + .2(153 –– 142)142)= 142 + 2.2= 142 + 2.2= 144.2 = 144.2 ≈≈ 144 cars144 cars


Effect ofEffect ofSmoothing ConstantsSmoothing Constants

Weight Assigned toWeight Assigned toMostMost 2nd Most2nd Most 3rd Most3rd Most 4th Most4th Most 5th Most5th Most

RecentRecent RecentRecent RecentRecent RecentRecent RecentRecentSmoothingSmoothing PeriodPeriod PeriodPeriod PeriodPeriod PeriodPeriod PeriodPeriodConstantConstant ((αα)) αα(1 (1 -- αα)) αα(1 (1 -- αα))22 αα(1 (1 -- αα))33 αα(1 (1 -- αα))44

αα = .1= .1 .1.1 .09.09 .081.081 .073.073 .066.066

αα = .5= .5 .5.5 .25.25 .125.125 .063.063 .031.031


Impact of Different Impact of Different αα

225 225 –

200 200 –

175 175 –

150 150 – | | | | | | | | |11 22 33 44 55 66 77 88 99

QuarterQuarter

Dem

and

Dem

and

αα = .1= .1

Actual Actual demanddemand

αα = .5= .5


Impact of Different Impact of Different αα

225 225 –

200 200 –

175 175 –

150 150 – | | | | | | | | |11 22 33 44 55 66 77 88 99

QuarterQuarter

Dem

and

Dem

and

αα = .1= .1

Actual Actual demanddemand

αα = .5= .5Chose high values of Chose high values of ααwhen underlying average when underlying average is likely to changeis likely to changeChoose low values of Choose low values of ααwhen underlying average when underlying average is stableis stable


Choosing Choosing αα

The objective is to obtain the most The objective is to obtain the most accurate forecast no matter the accurate forecast no matter the techniquetechnique

We generally do this by selecting the We generally do this by selecting the model that gives us the lowest forecast model that gives us the lowest forecast errorerror

Forecast errorForecast error = Actual demand = Actual demand -- Forecast valueForecast value

= A= Att -- FFtt


Common Measures of ErrorCommon Measures of Error

Mean Absolute Deviation Mean Absolute Deviation ((MADMAD))

MAD =MAD =∑∑ |Actual |Actual -- Forecast|Forecast|

nn

Mean Squared Error Mean Squared Error ((MSEMSE))

MSE =MSE =∑∑ ((Forecast ErrorsForecast Errors))22

nn


Common Measures of ErrorCommon Measures of Error

Mean Absolute Percent Error Mean Absolute Percent Error ((MAPEMAPE))

MAPE =MAPE =∑∑100100|Actual|Actualii -- ForecastForecastii|/Actual|/Actualii

nn

nn

i i = 1= 1


Comparison of Forecast Comparison of Forecast Error Error

RoundedRounded AbsoluteAbsolute RoundedRounded AbsoluteAbsoluteActualActual ForecastForecast DeviationDeviation ForecastForecast DeviationDeviation

TonnageTonnage withwith forfor withwith forforQuarterQuarter UnloadedUnloaded αα = .10= .10 αα = .10= .10 αα = .50= .50 αα = .50= .50

11 180180 175175 5.005.00 175175 5.005.0022 168168 175.5175.5 7.507.50 177.50177.50 9.509.5033 159159 174.75174.75 15.7515.75 172.75172.75 13.7513.7544 175175 173.18173.18 1.821.82 165.88165.88 9.129.1255 190190 173.36173.36 16.6416.64 170.44170.44 19.5619.5666 205205 175.02175.02 29.9829.98 180.22180.22 24.7824.7877 180180 178.02178.02 1.981.98 192.61192.61 12.6112.6188 182182 178.22178.22 3.783.78 186.30186.30 4.304.30

82.4582.45 98.6298.62





11 180180 175175 5.005.00 175175 5.005.0022 168168 175.5175.5 7.507.50 177.50177.50 9.509.5033 159159 174.75174.75 15.7515.75 172.75172.75 13.7513.7544 175175 173.18173.18 1.821.82 165.88165.88 9.129.1255 190190 173.36173.36 16.6416.64 170.44170.44 19.5619.5666 205205 175.02175.02 29.9829.98 180.22180.22 24.7824.7877 180180 178.02178.02 1.981.98 192.61192.61 12.6112.6188 182182 178.22178.22 3.783.78 186.30186.30 4.304.30

82.4582.45 98.6298.62

MAD =∑ |deviations|

n

= 82.45/8 = 10.31For α = .10

= 98.62/8 = 12.33For α = .50





11 180180 175175 5.005.00 175175 5.005.0022 168168 175.5175.5 7.507.50 177.50177.50 9.509.5033 159159 174.75174.75 15.7515.75 172.75172.75 13.7513.7544 175175 173.18173.18 1.821.82 165.88165.88 9.129.1255 190190 173.36173.36 16.6416.64 170.44170.44 19.5619.5666 205205 175.02175.02 29.9829.98 180.22180.22 24.7824.7877 180180 178.02178.02 1.981.98 192.61192.61 12.6112.6188 182182 178.22178.22 3.783.78 186.30186.30 4.304.30

82.4582.45 98.6298.62MADMAD 10.3110.31 12.3312.33

= 1,526.54/8 = 190.82For α = .10

= 1,561.91/8 = 195.24For α = .50

MSE =∑ (forecast errors)2

n





11 180180 175175 5.005.00 175175 5.005.0022 168168 175.5175.5 7.507.50 177.50177.50 9.509.5033 159159 174.75174.75 15.7515.75 172.75172.75 13.7513.7544 175175 173.18173.18 1.821.82 165.88165.88 9.129.1255 190190 173.36173.36 16.6416.64 170.44170.44 19.5619.5666 205205 175.02175.02 29.9829.98 180.22180.22 24.7824.7877 180180 178.02178.02 1.981.98 192.61192.61 12.6112.6188 182182 178.22178.22 3.783.78 186.30186.30 4.304.30

82.4582.45 98.6298.62MADMAD 10.3110.31 12.3312.33MSEMSE 190.82190.82 195.24195.24

= 44.75/8 = 5.59%For α = .10

= 54.05/8 = 6.76%For α = .50

MAPE =∑100|deviationi|/actuali

n

n

i = 1





11 180180 175175 5.005.00 175175 5.005.0022 168168 175.5175.5 7.507.50 177.50177.50 9.509.5033 159159 174.75174.75 15.7515.75 172.75172.75 13.7513.7544 175175 173.18173.18 1.821.82 165.88165.88 9.129.1255 190190 173.36173.36 16.6416.64 170.44170.44 19.5619.5666 205205 175.02175.02 29.9829.98 180.22180.22 24.7824.7877 180180 178.02178.02 1.981.98 192.61192.61 12.6112.6188 182182 178.22178.22 3.783.78 186.30186.30 4.304.30

82.4582.45 98.6298.62MADMAD 10.3110.31 12.3312.33MSEMSE 190.82190.82 195.24195.24MAPEMAPE 5.59%5.59% 6.76%6.76%


Exponential Smoothing with Exponential Smoothing with Trend AdjustmentTrend Adjustment

When a trend is present, exponential When a trend is present, exponential smoothing must be modifiedsmoothing must be modified

Forecast Forecast including including ((FITFITtt)) = = trendtrend

ExponentiallyExponentially ExponentiallyExponentiallysmoothed smoothed ((FFtt)) ++ ((TTtt)) smoothedsmoothedforecastforecast trendtrend


Exponential Smoothing with Exponential Smoothing with Trend AdjustmentTrend Adjustment

FFtt = = αα((AAtt -- 11) + (1 ) + (1 -- αα)()(FFtt -- 11 + + TTtt -- 11))

TTtt = = ββ((FFtt -- FFtt -- 11) + (1 ) + (1 -- ββ))TTtt -- 11

Step 1: Compute FStep 1: Compute Ftt

Step 2: Compute TStep 2: Compute Ttt

Step 3: Calculate the forecast FITStep 3: Calculate the forecast FITtt == FFtt + + TTtt


Exponential Smoothing with Exponential Smoothing with Trend Adjustment ExampleTrend Adjustment Example

ForecastForecastActualActual SmoothedSmoothed SmoothedSmoothed IncludingIncluding

MonthMonth((tt)) Demand Demand ((AAtt)) Forecast, FForecast, Ftt Trend, TTrend, Ttt Trend, FITTrend, FITtt

11 1212 1111 22 13.0013.0022 171733 202044 191955 242466 212177 313188 282899 3636

1010

Table 4.1Table 4.1





11 1212 1111 22 13.0013.0022 171733 202044 191955 242466 212177 313188 282899 3636

1010

Table 4.1Table 4.1

F2 = αA1 + (1 - α)(F1 + T1)F2 = (.2)(12) + (1 - .2)(11 + 2)

= 2.4 + 10.4 = 12.8 units

Step 1: Forecast for Month 2





11 1212 1111 22 13.0013.0022 1717 12.8012.8033 202044 191955 242466 212177 313188 282899 3636

1010

Table 4.1Table 4.1

T2 = β(F2 - F1) + (1 - β)T1

T2 = (.4)(12.8 - 11) + (1 - .4)(2)= .72 + 1.2 = 1.92 units

Step 2: Trend for Month 2





11 1212 1111 22 13.0013.0022 1717 12.8012.80 1.921.9233 202044 191955 242466 212177 313188 282899 3636

1010

Table 4.1Table 4.1

FIT2 = F2 + T1

FIT2 = 12.8 + 1.92= 14.72 units

Step 3: Calculate FIT for Month 2





11 1212 1111 22 13.0013.0022 1717 12.8012.80 1.921.92 14.7214.7233 202044 191955 242466 212177 313188 282899 3636

1010

Table 4.1Table 4.1

15.1815.18 2.102.10 17.2817.2817.8217.82 2.322.32 20.1420.1419.9119.91 2.232.23 22.1422.1422.5122.51 2.382.38 24.8924.8924.1124.11 2.072.07 26.1826.1827.1427.14 2.452.45 29.5929.5929.2829.28 2.322.32 31.6031.6032.4832.48 2.682.68 35.1635.16




| | | | | | | | |11 22 33 44 55 66 77 88 99

Time (month)Time (month)

Prod

uct d

eman

dPr

oduc

t dem

and

35 35 –

30 30 –

25 25 –

20 20 –

15 15 –

10 10 –

5 5 –

0 0 –

Actual demand Actual demand ((AAtt))

Forecast including trend Forecast including trend ((FITFITtt))withwith αα = .2 = .2 andand ββ = .4= .4


Trend ProjectionsTrend Projections

Fitting a trend line to historical data points Fitting a trend line to historical data points to project into the medium to longto project into the medium to long--rangerange

Linear trends can be found using the least Linear trends can be found using the least squares techniquesquares technique

y y = = a a + + bxbx^̂

where ywhere y = computed value of the variable to = computed value of the variable to be predicted (dependent variable)be predicted (dependent variable)

aa = y= y--axis interceptaxis interceptbb = slope of the regression line= slope of the regression linexx = the independent variable= the independent variable

^̂


Least Squares MethodLeast Squares Method

Time periodTime period

Valu

es o

f Dep

ende

nt V

aria

ble


DeviationDeviation11(error)(error)

DeviationDeviation55






Actual observation Actual observation (y value)(y value)

Trend line, y = a + bxTrend line, y = a + bx^̂


Least Squares MethodLeast Squares Method

Time periodTime period

Valu

es o

f Dep

ende

nt V

aria

ble









Actual observation Actual observation (y value)(y value)

Trend line, y = a + bxTrend line, y = a + bx^̂

Least squares method minimizes the sum of the

squared errors (deviations)


Least Squares MethodLeast Squares MethodEquations to calculate the regression variablesEquations to calculate the regression variables

b =b = ΣΣxy xy -- nxynxyΣΣxx22 -- nxnx22

y y = = a a + + bxbx^̂

a = y a = y -- bxbx


Least Squares ExampleLeast Squares Example

b b = = = 10.5= = = 10.544∑∑xy xy -- nxynxy∑∑xx22 -- nxnx22

3,063 3,063 -- (7)(4)(98.86)(7)(4)(98.86)140 140 -- (7)(4(7)(422))

aa = = yy -- bxbx = 98.86 = 98.86 -- 10.54(4) = 56.7010.54(4) = 56.70

TimeTime Electrical Power Electrical Power YearYear Period (x)Period (x) DemandDemand xx22 xyxy

20012001 11 7474 11 747420022002 22 7979 44 15815820032003 33 8080 99 24024020042004 44 9090 1616 36036020052005 55 105105 2525 52552520052005 66 142142 3636 85285220072007 77 122122 4949 854854

∑∑xx = 28= 28 ∑∑yy = 692= 692 ∑∑xx22 = 140= 140 ∑∑xyxy = 3,063= 3,063xx = 4= 4 yy = 98.86= 98.86



b b = = = 10.5= = = 10.544ΣΣxy xy -- nxynxyΣΣxx22 -- nxnx22

3,063 3,063 -- (7)(4)(98.86)(7)(4)(98.86)140 140 -- (7)(4(7)(422))

aa = = yy -- bxbx = 98.86 = 98.86 -- 10.54(4) = 56.7010.54(4) = 56.70

TimeTime Electrical Power Electrical Power YearYear Period (x)Period (x) DemandDemand xx22 xyxy

19991999 11 7474 11 747420002000 22 7979 44 15815820012001 33 8080 99 24024020022002 44 9090 1616 36036020032003 55 105105 2525 52552520042004 66 142142 3636 85285220052005 77 122122 4949 854854

ΣΣxx = 28= 28 ΣΣyy = 692= 692 ΣΣxx22 = 140= 140 ΣΣxyxy = 3,063= 3,063xx = 4= 4 yy = 98.86= 98.86

The trend line is

y = 56.70 + 10.54x^



| | | | | | | | |20012001 20022002 20032003 20042004 20052005 20062006 20072007 20082008 20092009

160 160 –150 150 –140 140 –130 130 –120 120 –110 110 –100 100 –90 90 –80 80 –70 70 –60 60 –50 50 –

YearYear

Pow

er d

eman

dPo

wer

dem

and

Trend line,Trend line,y y = 56.70 + 10.54x= 56.70 + 10.54x^̂


Least Squares RequirementsLeast Squares Requirements

1.1. We always plot the data to insure a We always plot the data to insure a linear relationshiplinear relationship

2.2. We do not predict time periods far We do not predict time periods far beyond the databasebeyond the database

3.3. Deviations around the least Deviations around the least squares line are assumed to be squares line are assumed to be randomrandom


Seasonal Variations In DataSeasonal Variations In Data

The multiplicative The multiplicative seasonal model seasonal model can adjust trend can adjust trend data for seasonal data for seasonal variations in variations in demanddemand


Seasonal Variations In DataSeasonal Variations In Data

1.1. Find average historical demand for each Find average historical demand for each season season

2.2. Compute the average demand over all Compute the average demand over all seasons seasons

3.3. Compute a seasonal index for each season Compute a seasonal index for each season 4.4. Estimate next yearEstimate next year’’s total demands total demand5.5. Divide this estimate of total demand by the Divide this estimate of total demand by the

number of seasons, then multiply it by the number of seasons, then multiply it by the seasonal index for that seasonseasonal index for that season

Steps in the process:Steps in the process:


Seasonal Index ExampleSeasonal Index Example

JanJan 8080 8585 105105 9090 9494FebFeb 7070 8585 8585 8080 9494MarMar 8080 9393 8282 8585 9494AprApr 9090 9595 115115 100100 9494MayMay 113113 125125 131131 123123 9494JunJun 110110 115115 120120 115115 9494JulJul 100100 102102 113113 105105 9494AugAug 8888 102102 110110 100100 9494SeptSept 8585 9090 9595 9090 9494OctOct 7777 7878 8585 8080 9494NovNov 7575 7272 8383 8080 9494DecDec 8282 7878 8080 8080 9494

DemandDemand AverageAverage AverageAverage Seasonal Seasonal MonthMonth 20052005 20062006 20072007 20052005--20072007 MonthlyMonthly IndexIndex



JanJan 8080 8585 105105 9090 9494FebFeb 7070 8585 8585 8080 9494MarMar 8080 9393 8282 8585 9494AprApr 9090 9595 115115 100100 9494MayMay 113113 125125 131131 123123 9494JunJun 110110 115115 120120 115115 9494JulJul 100100 102102 113113 105105 9494AugAug 8888 102102 110110 100100 9494SeptSept 8585 9090 9595 9090 9494OctOct 7777 7878 8585 8080 9494NovNov 7575 7272 8383 8080 9494DecDec 8282 7878 8080 8080 9494


0.9570.957

Seasonal index = average 2005-2007 monthly demand

average monthly demand

= 90/94 = .957



JanJan 8080 8585 105105 9090 9494 0.9570.957FebFeb 7070 8585 8585 8080 9494 0.8510.851MarMar 8080 9393 8282 8585 9494 0.9040.904AprApr 9090 9595 115115 100100 9494 1.0641.064MayMay 113113 125125 131131 123123 9494 1.3091.309JunJun 110110 115115 120120 115115 9494 1.2231.223JulJul 100100 102102 113113 105105 9494 1.1171.117AugAug 8888 102102 110110 100100 9494 1.0641.064SeptSept 8585 9090 9595 9090 9494 0.9570.957OctOct 7777 7878 8585 8080 9494 0.8510.851NovNov 7575 7272 8383 8080 9494 0.8510.851DecDec 8282 7878 8080 8080 9494 0.8510.851




JanJan 8080 8585 105105 9090 9494 0.9570.957FebFeb 7070 8585 8585 8080 9494 0.8510.851MarMar 8080 9393 8282 8585 9494 0.9040.904AprApr 9090 9595 115115 100100 9494 1.0641.064MayMay 113113 125125 131131 123123 9494 1.3091.309JunJun 110110 115115 120120 115115 9494 1.2231.223JulJul 100100 102102 113113 105105 9494 1.1171.117AugAug 8888 102102 110110 100100 9494 1.0641.064SeptSept 8585 9090 9595 9090 9494 0.9570.957OctOct 7777 7878 8585 8080 9494 0.8510.851NovNov 7575 7272 8383 8080 9494 0.8510.851DecDec 8282 7878 8080 8080 9494 0.8510.851


Expected annual demand = 1,200

Jan x .957 = 961,200

12

Feb x .851 = 851,200

12

Forecast for 2008



140 140 –

130 130 –

120 120 –

110 110 –

100 100 –

90 90 –

80 80 –

70 70 –| | | | | | | | | | | |JJ FF MM AA MM JJ JJ AA SS OO NN DD

TimeTime

Dem

and

Dem

and

2008 Forecast2008 Forecast2007 Demand 2007 Demand 2006 Demand2006 Demand2005 Demand2005 Demand


San Diego HospitalSan Diego Hospital

10,200 10,200 –

10,000 10,000 –

9,800 9,800 –

9,600 9,600 –

9,400 9,400 –

9,200 9,200 –

9,000 9,000 – | | | | | | | | | | | |JanJan FebFeb MarMar AprApr MayMay JuneJune JulyJuly AugAug SeptSept OctOct NovNov DecDec6767 6868 6969 7070 7171 7272 7373 7474 7575 7676 7777 7878

MonthMonth

Inpa

tient

Day

sIn

patie

nt D

ays

95309530

95519551

95739573

95949594

96169616

96379637

9659965996809680

97029702

97249724

97459745

97669766


Trend DataTrend Data



1.06 1.06 –

1.04 1.04 –

1.02 1.02 –

1.00 1.00 –

0.98 0.98 –

0.96 0.96 –

0.94 0.94 –

0.92 – | | | | | | | | | | | |JanJan FebFeb MarMar AprApr MayMay JuneJune JulyJuly AugAug SeptSept OctOct NovNov DecDec6767 6868 6969 7070 7171 7272 7373 7474 7575 7676 7777 7878

MonthMonth

Inde

x fo

r Inp

atie

nt D

ays

Inde

x fo

r Inp

atie

nt D

ays 1.041.04

1.021.021.011.01

0.990.99

1.031.031.041.04

1.001.00

0.980.98

0.970.97

0.990.99

0.970.970.960.96


Seasonal IndicesSeasonal Indices



10,200 10,200 –

10,000 10,000 –

9,800 9,800 –

9,600 9,600 –

9,400 9,400 –

9,200 9,200 –

9,000 9,000 – | | | | | | | | | | | |JanJan FebFeb MarMar AprApr MayMay JuneJune JulyJuly AugAug SeptSept OctOct NovNov DecDec6767 6868 6969 7070 7171 7272 7373 7474 7575 7676 7777 7878

MonthMonth

Inpa

tient

Day

sIn

patie

nt D

ays


99119911

92659265

97649764

95209520

96919691

94119411

99499949

97249724

95429542

93559355

1006810068

95729572

Combined Trend and Seasonal ForecastCombined Trend and Seasonal Forecast


Associative ForecastingAssociative ForecastingUsed when changes in one or more Used when changes in one or more

independent variables can be used to predict independent variables can be used to predict the changes in the dependent variablethe changes in the dependent variable

Most common technique is linear Most common technique is linear regression analysisregression analysis

We apply this technique just as we did We apply this technique just as we did in the time series examplein the time series example


Associative ForecastingAssociative Forecasting

Forecasting an outcome based on Forecasting an outcome based on predictor variables using the least squares predictor variables using the least squares techniquetechnique

y y = = a a + + bxbx^̂

where ywhere y = computed value of the variable to = computed value of the variable to be predicted (dependent variable)be predicted (dependent variable)

aa = y= y--axis interceptaxis interceptbb = slope of the regression line= slope of the regression linexx = the independent variable though to = the independent variable though to

predict the value of the dependent predict the value of the dependent variablevariable

^̂


Associative Forecasting Associative Forecasting ExampleExample

SalesSales Local PayrollLocal Payroll($ millions), y($ millions), y ($ billions), x($ billions), x

2.02.0 113.03.0 332.52.5 442.02.0 222.02.0 113.53.5 77

4.0 –

3.0 –

2.0 –

1.0 –

| | | | | | |0 1 2 3 4 5 6 7

Sale

s

Area payroll



Sales, y Payroll, x x2 xy2.0 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 = 51.5

xx = = ∑∑xx/6 = 18/6 = 3/6 = 18/6 = 3

yy = = ∑∑yy/6 = 15/6 = 2.5/6 = 15/6 = 2.5

bb = = = .25= = = .25∑∑xy xy -- nxynxy∑∑xx22 -- nxnx22

51.5 51.5 -- (6)(3)(2.5)(6)(3)(2.5)80 80 -- (6)(3(6)(322))

aa = = yy -- bbx = 2.5 x = 2.5 -- (.25)(3) = 1.75(.25)(3) = 1.75



4.0 –

3.0 –

2.0 –

1.0 –

| | | | | | |0 1 2 3 4 5 6 7

Sale

s

Area payroll

y y = 1.75 + .25= 1.75 + .25xx^̂ Sales Sales = 1.75 + .25(= 1.75 + .25(payrollpayroll))

If payroll next year If payroll next year is estimated to be is estimated to be $6$6 billion, then:billion, then:

Sales Sales = 1.75 + .25(6)= 1.75 + .25(6)SalesSales = $3,250,000= $3,250,000

3.25


Standard Error of the Standard Error of the EstimateEstimate

A forecast is just a point estimate of a A forecast is just a point estimate of a future valuefuture valueThis point is This point is actually the actually the mean of a mean of a probability probability distributiondistribution


4.0 –

3.0 –

2.0 –

1.0 –

| | | | | | |0 1 2 3 4 5 6 7

Sale

s

Area payroll

3.25



wherewhere yy == yy--value of each data pointvalue of each data pointyycc == computed value of the dependent computed value of the dependent

variable, from the regression variable, from the regression equationequation

nn == number of data pointsnumber of data points

SSy,xy,x == ∑∑((y y -- yycc))22

n n -- 22



Computationally, this equation is Computationally, this equation is considerably easier to useconsiderably easier to use

We use the standard error to set up We use the standard error to set up prediction intervals around the prediction intervals around the

point estimatepoint estimate

SSy,xy,x == ∑∑yy22 -- aa∑∑y y -- bb∑∑xyxyn n -- 22



4.0 –

3.0 –

2.0 –

1.0 –

| | | | | | |0 1 2 3 4 5 6 7

Sale

s

Area payroll

3.25

SSy,xy,x = == =∑∑yy22 -- aa∑∑y y -- bb∑∑xyxyn n -- 22

39.5 39.5 -- 1.75(15) 1.75(15) -- .25(51.5).25(51.5)6 6 -- 22

SSy,xy,x = = .306.306

The standard error The standard error of the estimate is of the estimate is $306,000$306,000 in salesin sales


How strong is the linear How strong is the linear relationship between the relationship between the variables?variables?Correlation does not necessarily Correlation does not necessarily imply causality!imply causality!Coefficient of correlation, r, Coefficient of correlation, r, measures degree of associationmeasures degree of association

Values range from Values range from --11 to to +1+1

CorrelationCorrelation


Correlation CoefficientCorrelation Coefficient

r = r = nnΣΣxyxy -- ΣΣxxΣΣy y

[[nnΣΣxx22 -- ((ΣΣxx))22][][nnΣΣyy22 -- ((ΣΣyy))22]]


Correlation CoefficientCorrelation Coefficient

r = r = nnΣΣxyxy -- ΣΣxxΣΣy y

[[nnΣΣxx22 -- ((ΣΣxx))22][][nnΣΣyy22 -- ((ΣΣyy))22]]

y

x(a) Perfect positive correlation: r = +1

y

x(b) Positive correlation: 0 < r < 1

y

x(c) No correlation: r = 0

y

x(d) Perfect negative correlation: r = -1


Coefficient of Determination, rCoefficient of Determination, r22, , measures the percent of change in measures the percent of change in y predicted by the change in xy predicted by the change in x

Values range from Values range from 00 to to 11Easy to interpretEasy to interpret

CorrelationCorrelation

For the Nodel Construction example:For the Nodel Construction example:r r = .901= .901rr22 = .81= .81


Multiple Regression Multiple Regression AnalysisAnalysis

If more than one independent variable is to be If more than one independent variable is to be used in the model, linear regression can be used in the model, linear regression can be

extended to multiple regression to extended to multiple regression to accommodate several independent variablesaccommodate several independent variables

y y = = a a + + bb11xx11 + b+ b22xx22 ……^̂

Computationally, this is quite Computationally, this is quite complex and generally done on the complex and generally done on the

computercomputer


Multiple Regression Multiple Regression AnalysisAnalysis

y y = 1.80 + .30= 1.80 + .30xx11 -- 5.05.0xx22^̂

In the Nodel example, including interest rates in In the Nodel example, including interest rates in the model gives the new equation:the model gives the new equation:

An improved correlation coefficient of r An improved correlation coefficient of r = .96= .96means this model does a better job of predicting means this model does a better job of predicting the change in construction salesthe change in construction sales

Sales Sales = 1.80 + .30(6) = 1.80 + .30(6) -- 5.0(.12) = 3.005.0(.12) = 3.00Sales Sales = $3,000,000= $3,000,000


Measures how well the forecast is Measures how well the forecast is predicting actual valuespredicting actual valuesRatio of running sum of forecast errors Ratio of running sum of forecast errors (RSFE) to mean absolute deviation (MAD)(RSFE) to mean absolute deviation (MAD)

Good tracking signal has low valuesGood tracking signal has low valuesIf forecasts are continually high or low, the If forecasts are continually high or low, the forecast has a bias errorforecast has a bias error

Monitoring and Controlling Monitoring and Controlling ForecastsForecasts

Tracking SignalTracking Signal


Monitoring and Controlling Monitoring and Controlling ForecastsForecasts

Tracking Tracking signalsignal

RSFERSFEMADMAD==

Tracking Tracking signalsignal ==

∑∑(Actual demand in (Actual demand in period i period i --

Forecast demand Forecast demand in period i)in period i)

((∑∑|Actual |Actual -- Forecast|/nForecast|/n))


Tracking SignalTracking Signal

Tracking signalTracking signal

++

00 MADsMADs

––

Upper control limitUpper control limit

Lower control limitLower control limit

TimeTime

Signal exceeding limitSignal exceeding limit

Acceptable Acceptable rangerange


Tracking Signal ExampleTracking Signal ExampleCumulativeCumulative

AbsoluteAbsolute AbsoluteAbsoluteActualActual ForecastForecast ForecastForecast ForecastForecast

QtrQtr DemandDemand DemandDemand ErrorError RSFERSFE ErrorError ErrorError MADMAD

11 9090 100100 --1010 --1010 1010 1010 10.010.022 9595 100100 --55 --1515 55 1515 7.57.533 115115 100100 +15+15 00 1515 3030 10.010.044 100100 110110 --1010 --1010 1010 4040 10.010.055 125125 110110 +15+15 +5+5 1515 5555 11.011.066 140140 110110 +30+30 +35+35 3030 8585 14.214.2


CumulativeCumulativeAbsoluteAbsolute AbsoluteAbsolute

ActualActual ForecastForecast ForecastForecast ForecastForecastQtrQtr DemandDemand DemandDemand ErrorError RSFERSFE ErrorError ErrorError MADMAD

11 9090 100100 --1010 --1010 1010 1010 10.010.022 9595 100100 --55 --1515 55 1515 7.57.533 115115 100100 +15+15 00 1515 3030 10.010.044 100100 110110 --1010 --1010 1010 4040 10.010.055 125125 110110 +15+15 +5+5 1515 5555 11.011.066 140140 110110 +30+30 +35+35 3030 8585 14.214.2

Tracking Signal ExampleTracking Signal ExampleTracking

Signal(RSFE/MAD)-10/10 = -1-15/7.5 = -2

0/10 = 0-10/10 = -1

+5/11 = +0.5+35/14.2 = +2.5

The variation of the tracking signal The variation of the tracking signal between between --2.02.0 and and +2.5+2.5 is within acceptable is within acceptable limitslimits


Adaptive ForecastingAdaptive Forecasting

ItIt’’s possible to use the computer to s possible to use the computer to continually monitor forecast error and continually monitor forecast error and adjust the values of the adjust the values of the αα and and ββcoefficients used in exponential coefficients used in exponential smoothing to continually minimize smoothing to continually minimize forecast errorforecast errorThis technique is called adaptive This technique is called adaptive smoothingsmoothing


Focus ForecastingFocus ForecastingDeveloped at American Hardware Supply, Developed at American Hardware Supply, focus forecasting is based on two principles:focus forecasting is based on two principles:

1.1. Sophisticated forecasting models are not Sophisticated forecasting models are not always better than simple onesalways better than simple ones

2.2. There is no single technique that should There is no single technique that should be used for all products or servicesbe used for all products or services

This approach uses historical data to test This approach uses historical data to test multiple forecasting models for individual itemsmultiple forecasting models for individual itemsThe forecasting model with the lowest error is The forecasting model with the lowest error is then used to forecast the next demandthen used to forecast the next demand


Forecasting in the Service Forecasting in the Service SectorSector

Presents unusual challengesPresents unusual challengesSpecial need for short term recordsSpecial need for short term recordsNeeds differ greatly as function of Needs differ greatly as function of industry and productindustry and productHolidays and other calendar eventsHolidays and other calendar eventsUnusual eventsUnusual events


Fast Food Restaurant Fast Food Restaurant ForecastForecast

20% 20% –

15% 15% –

10% 10% –

5% 5% –

1111--1212 11--22 33--44 55--66 77--88 99--10101212--11 22--33 44--55 66--77 88--99 1010--1111

(Lunchtime)(Lunchtime) (Dinnertime)(Dinnertime)Hour of dayHour of day

Perc

enta

ge o

f sal

esPe

rcen

tage

of s

ales



FedEx Call Center ForecastFedEx Call Center Forecast


12% 12% –

10% 10% –

8% 8% –

6% 6% –

4%4% –

2%2% –

0%0% –

Hour of dayHour of dayA.M.A.M. P.M.P.M.

22 44 66 88 1010 1212 22 44 66 88 1010 1212

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