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
Figure 2.5Figure 2.5
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’’
fluctuationsfluctuations
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
fluctuationsfluctuations
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
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
Exponential SmoothingExponential Smoothing (cont.)(cont.)
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
Exponential SmoothingExponential Smoothing (cont.)(cont.)
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
Exponential SmoothingExponential Smoothing (cont.)(cont.)
= 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
Exponential SmoothingExponential Smoothing
Exponential SmoothingExponential Smoothing
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
Predicted demand Predicted demand = 142= 142 Ford MustangsFord Mustangs
Actual demand Actual demand = 153= 153
Smoothing constant Smoothing constant = .20= .20
New forecastNew forecast = 142 + .2(153 = 142 + .2(153 –– 142)142)
Exponential SmoothingExponential SmoothingExampleExample
Predicted demand Predicted demand = 142= 142 Ford MustangsFord Mustangs
Actual demand Actual demand = 153= 153
Smoothing constant Smoothing constant = .20= .20
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
Comparison of Forecast ErrorComparison of Forecast Error
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
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
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
Comparison of Forecast ErrorComparison of Forecast Error
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
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
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
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
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
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
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 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
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 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
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 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
Exponential Smoothing with Exponential Smoothing with Trend AdjustmentTrend Adjustment ExampleExample
Figure 4.3Figure 4.3
| | | | | | | | |
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
Figure 4.4Figure 4.4
DeviationDeviation11
DeviationDeviation55
DeviationDeviation77
DeviationDeviation22
DeviationDeviation66
DeviationDeviation44
DeviationDeviation33
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
Va
lue
s o
f D
ep
en
de
nt
Va
ria
ble
Figure 4.4Figure 4.4
DeviationDeviation11
DeviationDeviation55
DeviationDeviation77
DeviationDeviation22
DeviationDeviation66
DeviationDeviation44
DeviationDeviation33
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 Method
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
Least Squares ExampleLeast Squares Example
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^
Least Squares ExampleLeast Squares Example
| | | | | | | | |
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
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
0.9570.957
Seasonal index = average 2003-2005 monthly demand
average monthly demand
= 90/94 = .957
Seasonal Index ExampleSeasonal Index Example
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
DemandDemand AverageAverage AverageAverage Seasonal Seasonal MonthMonth 20032003 20042004 20052005 20032003--20052005 MonthlyMonthly IndexIndex
Seasonal Index ExampleSeasonal Index Example
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
DemandDemand AverageAverage AverageAverage Seasonal Seasonal MonthMonth 20032003 20042004 20052005 20032003--20052005 MonthlyMonthly IndexIndex
Expected annual demand = 1,200
Jan x .957 = 961,200
12
Feb x .851 = 851,200
12
Forecast for 2006
Seasonal Index ExampleSeasonal Index Example
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
Figure 4.6Figure 4.6
Trend DataTrend Data
San Diego HospitalSan Diego Hospital
1.061.06 –
1.041.04 –
1.021.02 –
1.001.00 –
0.980.98 –
0.960.96 –
0.940.94 –
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
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
Figure 4.7Figure 4.7
Seasonal IndicesSeasonal Indices
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
Figure 4.8Figure 4.8
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
Associative Forecasting Associative Forecasting ExampleExample
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
Associative Forecasting Associative Forecasting ExampleExample
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
Figure 4.9Figure 4.9
4.0 –
3.0 –
2.0 –
1.0 –
| | | | | | |0 1 2 3 4 5 6 7
Sale
s
Area payroll
3.25
Standard Error of the EstimateStandard Error of the Estimate
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
Standard Error of the EstimateStandard Error of the Estimate
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
Standard Error of the EstimateStandard Error of the Estimate
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
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