dfmd 3513 chapter-6 forecasting

FORECASTINGFORECASTING

Ir. Haery Ir. Haery SihombingSihombing/IP/IPPensyarah Fakulti Kejuruteraan Pembuatan

Universiti Teknologi Malaysia Melaka

6

What is Forecasting?What is Forecasting?

Process of predicting a Process of predicting a

future eventfuture event

Underlying basis of Underlying basis of

all business decisionsall business decisions

ProductionProduction

InventoryInventory

PersonnelPersonnel

FacilitiesFacilities

??

ForecastingForecasting

Predicting the FuturePredicting the Future

Qualitative forecast Qualitative forecast

methodsmethods

subjectivesubjective

Quantitative forecast Quantitative forecast

methodsmethods

based on mathematical based on mathematical

formulasformulas

Forecasting and Supply Chain Management

Accurate forecasting determines how much Accurate forecasting determines how much inventory a company must keep at various inventory a company must keep at various points along its supply chainpoints along its supply chain

Continuous replenishmentContinuous replenishmentsupplier and customer share continuously updated datasupplier and customer share continuously updated data

typically managed by the suppliertypically managed by the supplier

reduces inventory for the companyreduces inventory for the company

speeds customer deliveryspeeds customer delivery

Variations of continuous replenishmentVariations of continuous replenishmentquick responsequick response

JIT (justJIT (just--inin--time)time)

VMI (vendorVMI (vendor--managed inventory)managed inventory)

stockless inventorystockless inventory

Forecasting and TQM

Accurate forecasting customer demand is a Accurate forecasting customer demand is a key to providing good quality servicekey to providing good quality service

Continuous replenishment and JIT Continuous replenishment and JIT complement TQMcomplement TQM

eliminates the need for buffer inventory, which, in eliminates the need for buffer inventory, which, in turn, reduces both waste and inventory costs, a turn, reduces both waste and inventory costs, a primary goal of TQMprimary goal of TQM

smoothes process flow with no defective itemssmoothes process flow with no defective items

meets expectations about onmeets expectations about on--time delivery, which is time delivery, which is perceived as goodperceived as good--quality servicequality service

Types of Forecasting MethodsTypes of Forecasting Methods

Depend onDepend on

time frametime frame

demand behaviordemand behavior

causes of behaviorcauses of behavior

Time FrameTime Frame

Indicates how far into the future is Indicates how far into the future is

forecastforecast

ShortShort-- to midto mid--range forecastrange forecast

typically encompasses the immediate futuretypically encompasses the immediate future

daily up to two yearsdaily up to two years

LongLong--range forecastrange forecast

usually encompasses a period of time longer usually encompasses a period of time longer

than two yearsthan two years

ShortShort--range forecastrange forecast

Up to 1 year, generally less than 3 monthsUp to 1 year, generally less than 3 months

Purchasing, job scheduling, workforce levels, job Purchasing, job scheduling, workforce levels, job

assignments, production levelsassignments, production levels

MediumMedium--range forecastrange forecast

3 months to 3 years3 months to 3 years

Sales and production planning, budgetingSales and production planning, budgeting

LongLong--range forecastrange forecast

3+ years3+ years

New product planning, facility location, research New product planning, facility location, research

and developmentand development

Forecasting Time HorizonsForecasting Time Horizons

Distinguishing DifferencesDistinguishing Differences

Medium/long range forecastsMedium/long range forecasts deal with deal with

more comprehensive issues and support more comprehensive issues and support

management decisions regarding planning management decisions regarding planning

and products, plants and processesand products, plants and processes

ShortShort--term forecastingterm forecasting usually employs usually employs

different methodologies than longerdifferent methodologies than longer--term term

forecastingforecasting

ShortShort--term forecaststerm forecasts tend to be more tend to be more

accurate than longeraccurate than longer--term forecaststerm forecasts

Influence of Product Life CycleInfluence of Product Life Cycle

Introduction and growth require longer Introduction and growth require longer

forecasts than maturity and declineforecasts than maturity and decline

As product passes through life cycle, As product passes through life cycle,

forecasts are useful in projectingforecasts are useful in projecting

Staffing levelsStaffing levels

Inventory levelsInventory levels

Factory capacityFactory capacity

Introduction Introduction –– GrowthGrowth –– MaturityMaturity –– DeclineDecline

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 critical

Defend market Defend market

positionposition

Cost control Cost control

criticalcritical

Introduction Growth Maturity Decline

Co

mp

an

y S

tra

teg

y/I

ss

ue

sC

om

pa

ny

Str

ate

gy

/Is

su

es

InternetInternet

FlatFlat--screen screen monitorsmonitors

SalesSales

DVDDVD

CDCD--ROMROM

DriveDrive--through through restaurantsrestaurants

Fax machinesFax machines

3 1/23 1/2””Floppy Floppy disksdisks

ColorColor printersprinters

Figure 2.5Figure 2.5

Product Life CycleProduct Life Cycle

Product design Product design andanddevelopment development criticalcritical

Frequent Frequent product and product and process design process design changeschanges

Short production Short production runsruns

High production High production costscosts

Limited modelsLimited models

Attention to Attention to qualityquality

Introduction Growth Maturity Decline

OM

Str

ate

gy

/Is

su

es

OM

Str

ate

gy

/Is

su

es

Forecasting Forecasting criticalcritical

Product and Product and process process reliabilityreliability

Competitive Competitive product product improvements improvements and optionsand options

Increase capacityIncrease capacity

Shift toward Shift toward product focusproduct focus

Enhance Enhance distributiondistribution

StandardizationStandardization

Less rapid Less rapid product changes product changes –– more minor more minor changeschanges

Optimum Optimum capacitycapacity

Increasing Increasing stability of stability of processprocess

Long production Long production runsruns

Product Product improvement improvement and cost cuttingand cost cutting

Little product Little product differentiationdifferentiation

CostCostminimizationminimization

Overcapacity Overcapacity in the in the industryindustry

Prune line to Prune line to eliminate eliminate items not items not returning returning good margingood margin

Reduce Reduce capacitycapacity


Types of ForecastsTypes of Forecasts

Economic forecastsEconomic forecasts

Address business cycle Address business cycle –– inflation rate, inflation rate,

money supply, housing starts, etc.money supply, housing starts, etc.

Technological forecastsTechnological forecasts

Predict rate of technological progressPredict rate of technological progress

Impacts development of new productsImpacts development of new products

Demand forecastsDemand forecasts

Predict sales of existing productPredict sales of existing product

Strategic Importance of ForecastingStrategic Importance of Forecasting

Human Resources Human Resources –– Hiring, training, laying Hiring, training, laying off workersoff workers

Capacity Capacity –– Capacity shortages can result in Capacity shortages can result in undependable delivery, loss of customers, undependable delivery, loss of customers, loss of market shareloss of market share

SupplySupply--Chain Management Chain Management –– Good supplier Good supplier relations and price advancerelations and price advance

Seven Steps in ForecastingSeven Steps in Forecasting

1.1. Determine the use of the forecastDetermine the use of the forecast

2.2. Select the items to be forecastedSelect the items to be forecasted

3.3. Determine the time horizon of the Determine the time horizon of the

forecastforecast

4.4. Select the forecasting model(s)Select the forecasting model(s)

5.5. Gather the dataGather the data

6.6. Make the forecastMake the forecast

7.7. Validate and implement resultsValidate and implement results

The Realities!The Realities!

Forecasts are seldom perfectForecasts are seldom perfect

Most techniques assume an Most techniques assume an underlying stability in the systemunderlying stability in the system

Product 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 and Used when situation is vague and

little data existlittle data exist

New productsNew products

New technologyNew technology

Involves intuition, experienceInvolves intuition, experience

e.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’’ andand

historical data existhistorical data exist

Existing productsExisting products

Current technologyCurrent technology

Involves mathematical techniquesInvolves mathematical techniques

e.g., forecasting sales of color e.g., forecasting sales of color

televisionstelevisions

Quantitative MethodsQuantitative Methods

Qualitative MethodsQualitative Methods

oo Management, marketing, purchasing, Management, marketing, purchasing,

and engineering are sources for and engineering are sources for

internal qualitative forecastsinternal qualitative forecasts

oo Delphi methodDelphi method

involves soliciting forecasts about technological advances from experts

Overview of Qualitative MethodsOverview of Qualitative Methods

Jury of executive opinionJury of executive opinion

Pool opinions of highPool opinions of high--level executives, sometimes level executives, sometimes

augment by statistical modelsaugment by statistical models

Delphi methodDelphi method

Panel of experts, queried iterativelyPanel of experts, queried iteratively

Sales force compositeSales force composite

Estimates from individual salespersons are reviewed Estimates from individual salespersons are reviewed

for reasonableness, then aggregated for reasonableness, then aggregated

Consumer Market SurveyConsumer Market Survey

Ask the customerAsk the customer

Involves small group of highInvolves small group of high--level managerslevel managers

Group estimates demand by working Group estimates demand by working

togethertogether

Combines managerial experience with Combines managerial experience with

statistical modelsstatistical models

Relatively quickRelatively quick

‘‘GroupGroup--thinkthink’’

disadvantagedisadvantage

Jury of Executive OpinionJury of Executive Opinion Sales Force CompositeSales Force Composite

Each salesperson projects his or her Each salesperson projects his or her

salessales

Combined at district and national Combined at district and national

levelslevels

Sales reps know customersSales reps know customers’’ wantswants

Tends to be overly optimisticTends to be overly optimistic

Delphi MethodDelphi Method

Iterative group Iterative group process, continues process, continues until consensus is until consensus is reachedreached

3 types of participants3 types of participantsDecision makersDecision makers

StaffStaff

RespondentsRespondents

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 plansAsk customers about purchasing plans

What consumers say, and what they What consumers say, and what they

actually do are often differentactually do are often different

Sometimes difficult to answerSometimes difficult to answer

Overview of Quantitative Overview of Quantitative ApproachesApproaches

1.1. Naive approachNaive approach

2.2. Moving averagesMoving averages

3.3. Exponential Exponential

smoothingsmoothing

4.4. Trend projectionTrend projection

5.5. Linear regressionLinear regression

TimeTime--SeriesSeriesModelsModels

AssociativeAssociativeModelModel

Set of evenly spaced numerical dataSet of evenly spaced numerical data

Obtained by observing response Obtained by observing response

variable at regular time periodsvariable at regular time periods

Forecast based only on past valuesForecast based only on past values

Assumes that factors influencing past Assumes that factors influencing past

and present will continue influence in and present will continue influence in

futurefuture

Time Series ForecastingTime Series Forecasting

Trend

Seasonal

Cyclical

Random

Time Series ComponentsTime Series Components Components of DemandComponents of Demand

Dem

an

d f

or

pro

du

ct

or

serv

ice

| | | |1 2 3 4

Year

Averagedemand over four years

Seasonal peaks

Trendcomponent

Actualdemand

Randomvariation

Demand BehaviorDemand Behavior

TrendTrenda gradual, longa gradual, long--term up or down movement of term up or down movement of demanddemand

Random variationsRandom variationsmovements in demand that do not follow a patternmovements in demand that do not follow a pattern

CycleCyclean upan up--andand--down repetitive movement in demanddown repetitive movement in demand

Seasonal patternSeasonal patternan upan up--andand--down repetitive movement in demand down repetitive movement in demand occurring periodicallyoccurring periodically

TimeTime(a) Trend(a) Trend

TimeTime(d) Trend with seasonal pattern(d) Trend with seasonal pattern

TimeTime(c) Seasonal pattern(c) Seasonal pattern

TimeTime(b) Cycle(b) Cycle

Dem

an

dD

em

an

dD

em

an

dD

em

an

d

Dem

an

dD

em

an

dD

em

an

dD

em

an

d

Random Random movementmovement

Forms of Forecast Movement

Persistent, overall upward or Persistent, overall upward or

downward patterndownward pattern

Changes due to population, Changes due to population,

technology, age, culture, etc.technology, age, culture, etc.

Typically several years duration Typically several years duration

Trend ComponentTrend Component

Regular pattern of up and down Regular pattern of up and down

fluctuationsfluctuations

Due 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 Seasons

Week Day 7Month Week 4-4.5Month Day 28-31Year Quarter 4Year Month 12Year Week 52

Repeating up and down movementsRepeating up and down movements

Affected by business cycle, political, Affected by business cycle, political,

and economic factorsand economic factors

Multiple years durationMultiple years duration

Often causal or Often causal or

associative associative

relationshipsrelationships

Cyclical ComponentCyclical Component

00 55 1010 1515 2020

Erratic, unsystematic, Erratic, unsystematic, ‘‘residualresidual’’


Due to random variation or Due to random variation or

unforeseen eventsunforeseen events

Short duration and Short duration and

nonrepeating nonrepeating

Random ComponentRandom Component

MM TT WW TT FF

Forecasting Methods

QualitativeQualitative

use management judgment, expertise, and use management judgment, expertise, and opinion to predict future demandopinion to predict future demand

Time seriesTime series

statistical techniques that use historical statistical techniques that use historical demand data to predict future demanddemand data to predict future demand

Regression methodsRegression methods

attempt to develop a mathematical relationship attempt to develop a mathematical relationship between demand and factors that cause its between demand and factors that cause its behaviorbehavior

Forecasting ProcessForecasting Process

6. Check forecast

accuracy with one or

more measures

4. Select a forecast

model that seems

appropriate for data

5. Develop/compute

forecast for period of

historical data

8a. Forecast over

planning horizon

9. Adjust forecast based

on additional qualitative

information and insight

10. Monitor results

and measure forecast

accuracy

8b. Select new

forecast model or

adjust parameters of

existing model

7.

Is accuracy of

forecast

acceptable?

1. Identify the

purpose of forecast

3. Plot data and identify

patterns

2. Collect historical

data

No

Yes

Time SeriesTime Series

Assume that what has occurred in the past will Assume that what has occurred in the past will

continue to occur in the futurecontinue to occur in the future

Relate the forecast to only one factor Relate the forecast to only one factor -- timetime

IncludeInclude

moving averagemoving average

exponential smoothingexponential smoothing

linear trend linelinear trend line

Moving Average

NaiveNaive forecastforecastdemand the current period is used as next demand the current period is used as next periodperiod’’s forecasts forecast

Simple moving averageSimple moving averagestable demand with no pronounced behavioral stable demand with no pronounced behavioral patternspatterns

Weighted moving averageWeighted moving averageweights are assigned to most recent data

Naive ApproachNaive Approach

Assumes demand in next period is the Assumes demand in next period is the

same as demand in most recent periodsame as demand in most recent period

e.g., If October sales were 90, then e.g., If October sales were 90, then

November sales will be 90November sales will be 90

Sometimes cost effective and efficientSometimes cost effective and efficient

NaNaïïve Approachve Approach

JanJan 120120

FebFeb 9090

MarMar 100100

AprApr 7575

MayMay 110110

JuneJune 5050

JulyJuly 7575

AugAug 130130

SeptSept 110110

OctOct 9090

ORDERSORDERS

MONTHMONTH PER MONTHPER MONTH

--

120120

9090

100100

7575

110110

5050

7575

130130

110110

9090Nov Nov --

FORECASTFORECAST

Simple Moving Average Simple Moving Average

MAMAnn ==

nn

ii = 1= 1DDii

nn

wherewhere

nn =number of periods in the =number of periods in the

moving averagemoving average

DDii == demand in period demand in period ii

MA is a series of arithmetic means MA is a series of arithmetic means

Used if little or no trendUsed if little or no trend

Used often for smoothingUsed often for smoothing

Provides overall impression of data over Provides overall impression of data over

timetime

Moving average =Moving average =demand in previous n periodsdemand in previous n periods

nn

Simple Moving AverageSimple Moving Average

33--month Simple Moving Averagemonth Simple Moving AverageEXAMPLEEXAMPLE

JanJan 120120

FebFeb 9090MarMar 100100

AprApr 7575MayMay 110110

JuneJune 5050

JulyJuly 7575AugAug 130130

SeptSept 110110

OctOct 9090NovNov --

ORDERSORDERS

MONTHMONTH PER MONTHPER MONTHMAMA33 ==

33

ii = 1= 1

DDii

33

==90 + 110 + 13090 + 110 + 130

33

= 110 orders= 110 orders

for Novfor Nov

––

––––

103.3103.388.388.3

95.095.0

78.378.378.378.3

85.085.0

105.0105.0110.0110.0

MOVING MOVING

AVERAGEAVERAGE

55--month Simple Moving Averagemonth Simple Moving Average

EXAMPLEEXAMPLE

JanJan 120120

FebFeb 9090MarMar 100100

AprApr 7575MayMay 110110

JuneJune 5050

JulyJuly 7575AugAug 130130

SeptSept 110110

OctOct 9090NovNov --

ORDERSORDERS

MONTHMONTH PER MONTHPER MONTH

MAMA55 ==

55

ii = 1= 1

DDii

55

==90 + 110 + 130+75+5090 + 110 + 130+75+50

55

= 91 orders= 91 orders

for Novfor Nov

––

––––

––––

99.099.0

85.085.082.082.0

88.088.0

95.095.091.091.0

MOVING MOVING

AVERAGEAVERAGE

Smoothing EffectsSmoothing Effects

150150 –

125125 –

100100 –

7575 –

5050 –

2525 –

00 – | | | | | | | | | | |

JanJan FebFeb MarMar AprApr MayMay JuneJune JulyJuly AugAug SeptSept OctOct NovNov

ActualActual

Ord

ers

Ord

ers

MonthMonth

55--monthmonth

33--monthmonth

Weighted Moving AverageWeighted Moving Average

WMAWMAnn ==ii = 1= 1

WWii DDii

wherewhere

WWii = the weight for period = the weight for period ii,,

between 0 and 100 between 0 and 100

percentpercent

WWii = 1.00= 1.00

AdjustsAdjusts

movingmoving

averageaverage

method to method to

more closely more closely

reflect data reflect data


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

WeightedWeightedmoving averagemoving average ==

((weight for period nweight for period n))xx ((demand in period ndemand in period n))

weightsweights

Weighted Moving AverageWeighted Moving Average Weighted Moving AverageWeighted Moving AverageExample 1Example 1

MONTH MONTH WEIGHTWEIGHT DATADATA

AugustAugust 17%17% 130130

SeptemberSeptember 33%33% 110110

OctoberOctober 50%50% 9090

WMAWMA33 ==33

ii = 1= 1WWii DDii

= (0.50)(90) + (0.33)(110) + (0.17)(130)= (0.50)(90) + (0.33)(110) + (0.17)(130)

= 103.4 orders= 103.4 orders

November ForecastNovember Forecast

JanuaryJanuary 1010

FebruaryFebruary 1212

MarchMarch 1313

AprilApril 1616

MayMay 1919

JuneJune 2323

JulyJuly 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

1010

1212

1313

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

Example 2Example 2 Weights Applied Period

3 Last month2 Two months ago1 Three months ago6 Sum of weights Increasing n smooths the forecast but Increasing n smooths the forecast but

makes it less sensitive to changesmakes it less sensitive to changes

Do not forecast trends wellDo not forecast trends well

Require extensive historical dataRequire extensive historical data

Potential Problems WithPotential Problems WithMoving AverageMoving Average

Moving Average And Moving Average And Weighted Moving AverageWeighted Moving Average

3030 –

2525 –

2020 –

1515 –

1010 –

55 –

Sa

les

de

ma

nd

Sa

les

de

ma

nd

| | | | | | | | | | | |

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

ActualActualsalessales

Moving Moving averageaverage

Weighted Weighted movingmovingaverageaverage

Averaging method Averaging method

Weights most recent data more stronglyWeights most recent data more strongly

Reacts more to recent changesReacts more to recent changes

Widely used, accurate methodWidely used, accurate method

Exponential SmoothingExponential Smoothing


Form of weighted moving averageForm of weighted moving average

Weights decline exponentiallyWeights decline exponentially

Most recent data weighted mostMost recent data weighted most

Requires smoothing constant Requires smoothing constant (( ))

Ranges from 0 to 1Ranges from 0 to 1

Subjectively chosenSubjectively chosen

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

datadata

FFtt +1 +1 == DDtt + (1 + (1 -- ))FFtt

where:where:

FFtt +1+1 == forecast for next periodforecast for next period

DDtt == actual demand for present periodactual demand for present period

FFtt == previously determined forecast for previously determined forecast for

present periodpresent period

== weighting factor, smoothing constantweighting factor, smoothing constant

Exponential SmoothingExponential Smoothing (cont.)(cont.)

OR


New forecast =New forecast = last periodlast period’’s forecasts forecast

++ ((last periodlast period’’s actual demand s actual demand

–– last periodlast period’’s forecasts forecast))

FFtt = F= Ftt –– 11 ++ ((AAtt –– 11 -- FFtt –– 11))

wherewhere FFtt == new forecastnew forecast

FFtt –– 11 == previous forecastprevious forecast

== smoothing (or weighting) smoothing (or weighting)

constant constant (0(0 1)1)

Effect of Smoothing ConstantEffect of Smoothing Constant

0.00.0 1.01.0

IfIf = 0.20, then = 0.20, then FFtt +1+1 = 0.20= 0.20 DDtt + 0.80 + 0.80 FFtt

IfIf = 0, then = 0, then FFtt +1+1 = 0= 0 DDtt + 1 + 1 FFtt 0 = 0 = FFtt

Forecast does not reflect recent dataForecast does not reflect recent data

IfIf = 1, then = 1, then FFtt +1+1 = 1= 1 DDtt + 0 + 0 FFtt == DDtt

Forecast based only on most recent dataForecast based only on most recent data

FF22 == DD11 + (1 + (1 -- ))FF11

= (0.30)(37) + (0.70)(37)= (0.30)(37) + (0.70)(37)

= 37= 37

FF33 == DD22 + (1 + (1 -- ))FF22

= (0.30)(40) + (0.70)(37)= (0.30)(40) + (0.70)(37)

= 37.9= 37.9

FF1313 == DD1212 + (1 + (1 -- ))FF1212

= (0.30)(54) + (0.70)(50.84)= (0.30)(54) + (0.70)(50.84)

= 51.79= 51.79

Exponential SmoothingExponential Smoothing (( =0.30)=0.30)

PERIODPERIOD MONTHMONTH DEMANDDEMAND

11 JanJan 3737

22 FebFeb 4040

33 MarMar 4141

44 AprApr 3737

55 May May 4545

66 JunJun 5050

77 JulJul 4343

88 Aug Aug 4747

99 SepSep 5656

1010 OctOct 5252

1111 NovNov 5555

1212 Dec Dec 5454

FORECAST, FORECAST, FFtt + 1+ 1

PERIODPERIOD MONTHMONTH DEMANDDEMAND (( = 0.3)= 0.3) (( = 0.5)= 0.5)

11 JanJan 3737 –– ––

22 FebFeb 4040 37.0037.00 37.0037.00

33 MarMar 4141 37.9037.90 38.5038.50

44 AprApr 3737 38.8338.83 39.7539.75

55 May May 4545 38.2838.28 38.3738.37

66 JunJun 5050 40.2940.29 41.6841.68

77 JulJul 4343 43.2043.20 45.8445.84

88 Aug Aug 4747 43.1443.14 44.4244.42

99 SepSep 5656 44.3044.30 45.7145.71

1010 OctOct 5252 47.8147.81 50.8550.85

1111 NovNov 5555 49.0649.06 51.4251.42

1212 Dec Dec 5454 50.8450.84 53.2153.21

1313 JanJan –– 51.7951.79 53.6153.61


7070 –

6060 –

5050 –

4040 –

3030 –

2020 –

1010 –

00 –| | | | | | | | | | | | |

11 22 33 44 55 66 77 88 99 1010 1111 1212 1313

ActualActual

Ord

ers

Ord

ers

MonthMonth


= 0.50= 0.50

= 0.30= 0.30

AFAFtt +1+1 == FFtt +1+1 ++ TTtt +1+1

wherewhere

TT = an exponentially smoothed trend factor= an exponentially smoothed trend factor

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

wherewhere

TTtt = the last period trend factor= the last period trend factor

= a smoothing constant for trend= a smoothing constant for trend

Adjusted Exponential SmoothingAdjusted Exponential Smoothing

Adjusted Exponential SmoothingAdjusted Exponential Smoothing(( =0.30)=0.30)

PERIODPERIOD MONTHMONTH DEMANDDEMAND

11 JanJan 3737

22 FebFeb 4040

33 MarMar 4141

44 AprApr 3737

55 May May 4545

66 JunJun 5050

77 JulJul 4343

88 Aug Aug 4747

99 SepSep 5656

1010 OctOct 5252

1111 NovNov 5555

1212 Dec Dec 5454

TT33 == ((FF33 -- FF22) + (1 ) + (1 -- )) TT22

= (0.30)(38.5 = (0.30)(38.5 -- 37.0) + (0.70)(0)37.0) + (0.70)(0)

= 0.45= 0.45

AFAF33 == FF33 ++ TT33 = 38.5 + 0.45= 38.5 + 0.45

= 38.95= 38.95

TT1313 == ((FF1313 -- FF1212) + (1 ) + (1 -- )) TT1212

= (0.30)(53.61 = (0.30)(53.61 -- 53.21) + (0.70)(1.77)53.21) + (0.70)(1.77)

= 1.36= 1.36

AFAF1313 == FF1313 ++ TT1313 = 53.61 + 1.36 = 54.96= 53.61 + 1.36 = 54.96

Adjusted Exponential Smoothing:Adjusted Exponential Smoothing:ExampleExample

FORECASTFORECAST TRENDTREND ADJUSTEDADJUSTED

PERIODPERIOD MONTHMONTH DEMANDDEMAND FFtt +1+1 TTtt +1+1 FORECAST AFFORECAST AFtt +1+1

11 JanJan 3737 37.0037.00 –– ––

22 FebFeb 4040 37.0037.00 0.000.00 37.0037.00

33 MarMar 4141 38.5038.50 0.450.45 38.9538.95

44 AprApr 3737 39.7539.75 0.690.69 40.4440.44

55 May May 4545 38.3738.37 0.070.07 38.4438.44

66 JunJun 5050 38.3738.37 0.070.07 38.4438.44

77 JulJul 4343 45.8445.84 1.971.97 47.8247.82

88 Aug Aug 4747 44.4244.42 0.950.95 45.3745.37

99 SepSep 5656 45.7145.71 1.051.05 46.7646.76

1010 OctOct 5252 50.8550.85 2.282.28 58.1358.13

1111 NovNov 5555 51.4251.42 1.761.76 53.1953.19

1212 Dec Dec 5454 53.2153.21 1.771.77 54.9854.98

1313 JanJan –– 53.6153.61 1.361.36 54.9654.96

Adjusted Exponential Smoothing Adjusted Exponential Smoothing ForecastsForecasts

7070 –

6060 –

5050 –

4040 –

3030 –

2020 –

1010 –

00 –| | | | | | | | | | | | |

11 22 33 44 55 66 77 88 99 1010 1111 1212 1313

ActualActual

De

man

dD

em

an

d

PeriodPeriod

Forecast (Forecast ( = 0.50)= 0.50)

Adjusted forecast (Adjusted forecast ( ==

yy == aa ++ bxbx

wherewhere

aa = intercept= intercept

bb = slope of the line= slope of the line

xx = time period= time period

yy = forecast for = forecast for demand for period demand for period xx

Linear Trend LineLinear Trend Line

b =

a = y - b x

wheren = number of periods

x = = mean of the x values

y = = mean of the y values

xy - nxy

x2 - nx2

x

n

y

n

Least SquaresLeast Squares ExampleExample

xx(PERIOD)(PERIOD) yy(DEMAND)(DEMAND) xyxy xx22

11 7373 3737 11

22 4040 8080 44

33 4141 123123 99

44 3737 148148 1616

55 4545 225225 2525

66 5050 300300 3636

77 4343 301301 4949

88 4747 376376 6464

99 5656 504504 8181

1010 5252 520520 100100

1111 5555 605605 121121

1212 5454 648648 144144

7878 557557 38673867 650650

x = = 6.5

y = = 46.42

b = = =1.72

a = y - bx

= 46.42 - (1.72)(6.5) = 35.2

3867 - (12)(6.5)(46.42)

650 - 12(6.5)2

xy - nxy

x2 - nx2

7812

55712

Least SquaresLeast Squares Example (cont.)Example (cont.)

Linear trend line y = 35.2 + 1.72x

Forecast for period 13 y = 35.2 + 1.72(13) = 57.56 units

7070 –

6060 –

5050 –

4040 –

3030 –

2020 –

1010 –

00 –

| | | | | | | | | | | | |

11 22 33 44 55 66 77 88 99 1010 1111 1212 1313

ActualActual

De

man

dD

em

an

d

PeriodPeriod

Linear trend lineLinear trend line

The multiplicative seasonal model can The multiplicative seasonal model can modify trend data to accommodate seasonal modify trend data to accommodate seasonal variations in demandvariations in demand

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

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

5.5. 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

Seasonal AdjustmentsSeasonal Adjustments

Seasonal AdjustmentsSeasonal Adjustments

Repetitive increase/ decrease in demandRepetitive increase/ decrease in demand

Use seasonal factor to adjust forecastUse seasonal factor to adjust forecast

Seasonal factor = Seasonal factor = SSii ==DDii

DD

Seasonal AdjustmentSeasonal Adjustment (cont.)(cont.)

2002 12.62002 12.6 8.68.6 6.36.3 17.517.5 45.045.0

2003 14.12003 14.1 10.310.3 7.57.5 18.218.2 50.150.1

2004 15.32004 15.3 10.610.6 8.18.1 19.619.6 53.653.6

Total 42.0Total 42.0 29.529.5 21.921.9 55.355.3 148.7148.7

DEMAND (1000DEMAND (1000’’S PER QUARTER)S PER QUARTER)

YEARYEAR 11 22 33 44 TotalTotal

SS11 = = = 0.28 = = = 0.28 DD11

DD

42.042.0

148.7148.7

SS22 = = = 0.20 = = = 0.20 DD22

DD

29.529.5

148.7148.7SS44 = = = 0.37 = = = 0.37

DD44

DD

55.355.3

148.7148.7

SS33 = = = 0.15 = = = 0.15 DD33

DD

21.921.9

148.7148.7

Seasonal AdjustmentSeasonal Adjustment (cont.)(cont.)

SFSF11 = (= (SS11) () (FF55) = (0.28)(58.17) = 16.28) = (0.28)(58.17) = 16.28

SFSF22 = (= (SS22) () (FF55) = (0.20)(58.17) = 11.63) = (0.20)(58.17) = 11.63

SFSF33 = (= (SS33) () (FF55) = (0.15)(58.17) = 8.73) = (0.15)(58.17) = 8.73

SFSF44 = (= (SS44) () (FF55) = (0.37)(58.17) = 21.53) = (0.37)(58.17) = 21.53

yy = 40.97 + 4.30= 40.97 + 4.30xx = 40.97 + 4.30(4) = 58.17= 40.97 + 4.30(4) = 58.17

For 2005For 2005

Forecast AccuracyForecast Accuracy

Forecast errorForecast error

difference between forecast and actual difference between forecast and actual

demanddemand

MADMAD

mean absolute deviationmean absolute deviation

MAPDMAPD

mean absolute percent deviationmean absolute percent deviation

Cumulative errorCumulative error

Average error or biasAverage error or bias

Mean Absolute DeviationMean Absolute Deviation (MAD)(MAD)

wherewhere

tt = period number= period number

DDtt = demand in period = demand in period tt

FFtt = forecast for period = forecast for period tt

nn = total number of periods= total number of periods

= absolute value= absolute value

DDtt -- FFtt

nnMAD =MAD =

MADMAD ExampleExample

11 3737 37.0037.00 –– ––

22 4040 37.0037.00 3.003.00 3.003.00

33 4141 37.9037.90 3.103.10 3.103.10

44 3737 38.8338.83 --1.831.83 1.831.83

55 4545 38.2838.28 6.726.72 6.726.72

66 5050 40.2940.29 9.699.69 9.699.69

77 4343 43.2043.20 --0.200.20 0.200.20

88 4747 43.1443.14 3.863.86 3.863.86

99 5656 44.3044.30 11.7011.70 11.7011.70

1010 5252 47.8147.81 4.194.19 4.194.19

1111 5555 49.0649.06 5.945.94 5.945.94

1212 5454 50.8450.84 3.153.15 3.153.15

557557 49.3149.31 53.3953.39

PERIODPERIOD DEMAND, DEMAND, DDtt FFtt (( =0.3)=0.3) ((DDtt -- FFtt)) ||DDtt -- FFtt||

Dt - Ft

nMAD =

=

= 4.85

53.39

11

Other Accuracy MeasuresOther Accuracy Measures

Mean absolute percent deviation (MAPD)Mean absolute percent deviation (MAPD)

MAPD =MAPD =|D|Dtt -- FFtt||

DDtt

Cumulative errorCumulative error

E = E = eett

Average errorAverage error

E =E =eett

nn

Comparison of ForecastsComparison of Forecasts

FORECASTFORECAST MADMAD MAPDMAPD EE ((EE))

Exponential smoothing (Exponential smoothing ( = 0.30)= 0.30) 4.854.85 9.6%9.6% 49.3149.31 4.484.48

Exponential smoothing (Exponential smoothing ( = 0.50)= 0.50) 4.044.04 8.5%8.5% 33.2133.21 3.023.02

Adjusted exponential smoothingAdjusted exponential smoothing 3.813.81 7.5%7.5% 21.1421.14 1.921.92

(( = 0.50, = 0.50, = 0.30)= 0.30)

Linear trend lineLinear trend line 2.292.29 4.9%4.9% –– ––

Forecast ControlForecast Control

Tracking signalTracking signalmonitors the forecast to see if it is biased monitors the forecast to see if it is biased high or lowhigh or low

1 MAD 1 MAD 0.80.8

Control limits of 2 to 5 MADs are used most Control limits of 2 to 5 MADs are used most frequentlyfrequently

Tracking signal = =Tracking signal = =((DDtt -- FFtt))

MADMAD

EE

MADMAD

Tracking Signal ValuesTracking Signal Values

11 3737 37.0037.00 –– –– ––

22 4040 37.0037.00 3.003.00 3.003.00 3.003.00

33 4141 37.9037.90 3.103.10 6.106.10 3.053.05

44 3737 38.8338.83 --1.831.83 4.274.27 2.642.64

55 4545 38.2838.28 6.726.72 10.9910.99 3.663.66

66 5050 40.2940.29 9.699.69 20.6820.68 4.874.87

77 4343 43.2043.20 --0.200.20 20.4820.48 4.094.09

88 4747 43.1443.14 3.863.86 24.3424.34 4.064.06

99 5656 44.3044.30 11.7011.70 36.0436.04 5.015.01

1010 5252 47.8147.81 4.194.19 40.2340.23 4.924.92

1111 5555 49.0649.06 5.945.94 46.1746.17 5.025.02

1212 5454 50.8450.84 3.153.15 49.3249.32 4.854.85

DEMANDDEMAND FORECAST,FORECAST, ERRORERROR EE ==

PERIODPERIOD DDtt FFtt DDtt -- FFtt ((DDtt -- FFtt)) MADMAD

TS3 = = 2.006.10

3.05

Tracking signal for period 3

––

1.001.00

2.002.00

1.621.62

3.003.00

4.254.25

5.015.01

6.006.00

7.197.19

8.188.18

9.209.20

10.1710.17

TRACKINGTRACKING

SIGNALSIGNAL

Tracking Signal PlotTracking Signal Plot

33 –

22 –

11 –

00 –

--11 –

--22 –

--33 –

| | | | | | | | | | | | |

00 11 22 33 44 55 66 77 88 99 1010 1111 1212

Tra

ck

ing

sig

na

l (M

AD

)T

rack

ing

sig

na

l (M

AD

)

PeriodPeriod

Exponential smoothing ( = 0.30)

Linear trend line

Statistical Control ChartsStatistical Control Charts

==((DDtt -- FFtt))

22

nn -- 11

UsingUsing we can calculate statistical we can calculate statistical

control limits for the forecast errorcontrol limits for the forecast error

Control limits are typically set at Control limits are typically set at 33

Statistical Control ChartsStatistical Control Charts

Err

ors

Err

ors

18.3918.39 –

12.2412.24 –

6.126.12 –

00 –

--6.126.12 –

--12.2412.24 –

--18.3918.39 –

| | | | | | | | | | | | |

00 11 22 33 44 55 66 77 88 99 1010 1111 1212

PeriodPeriod

UCL = +3

LCL = -3

Regression Methods

Linear regressionLinear regression

a mathematical technique that relates a a mathematical technique that relates a dependent variable to an independent dependent variable to an independent variable in the form of a linear equationvariable in the form of a linear equation

CorrelationCorrelation

a measure of the strength of the a measure of the strength of the relationship between independent and relationship between independent and dependent variablesdependent variables

Linear RegressionLinear Regression

yy == aa ++ bxbx aa == yy -- b xb x

bb ==

wherewhere

aa == interceptintercept

bb == slope of the line slope of the line

xx == = mean of the = mean of the xx datadata

yy == = mean of the = mean of the yy datadata

xyxy -- nxynxy

xx22 -- nxnx22

xx

nn

yy

nn

Linear Regression Linear Regression ExampleExample

xx yy

(WINS)(WINS) (ATTENDANCE) (ATTENDANCE) xyxy xx22

44 36.336.3 145.2145.2 1616

66 40.140.1 240.6240.6 3636

66 41.241.2 247.2247.2 3636

88 53.053.0 424.0424.0 6464

66 44.044.0 264.0264.0 3636

77 45.645.6 319.2319.2 4949

55 39.039.0 195.0195.0 2525

77 47.547.5 332.5332.5 4949

4949 346.7346.7 2167.72167.7 311311

Linear RegressionLinear Regression Example (cont.)Example (cont.)

x = = 6.125

y = = 43.36

b =

=

= 4.06

a = y - bx

= 43.36 - (4.06)(6.125)

= 18.46

49

8

346.9

8

xy - nxy2

x2 - nx2

(2,167.7) - (8)(6.125)(43.36)

(311) - (8)(6.125)2

| | | | | | | | | | |

00 11 22 33 44 55 66 77 88 99 1010

60,000 60,000 –

50,000 50,000 –

40,000 40,000 –

30,000 30,000 –

20,000 20,000 –

10,000 10,000 –

Linear regression line, Linear regression line, yy = 18.46 + 4.06= 18.46 + 4.06xx

Wins, x

Att

en

da

nce

, y

Linear RegressionLinear Regression Example (cont.)Example (cont.)

y = 18.46 + 4.06x y = 18.46 + 4.06(7)= 46.88, or 46,880

Regression equation Attendance forecast for 7 wins

Correlation and Coefficient of Correlation and Coefficient of DeterminationDetermination

CorrelationCorrelation,, rr

Measure of strength of relationshipMeasure of strength of relationship

Varies between Varies between --1.00 and +1.001.00 and +1.00

Coefficient of determinationCoefficient of determination,, rr22

Percentage of variation in dependent Percentage of variation in dependent

variable resulting from changes in the variable resulting from changes in the

independent variableindependent variable

Computing CorrelationComputing Correlation

nn xyxy -- xx yy

[[nn xx22 -- (( xx))22] [] [nn yy22 -- (( yy))22]]rr ==

Coefficient of determination Coefficient of determination

rr22 = (0.947)= (0.947)22 = 0.897= 0.897

rr ==(8)(2,167.7)(8)(2,167.7) -- (49)(346.9)(49)(346.9)

[(8)(311)[(8)(311) -- (49(49)2)2] [(8)(15,224.7) ] [(8)(15,224.7) -- (346.9)(346.9)22]]

rr = 0.947= 0.947

Multiple RegressionMultiple Regression

Study the relationship of demand to two or Study the relationship of demand to two or

more independent variablesmore independent variables

y = y = 00 ++ 11xx11 ++ 22xx22 …… ++ kkxxkk

wherewhere

00 == the interceptthe intercept

11,, …… ,, kk == parameters for the parameters for the

independent variablesindependent variables

xx11,, …… ,, xxkk == independent variablesindependent variables

THE ENDTHE END

•• EXERCISE : TUTORIALEXERCISE : TUTORIALForm of weighted moving averageForm of weighted moving average

Weights decline exponentiallyWeights decline exponentially

Most recent data weighted mostMost recent data weighted most

Requires smoothing constant Requires smoothing constant (( ))

Ranges from 0 to 1Ranges from 0 to 1

Subjectively chosenSubjectively chosen

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



New forecast =New forecast = last periodlast period’’s forecasts forecast

++ ((last periodlast period’’s actual demand s actual demand

–– last periodlast period’’s forecasts forecast))

FFtt = F= Ftt –– 11 ++ ((AAtt –– 11 -- FFtt –– 11))

wherewhere FFtt == new forecastnew forecast

FFtt –– 11 == previous forecastprevious forecast

== smoothing (or weighting) smoothing (or weighting)

constant constant (0(0 1)1)

Exponential Smoothing Exponential Smoothing ExampleExample

Predicted demand Predicted demand = 142= 142 Ford MustangsFord Mustangs

Actual demand Actual demand = 153= 153

Smoothing constant Smoothing constant = .20= .20

Exponential SmoothingExponential SmoothingExampleExample




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

Exponential SmoothingExponential SmoothingExampleExample




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 of Smoothing ConstantsEffect of Smoothing Constants

Weight Assigned toWeight Assigned to

MostMost 2nd Most2nd Most 3rd Most3rd Most 4th Most4th Most 5th Most5th MostRecentRecent RecentRecent RecentRecent RecentRecent RecentRecent

SmoothingSmoothing PeriodPeriod PeriodPeriod PeriodPeriod PeriodPeriod PeriodPeriodConstantConstant (( )) (1(1 -- )) (1(1 -- ))22 (1(1 -- ))33 (1(1 -- ))44

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

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

Impact of DifferentImpact of Different

225225 –

200200 –

175175 –

150150 – | | | | | | | | |

11 22 33 44 55 66 77 88 99

QuarterQuarter

De

ma

nd

De

ma

nd

= .1= .1

Actual Actual demanddemand

= .5= .5

ChoosingChoosing

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

ii = 1= 1

Comparison of Forecast ErrorComparison of Forecast Error

RoundedRounded AbsoluteAbsolute RoundedRounded AbsoluteAbsoluteActualActual ForecastForecast DeviationDeviation ForecastForecast DeviationDeviation

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

11 180180 175175 55 175175 55

22 168168 176176 88 178178 1010

33 159159 175175 1616 173173 1414

44 175175 173173 22 166166 99

55 190190 173173 1717 170170 2020

66 205205 175175 3030 180180 2525

77 180180 178178 22 193193 1313

88 182182 178178 44 186186 44

8484 100100


RoundedRounded AbsoluteAbsolute RoundedRounded AbsoluteAbsoluteActualActual ForecastForecast DeviationDeviation ForecastForecast DeviationDeviationTonageTonage withwith forfor withwith forfor

QuarterQuarter UnloadedUnloaded = .10= .10 = .10= .10 = .50= .50 = .50= .50

11 180180 175175 55 175175 55

22 168168 176176 88 178178 1010

33 159159 175175 1616 173173 1414

44 175175 173173 22 166166 99

55 190190 173173 1717 170170 2020

66 205205 175175 3030 180180 2525

77 180180 178178 22 193193 1313

88 182182 178178 44 186186 44

8484 100100

MAD =|deviations|

n

= 84/8 = 10.50

For = .10

= 100/8 = 12.50

For = .50

Comparison of ForecastComparison of Forecast ErrorError



11 180180 175175 55 175175 55

22 168168 176176 88 178178 1010

33 159159 175175 1616 173173 1414

44 175175 173173 22 166166 99

55 190190 173173 1717 170170 2020

66 205205 175175 3030 180180 2525

77 180180 178178 22 193193 1313

88 182182 178178 44 186186 44

8484 100100

MADMAD 10.5010.50 12.5012.50

= 1,558/8 = 194.75

For = .10

= 1,612/8 = 201.50

For = .50

MSE =(forecast errors)2

n




11 180180 175175 55 175175 55

22 168168 176176 88 178178 1010

33 159159 175175 1616 173173 1414

44 175175 173173 22 166166 99

55 190190 173173 1717 170170 2020

66 205205 175175 3030 180180 2525

77 180180 178178 22 193193 1313

88 182182 178178 44 186186 44

8484 100100

MADMAD 10.5010.50 12.5012.50

MSEMSE 194.75194.75 201.50201.50

= 45.62/8 = 5.70%

For = .10

= 54.8/8 = 6.85%

For = .50

MAPE =100 |deviationi|/actuali

n

n

i = 1


RoundedRounded AbsoluteAbsolute RoundedRounded AbsoluteAbsoluteActualActual ForecastForecast DeviationDeviation ForecastForecast DeviationDeviation

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

11 180180 175175 55 175175 55

22 168168 176176 88 178178 1010

33 159159 175175 1616 173173 1414

44 175175 173173 22 166166 99

55 190190 173173 1717 170170 2020

66 205205 175175 3030 180180 2525

77 180180 178178 22 193193 1313

88 182182 178178 44 186186 44

8484 100100

MADMAD 10.5010.50 12.5012.50

MSEMSE 194.75194.75 201.50201.50

MAPEMAPE 5.70%5.70% 6.85%6.85%

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

TTtt == ((FFtt -- FFtt -- 11) + (1 ) + (1 -- ))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 AdjustmentTrend Adjustment ExampleExample

ForecastForecastActualActual SmoothedSmoothed SmoothedSmoothed IncludingIncluding

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

11 1212 1111 22 13.0013.00

22 1717

33 2020

44 1919

55 2424

66 2121

77 3131

88 2828

99 3636

1010

Table 4.1Table 4.1




11 1212 1111 22 13.0013.00

22 1717

33 2020

44 1919

55 2424

66 2121

77 3131

88 2828

99 3636

1010

Table 4.1Table 4.1

F2 = A1 + (1 - )(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 13.0013.00

22 1717 12.8012.80

33 2020

44 1919

55 2424

66 2121

77 3131

88 2828

99 3636

1010

Table 4.1Table 4.1

T2 = (F2 - F1) + (1 - )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 13.0013.00

22 1717 12.8012.80 1.921.92

33 2020

44 1919

55 2424

66 2121

77 3131

88 2828

99 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 13.0013.00

22 1717 12.8012.80 1.921.92 14.7214.72

33 2020

44 1919

55 2424

66 2121

77 3131

88 2828

99 3636

1010

Table 4.1Table 4.1

15.1815.18 2.102.10 17.2817.28

17.8217.82 2.322.32 20.1420.14

19.9119.91 2.232.23 22.1422.14

22.5122.51 2.382.38 24.8924.89

24.1124.11 2.072.07 26.1826.18

27.1427.14 2.452.45 29.5929.59

29.2829.28 2.322.32 31.6031.60

32.4832.48 2.682.68 35.1635.16



| | | | | | | | |

11 22 33 44 55 66 77 88 99

Time (month)Time (month)

Pro

du

ct

dem

an

dP

rod

uct

dem

an

d

3535 –

3030 –

2525 –

2020 –

1515 –

1010 –

55 –

00 –

Actual demand Actual demand ((AAtt))

Forecast including trend Forecast including trend ((FITFITtt))

Trend ProjectionsTrend Projections

Fitting a trend line to historical data points Fitting a trend line to historical data points to project into the mediumto project into the medium--toto--longlong--rangerange

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

yy == aa ++ 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

Va

lue

s o

f D

ep

en

de

nt

Va

ria

ble


DeviationDeviation11







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

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


Time periodTime period

Va

lue

s o

f D

ep

en

de

nt

Va

ria

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)


Equations to calculate the regression variablesEquations to calculate the regression variables

b =b =xyxy -- nxynxy

xx22 -- nxnx22

yy == aa ++ bxbx^̂

a = y a = y -- bxbx

Least Squares ExampleLeast Squares Example

bb = = = 10.5= = = 10.544xyxy -- nxynxy

xx22 -- nxnx22

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

140140 -- (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 7474

20002000 22 7979 44 158158

20012001 33 8080 99 240240

20022002 44 9090 1616 360360

20032003 55 105105 2525 525525

20042004 66 142142 3636 852852

20052005 77 122122 4949 854854

xx = 28= 28 yy = 692= 692 xx22 = 140= 140 xyxy = 3,063= 3,063

xx = 4= 4 yy = 98.86= 98.86


bb = = = 10.5= = = 10.544xy xy -- nxynxy

xx22 -- nxnx22

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

140140 -- (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 7474

20002000 22 7979 44 158158

20012001 33 8080 99 240240

20022002 44 9090 1616 360360

20032003 55 105105 2525 525525

20042004 66 142142 3636 852852

20052005 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

The trend line is

y = 56.70 + 10.54x^


| | | | | | | | |

19991999 20002000 20012001 20022002 20032003 20042004 20052005 20062006 20072007

160160 –

150150 –

140140 –

130130 –

120120 –

110110 –

100100 –

9090 –

8080 –

7070 –

6060 –

5050 –

YearYear

Po

wer

dem

an

dP

ow

er

dem

an

d

Trend line,Trend line,

yy = 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 seasonal model can The multiplicative seasonal model can modify trend data to accommodate modify trend data to accommodate seasonal variations in demandseasonal variations in demand

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

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

5.5. 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

Seasonal Index ExampleSeasonal Index Example

JanJan 8080 8585 105105 9090 9494

FebFeb 7070 8585 8585 8080 9494

MarMar 8080 9393 8282 8585 9494

AprApr 9090 9595 115115 100100 9494

MayMay 113113 125125 131131 123123 9494

JunJun 110110 115115 120120 115115 9494

JulJul 100100 102102 113113 105105 9494

AugAug 8888 102102 110110 100100 9494

SeptSept 8585 9090 9595 9090 9494

OctOct 7777 7878 8585 8080 9494

NovNov 7575 7272 8383 8080 9494

DecDec 8282 7878 8080 8080 9494

DemandDemand AverageAverage AverageAverage Seasonal Seasonal MonthMonth 20032003 20042004 20052005 20032003--20052005 MonthlyMonthly IndexIndex


JanJan 8080 8585 105105 9090 9494

FebFeb 7070 8585 8585 8080 9494

MarMar 8080 9393 8282 8585 9494

AprApr 9090 9595 115115 100100 9494

MayMay 113113 125125 131131 123123 9494

JunJun 110110 115115 120120 115115 9494

JulJul 100100 102102 113113 105105 9494

AugAug 8888 102102 110110 100100 9494

SeptSept 8585 9090 9595 9090 9494

OctOct 7777 7878 8585 8080 9494

NovNov 7575 7272 8383 8080 9494

DecDec 8282 7878 8080 8080 9494


0.9570.957

Seasonal index = average 2003-2005 monthly demand

average monthly demand

= 90/94 = .957


JanJan 8080 8585 105105 9090 9494 0.9570.957

FebFeb 7070 8585 8585 8080 9494 0.8510.851

MarMar 8080 9393 8282 8585 9494 0.9040.904

AprApr 9090 9595 115115 100100 9494 1.0641.064

MayMay 113113 125125 131131 123123 9494 1.3091.309

JunJun 110110 115115 120120 115115 9494 1.2231.223

JulJul 100100 102102 113113 105105 9494 1.1171.117

AugAug 8888 102102 110110 100100 9494 1.0641.064

SeptSept 8585 9090 9595 9090 9494 0.9570.957

OctOct 7777 7878 8585 8080 9494 0.8510.851

NovNov 7575 7272 8383 8080 9494 0.8510.851

DecDec 8282 7878 8080 8080 9494 0.8510.851



JanJan 8080 8585 105105 9090 9494 0.9570.957

FebFeb 7070 8585 8585 8080 9494 0.8510.851

MarMar 8080 9393 8282 8585 9494 0.9040.904

AprApr 9090 9595 115115 100100 9494 1.0641.064

MayMay 113113 125125 131131 123123 9494 1.3091.309

JunJun 110110 115115 120120 115115 9494 1.2231.223

JulJul 100100 102102 113113 105105 9494 1.1171.117

AugAug 8888 102102 110110 100100 9494 1.0641.064

SeptSept 8585 9090 9595 9090 9494 0.9570.957

OctOct 7777 7878 8585 8080 9494 0.8510.851

NovNov 7575 7272 8383 8080 9494 0.8510.851

DecDec 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 2006


140140 –

130130 –

120120 –

110110 –

100100 –

9090 –

8080 –

7070 –| | | | | | | | | | | |

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

TimeTime

Dem

an

dD

em

an

d

2006 Forecast2006 Forecast

2005 Demand 2005 Demand

2004 Demand2004 Demand

2003 Demand2003 Demand

San Diego HospitalSan Diego Hospital

10,20010,200 –

10,00010,000 –

9,8009,800 –

9,6009,600 –

9,4009,400 –

9,2009,200 –

9,0009,000 – | | | | | | | | | | | |

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

MonthMonth

Inp

ati

en

t D

ays

Inp

ati

en

t D

ays

95309530

95519551

95739573

95949594

96169616

96379637

96599659

96809680

97029702

97239723

97459745

97669766


Trend DataTrend Data


1.061.06 –

1.041.04 –

1.021.02 –

1.001.00 –

0.980.98 –

0.960.96 –

0.940.94 –

0.92 – | | | | | | | | | | | |


MonthMonth

Ind

ex f

or

Inp

ati

en

t D

ays

Ind

ex f

or

Inp

ati

en

t 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


10,20010,200 –

10,00010,000 –

9,8009,800 –

9,6009,600 –

9,4009,400 –

9,2009,200 –

9,0009,000 – | | | | | | | | | | | |


MonthMonth

Inp

ati

en

t D

ays

Inp

ati

en

t 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 Forecasting

Used 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

yy == aa ++ 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($000,000), y($000,000), y ($000,000,000), x($000,000,000), x

2.02.0 11

3.03.0 33

2.52.5 44

2.02.0 22

2.02.0 11

3.53.5 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 xy

2.0 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= = = .25xyxy -- nxynxy

xx22 -- nxnx22

51.5 51.5 -- (6)(3)(2.5)(6)(3)(2.5)

8080 -- (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

yy = 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 $600$600 million, then:million, then:

SalesSales = 1.75 + .25(6)= 1.75 + .25(6)

SalesSales = $325,000= $325,000

3.25

Standard Error of the EstimateStandard Error of the Estimate

A forecast is just a point estimate of a A forecast is just a point estimate of a future valuefuture value

This point is This point is actually the actually the mean of a mean of a probabilityprobabilitydistributiondistribution


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 point

yycc == 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 ==((yy -- yycc))22

nn -- 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 yy -- bb xyxy

nn -- 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 yy -- bb xyxy

nn -- 22

39.539.5 -- 1.75(15) 1.75(15) -- .25(51.5).25(51.5)

66 -- 22

SSy,xy,x == .306.306

The standard error The standard error of the estimate is of the estimate is $30,600$30,600 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 toto +1+1

CorrelationCorrelation Correlation CoefficientCorrelation Coefficient

r = r = nn xyxy -- xx yy

[[nn xx22 -- (( xx))22][][nn yy22 -- (( yy))22]]

Correlation CoefficientCorrelation Coefficient

r = r = nn xyxy -- xx yy

[[nn xx22 -- (( xx))22][][nn yy22 -- (( yy))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 toto 11

Easy to interpretEasy to interpret

CorrelationCorrelation

For the Nodel Construction example:For the Nodel Construction example:

rr = .901= .901

rr22 = .81= .81

Multiple Regression AnalysisMultiple Regression Analysis

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

yy == aa ++ 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 AnalysisMultiple Regression Analysis

yy = 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

SalesSales = 1.80 + .30(6) = 1.80 + .30(6) -- 5.0(.12) = 3.005.0(.12) = 3.00

SalesSales = $300,000= $300,000

Measures how well the forecast is Measures how well the forecast is predicting actual valuespredicting actual values

Ratio 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 values

If 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

RSFERSFE

MADMAD==

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 Tracking Signal ExampleExample

CumulativeCumulativeAbsoluteAbsolute AbsoluteAbsolute

ActualActual ForecastForecast ForecastForecast ForecastForecastQtrQtr DemandDemand DemandDemand ErrorError RSFERSFE ErrorError ErrorError MADMAD

11 9090 100100 --1010 --1010 1010 1010 10.010.0

22 9595 100100 --55 --1515 55 1515 7.57.5

33 115115 100100 +15+15 00 1515 3030 10.010.0

44 100100 110110 --1010 --1010 1010 4040 10.010.0

55 125125 110110 +15+15 +5+5 1515 5555 11.011.0

66 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 10.010.0

22 9595 100100 --55 --1515 55 1515 7.57.5

33 115115 100100 +15+15 00 1515 3030 10.010.0

44 100100 110110 --1010 --1010 1010 4040 10.010.0

55 125125 110110 +15+15 +5+5 1515 5555 11.011.0

66 140140 110110 +30+30 +35+35 3030 8585 14.214.2

Tracking Signal Tracking Signal ExampleExample

TrackingSignal

(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 andand +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 and and coefficients used in exponential coefficients used in exponential smoothing to continually minimize smoothing to continually minimize forecast errorforecast error

This technique is called adaptive This technique is called adaptive smoothingsmoothing

Focus ForecastingFocus Forecasting

Developed 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 modelsalways better than simple models

2.2. There is no single techniques that should There is no single techniques 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 items

The 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

dfmd 3513 chapter-6 forecasting

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