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ForecastingPPC Course 2
Industrial Engineering Department
Sepuluh Nopember Institute of Technology
Indonesia 2008
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What is Forecasting ?
Forecasting
Y
n n + 1 n + 2Function of
Time
Forecasting is an approach to estimate
or deal with something that contains
uncertainty and related with time in the
future
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What is forecasting ?
• The process of estimating future demand in terms of thequantity, timing, quality, and location for desired productsand services
• Rely on logical methods of manipulating data that havebeen generated by historical events
• Forecasting is an essential element of capital budgeting.
Sales will be$200 Million!
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why we need forecasting?
• All organizations operate in an atmosphere of uncertainty and become more complex
• All decisions must be made for uncertainty
future based on imperfect knowledge• Educated guesses more valuable than
uneducated guesses
• Not to say that intuitive forecasting is bad• The quantitative forecasting technique to bethe starting point in the effective forecastingand valuable supplement
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Who needs forecasts?
• Every organization, large and small, privateand public, must plan to meet the condition of the future for which it has imperfectknowledge.
• Across all functional line: finance, marketing,personnel, and production areas.
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Characteristics of forecasting
• Forecasts are usually wrong, seldom correct, andinvolves error find the best method
• Forecast should include a measure of forecast
error• Forecasting methods assume there is some
underlying stability in the system• Family / grouped / aggregated data forecasts
are usually more accurate than item forecast• Short range forecasts are more accurate than
long-range forecast
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Forecasting in Business
• Marketing - sale forecast
• Operations - capacity, scheduling,
inventory
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Assumptions of Forecast
• Information (data) about the past is
available
• The pattern of the past will continue into thefuture (Time Series Models).
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Forecast in MTO
•Forecast tidak banyak dikenal dan dipergunakan diperusahaan Make To Order
• Overproduction di perusahaan dengankarakteristik MTO justru adalah kerugian
• Forecast bukan merupakan isu utama di MTO, justru isu utama adalah nervousness system,responsiveness, dan material management (Pujawan, 2000).
• Pada MTO, forecast tidak lagi dilakukan terhadapdemand, melainkan pada penggunaan resource dimasa datang.
But, demand forecast is very useful in MTS
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Demand Management
A
B(4) C(2)
D(2) E(1) D(3) F(2)
Dependent Demand:
Raw Materials,
Component parts,
Sub-assemblies, etc.
Independent Demand:Finished Goods
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Forecasting Steps
• Decide what needs to be forecast – Level of detail, units of analysis & time horizonrequired
• Evaluate and analyze appropriate data
– Identify needed data & whether it’s available• Select and test the forecasting model – Cost, ease of use & accuracy
• Generate the forecast
• Monitor forecast accuracy over time
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Characteristics of a good forecast
• Accuracy bias (when forecast arepersistently too high or too low) & consistency (concerned with the size of forecast error)
• Cost
• Response stability & responsive
• Simplicity easy to make, understand & use
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Types of Forecasting Methods
Depend on : – TIME FRAME
Indicates how far into the future is forecast
• Short- to mid-range forecast – typically encompasses the immediate future
– daily up to two years• Long-range forecast
– usually encompasses a period of time longer than twoyears
– DEMAND BEHAVIOR
– CAUSES OF BEHAVIOR
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Demand Behavior
• TrendTrend
– a gradual, long-term up or down movement of demand – Due to population, technology etc
• Random variationsRandom variations – movements in demand that do not follow a pattern
• CycleCycle – an up-and-down repetitive movement in demand – Non-annual; multi-year – Due to interactions of factors influencing economy
• Seasonal patternSeasonal pattern – an up-and-down repetitive movement in demand occurring periodically – Occurs within one year – Due to weather, customs etc
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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
D e m a n d
D e m a n d
D e m a n
d
D e m a n d
D e m a n d
D e m a n d
D e m a n d
D e m a n d
RandomRandommovementmovement
Forms of Forecast Movement
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Components of an Observation
Observed demand (O) =
Systematic component (S) + Random component(R)
Level (current deseasonalized demand)
Trend (growth or decline in demand)
Seasonality (predictable seasonal fluctuation)
• Systematic component: Expected value of demand• Random component: The part of the forecast that deviates
from the systematic component• Forecast error: difference between forecast and actual demand
Chopra, 2007
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Forecasting Process (in general)
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
Copyright 2006 John Wiley & Sons, Inc.Copyright 2006 John Wiley & Sons, Inc.
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Forecasting Technique
Forecasting
Models
Qualitative Quantitative
CausalTime serie
Regression EconometricMoving
average DecompositionExponential
smoothing
Sales forc
composite
Consume
survey
Jury of
executiv
Delphi
method
ARIMA Neural
networks
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Forecasting
• Predicting the Future
• Qualitative forecast methods
– Subjective (uses experience
and judgment to establishfuture behaviours)
• Quantitative forecast methods
– based on mathematicalformulas
– uses historical data toestablish relationships andtrends which can beprojected into the future
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Types of Forecasts
• Qualitative (Extrinsic) : – requiring no manipulation of data, – used only judgment of the forecaster, – Evaluating factors other than historical data – concern with identifying various factors that can influence
demand – suitable for long term forecasting
• Quantitative (Intrinsic) : – no input of judgment, – mechanical procedure that produce quantitative
result, – Rely on historical information – using statistical techniques – suitable for short term forecasting
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• Causal• Judgment
• Causal• Judgment
• Time series• Causal• Judgment
ForecastingTechnique
• Facil ity location• Capacityplanning
• Processmanagement
• Staff planning• Productionplanning
• Master productionscheduling
• Purchasing• Distribution
• Inventorymanagement
• Final assemblyscheduling
• Workforce
scheduling• Master productionscheduling
Decision
Area
• Total salesTotal sales• Groups or families
of products or
services
• Individual
products orservices
ForecastQuality
Long Term(more than 2 years)
Medium Term(3 months– 2
years)
Short Term
(0–3 months)
Application
Time Horizon
Demand Forecast Applications
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Detail steps inchoosing
forecast method
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The keys to employing qualitative forecasting are:
• Data as an historicalseries is notavailable,or is not
relevant to futureneeds.
♦An unusual product or a
unique project is being
contemplated.
1. Qualitative Methods (Extrinsic)
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1. Qualitative Methods (Extrinsic)
• Applications: New product Development,new technology
• Technique : – Management Decision – Jury of executive opinion
– Delphi Technique – Sales Force Composite – Growth curve – Scenario writing
– Market Research – Historical Analogies – Life Cycle Curves – Focus groups
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1. Qualitative Methods
Type Characteristics Strengths WeaknessesExecutive
opinion
A group of managers
meet & come up with
a forecast
Good for strategic or
new-product
forecasting
One person's opinion
can dominate the
forecast
Market
research
Uses surveys &
interviews to identify
customer preferences
Good determinant of
customer preferences
It can be difficult to
develop a good
questionnaire
Delphi
method
Seeks to develop a
consensus among a
group of experts
Excellent for
forecasting long-term
product demand,
technological
Time consuming to
develop
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1. Qualitative Methods- in g e ne r a l -i n g ene r a l -
Kelebihan :– Mampu melakukan
prediksi walaupuntidak ada dukungan
data historis– Umumnya cukup valid
karena melibatkanpara expert yang
kompeten denganpermasalahan yangterjadi, sehinggamodel dan metodeyang dipergunakancukup akurat
Kelemahan :
– Cost – nya sangattinggi karenamelibatkan expert terkait denganlabour time
– Memakan waktuyang cenderunglama apalagi
“Building Models &Methods”memerlukanvalidasi guna hasil
yang relevan
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2. Quantitative methods(Intrinsic)
Used when sufficient historical data are available and when
these data values are judged to be representative of theunknown future
Assumption : the past can be extended into the future insome meaningful manner
Can be categorized :• Time series methods : focus entirely on pattern, pattern
change, disturbance caused by random influence
– Moving average, exponential smoothing, Holts, winter• causal methods : identification and determination of relationship between the variable to be forecast and otherinfluencing variable – Regression
Future pattern following past pattern
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2.1 Time series methods
Time series consist of data that are collected /observed over successive increment of time
Assumption : What happen in the past willcontinued and occurs in the future with special
pattern followed.Exploring the data pattern
• Display data → time series graph
• Autocorrelation test • Understanding what the data are suggesting
Future pattern following past pattern
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Exploring data pattern usingTime series graph
• Component of time series – Trend (T)
– Cycle (C)
– Seasonal (S)
– Random (irregular variation, noise)
• Note : Cyclical (fluctuations > a year) aredifficult to identify, hence are often regardedas part of the trend
( trend-cycle component)
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Types of Time Series Models
• Nonseasonal Model
– Trend, Naïve – Moving average – Weighted moving average – Exponential Smoothing
• Seasonal Model
– Time Series Decomposition – ARIMA – Artificial Neural Network (ANN)
• Seasonal & Trend
– Winter
(Trend & Seasonality CorrectedExponential Smoothing)
• Trend Model
– Holt’s Model
(Trend corrected Exponential Smoothing)
Moving Average Model
Capture Trend & Seasonal
Exponential Smoothing Model Trend and sometimes Seasonal(Holt and Winter Model)
Decomposition Almost all, except Cycle (Candecompose but the value for recompose need judgment fromthe user)
Not discussed
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Trend Model
• Trend Model sangat tepat dipergunakan apabila karakteristik data cenderung jelas
bersifat trend.• Prinsip Trend adalah mencoba melakukan Curve Fitting berdasarkan suatu model
persamaan tertentu untuk mendapatkan persamaan garis yang merefleksikan kondisidata aktual dengan menjadikan nilai t (waktu) sebagai variabel independen
• Beberapa model persamaan garis yang dipergunakan : – Linear Simple Linear Regression sebagai fungsi t y = ax + b + e
– Kuadratik Y t = a + bt + ct 2
– Power Y t = at b
– Model persamaan garis lainnya S – Curve, Eksponential, dll
0
0
0
0
0
0
0
0
0 0 0 0 0 0 0 0 0 00
0
000
0000
0000
0000
0000
0000
0 0 0 0 0 0 0 0 0 00
Power
Quadratic
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Application of Trend using Software
Using Minitab
• Minitab pada perhitungan Trendmempergunakan 4 persamaangaris
– Linear
– Kuadratik
– Eksponential – S – Curve
• Klik Analyze Time Series Trend Analysis
SPPS 10.0 for Windows• SPSS menggunakan 11 Persamaangaris, yaitu
– Linear - Logaritma
– Inverse - Kuadratik
– Kubik - Power – Compound - S – Curve
– Logistics - Growth
– Eksponential
• Klik Analyze
Regression
CurveEstimation
MINITAB.lnk
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EXAMPLE – (Trend Projection)
Periods Sales
January 185
February 174
March 200
April 210May 205
June 245
July 234
August 250
September 264
October 245
November 235
December 242
PT Makmur Jaya mempunyai data sales selama 2003
sebagaimana data disamping. Anda sebagai Planner
perusahaan ditugaskan untuk membuat estimasi sales Januari
– Februari 2004. Berdasarkan hasil plotting, anda melihat
kecenderungan data yang menaik tanpa adanya efek seasonal,
sehingga anda memutuskan akan menggunakan trend
projection, dengan 4 pers. Garis, linear, kuadratik, power, dan
kubik. Setelah diperhitungkan, mana yang akan anda pilihsebagai rumusan anda ???
Sales
000111
000 000 000
000111
000 111000 000 000
0
00
000
000
000
000
000
J a n u
a r
F e b r
u a r
M a r c h
A p r i l
M a y
J u n e
J u l y
A u g u
s
S e p t e m b
O c t o b e
N o v e
m b e
D e c e m b e
Moths
S a l e
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EXAMPLE (Trend Projection) – Cont’d
Power Kubik Kuadratik Linear HistoryError Powe Fit Powe Error Cubic Fit Cubic Error Kuadrat Fit Kuadrat Error Linear Fit Linear Sales Periods
184,00 1,00 93,85 91,15 121,56 63,44 156,66 28,34 185 January
178,26 6,74 27,36 157,64 66,52 118,48 128,32 56,68 174 February
164,40 20,60 18,07 203,07 19,88 165,12 99,98 85,02 200 March
139,51 45,49 46,01 231,01 18,37 203,37 71,64 113,36 210 April
100,90 84,10 60,06 245,06 48,22 233,22 43,30 141,70 205 May
46,05 138,95 63,80 248,80 69,68 254,68 14,96 170,04 245 June
27,43 212,43 60,83 245,83 82,74 267,74 13,38 198,38 234 July
121,83 306,83 54,72 239,72 87,40 272,40 41,72 226,72 250 August
239,39 424,39 49,08 234,08 83,66 268,66 70,06 255,06 264 SEPT.
382,25 567,25 47,48 232,48 71,53 256,53 98,40 283,40 245 October
552,49 737,49 53,52 238,52 51,00 236,00 126,74 311,74 235 NOV
752,17 937,17 70,78 255,78 22,08 207,08 155,08 340,08 242 DECEM
240,72 53,80 61,89 85,02 MAD
101204,41 3242,43 4733,66 9571,56 MSD
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Moving Average
• Na i v e forecast – demand the current period is used as nextperiod’s forecast
• Simple moving average
– stable demand with no pronounced behavioralpatterns
• Weighted moving average
– weights are assigned to most recent data
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Moving Average:Naïve Approach
JanJan 120120
FebFeb 9090Mar Mar 100100
Apr Apr 7575
MayMay 110110
JuneJune 5050
JulyJuly 7575
AugAug 130130
SeptSept 110110
OctOct 9090
ORDERSORDERS
MONTHMONTH PER MONTHPER MONTH
--
1201209090
100100
7575
110110
5050
7575
130130
110110
9090Nov -Nov -
FORECASTFORECAST
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Simple Moving Average
MAMAnn ==
nn
i i = 1= 1 DDi i
nn
wherewhere
nn == number of periodsnumber of periods
in the movingin the moving
averageaverageDDi i == demand in perioddemand in period i i
3 month Simple Moving3 month Simple Moving
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3-month Simple Moving3-month Simple Moving
AverageAverage
JanJan 120120
FebFeb 9090
Mar Mar 100100
Apr Apr 7575
MayMay 110110
JuneJune 5050
JulyJuly 7575
ORDERSORDERS
MONTHMONTH PERPER
MONTHMONTH MAMA33 ==
33
i i = 1= 1DDi i
33
==90 + 110 + 13090 + 110 + 130
33
= 110 orders= 110 ordersfor Novfor Nov
– –
– – – –
103.3103.3
88.388.3
95.095.0
78.378.3
78.378.385.085.0
105.0105.0
110.0110.0
MOVINGMOVING
AVERAGEAVERAGE
5 month Simple Mo ing
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5-month Simple MovingAverage
JanJan 120120
FebFeb 9090
Mar Mar 100100
Apr Apr 7575
MayMay 110110
JuneJune 5050
JulyJuly 7575
AugAug 130130
ORDERSORDERS
MONTHMONTH PERPER
MONTHMONTH MAMA5 5 ==
55
i i = 1= 1DDi i
55
==90 + 110 + 130+75+5090 + 110 + 130+75+50
55
= 91 orders= 91 orders
for Novfor Nov
– –
– –
– – – –
– –
99.099.0
85.085.0
82.082.0
88.088.0
95.095.0
91.091.0
MOVINGMOVING
AVERAGEAVERAGE
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Smoothing Effects
150150 –
125125 –
100100 –
7575 –
5050 –
2525 –
00 –
| | | | | | | | | | |
JanJan FebFeb Mar Mar Apr Apr MayMay JuneJune JulyJuly AugAug SeptSept OctOct NovNov
ActualActual
O r d e r s
O r d e r s
MonthMonth
5-month5-month
3-month3-month
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Weighted Moving Average
WMAWMAnn ==
i i = 1= 1Σ W W
i i DDi i
wherewhere
W W i i = the weight for period= the weight for period i i ,,
between 0 and 100between 0 and 100
percentpercent
Σ W W i i = 1.00= 1.00
Adjusts Adjusts
movingmoving
averageaveragemethod tomethod to
more closelymore closely
reflect datareflect datafluctuationsfluctuations
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Weighted Moving Average Example
MONTH MONTH WEIGHT WEIGHT DATADATA
August August 17%17% 130130
September September 33%33% 110110October October 50%50% 9090
WMAWMA33 ==
33
i i = 1= 1 W W i i DDi i
= (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
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• Increasing n makesforecast less sensitive to
changes• Do not forecast trends well
• Require sufficient historicaldata
Disadvantages of M.A. Methods
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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 Smoothing
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Exponential Smoothing: Notation
• Level of the time series at time t :• Trend in the time series at time t :
• Seasonal index in the the time series
at time t :• Level smoothing parameter:
• Trend smoothing parameter:
• Seasonal index smoothing parameter:
• Number of seasons: M
t
L
t T
t S
00 ≤≤α
00 ≤≤ β
00 ≤≤ γ
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F F t t +1+1 == αα DD
t t + (1 -+ (1 - αα))F F
t t
where:where:F F
t t +1+1 == forecast for next periodforecast for next period
DDt t == actual demand for present periodactual demand for present period
F F t t == previously determined forecast for previously determined forecast for present periodpresent period
αα == weighting factor, smoothing constantweighting factor, smoothing constant
Exponential Smoothing (cont.)
Level smoothing parameter
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Effect of Smoothing Constant
0.00.0 ≤ α ≤≤ α ≤ 1.01.0
If If αα = 0.20, then= 0.20, then F F t t +1+1 = 0.20= 0.20 DDt t + 0.80+ 0.80 F F t t
If If αα = 0, then= 0, then F F t t +1+1 = 0= 0 DD
t t + 1+ 1 F F
t t 0 =0 = F F t t
Forecast does not reflect recent dataForecast does not reflect recent data
If If αα = 1, then= 1, then F F t t +1+1 = 1= 1 DD
t t + 0+ 0 F F
t t == DDt t
Forecast based only on most recent dataForecast based only on most recent data
F F t t +1+1 == α DDt t + (1 -+ (1 - α))F F t t
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F F 22 == αDD11 + (1 -+ (1 - α))F F 11
= (0.30)(37) + (0.70)(37)= (0.30)(37) + (0.70)(37)
= 37= 37
F F 33 == αDD22 + (1 -+ (1 - α))F F 22
= (0.30)(40) + (0.70)(37)= (0.30)(40) + (0.70)(37)
= 37.9= 37.9
F F 1313 == αDD1212 + (1 -+ (1 - α))F F 1212
= (0.30)(54) + (0.70)(50.84)= (0.30)(54) + (0.70)(50.84)
= 51.79= 51.79
Exponential Smoothing (α=0.30)
PERIODPERIOD MONTHMONTH
DEMANDDEMAND
11 JanJan 3737
22 FebFeb 4040
33 Mar Mar 4141
44 Apr Apr 3737
55 MayMay 4545
66 JunJun 5050
77 JulJul 4343
F F t t +1+1 == α DDt t + (1 -+ (1 - α))F F t t
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FORECAST,FORECAST, F F t t + 1+ 1
PERIODPERIOD MONTHMONTH DEMANDDEMAND ((α = 0.3)= 0.3) ((α = 0.5)= 0.5)
11 JanJan 3737 – – – –
22 FebFeb 4040 37.0037.00 37.0037.00
33 Mar Mar 4141 37.9037.90 38.5038.50
44 Apr Apr 3737 38.8338.83 39.7539.75
55 MayMay 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 AugAug 4747 43.1443.14 44.4244.42
99 SepSep 5656 44.3044.30 45.7145.71
1010 OctOct 5252 47.8147.81 50.8550.851111 NovNov 5555 49.0649.06 51.4251.42
1212 DecDec 5454 50.8450.84 53.2153.21
1313 JanJan – – 51.7951.79 53.6153.61
Exponential Smoothing (cont.)
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7070 –
6060 –
5050 –
4040 –
3030 –
2020 –
1010 –
00 –
| | | | | | | | | | | | |
11 22 33 44 55 66 77 88 99 1010 1111 1212 1313
ActualActual
O r d e r s
O r d e r s
MonthMonth
Exponential Smoothing (cont.)
α = 0.50= 0.50
α = 0.30= 0.30
Larger α, more responsive forecast;
Smaller α, smoother forecast
“Best” α can be found by Solver Suitable for relatively stable time
series
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Simple Exponential Smoothing
• A special type of weighted moving average – Include all past observations – Use a unique set of weights that weight recent observations
much more heavily than very old observations
α
α α
α α
α α
( )
( )
( )
0
0
0
0
0
−
−
−
weightDecreasing weightsgiven
to olderobservations
0 0< <α
Toda
Compa ison of E ponential Smoothing and Simple
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Comparison of Exponential Smoothing and SimpleMoving Average
• Both Methods – Are designed for stationary demand – Require a single parameter – Lag behind a trend, if one exists
– Have the same distribution of forecast error if
• Moving average uses only the last N periods data,exponential smoothing uses all data
• Exponential smoothing uses less memory and requiresfewer steps of computation; store only the most recentforecast!
)0/(0 +=α N
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Trend-Corrected ExponentialSmoothing (Holt ’s Model)
• Appropriate when the demand is assumed to have alevel and trend in the systematic component of demand but no seasonality
• Obtain initial estimate of level and trend by running a
linear regression of the following form:D t = at + b
T0 = a
L0 = b
In period t, the forecast for future periods isexpressed as follows:Ft+1 = Lt + Tt
Ft+n = Lt + nTt
Demand & time
correlation is linear
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Trend-Corrected ExponentialSmoothing (Holt ’s Model)
After observing demand for period t, revise theestimates for level and trend as follows:Lt+1 = αDt+1 + (1-α)(Lt + Tt)
Tt+1 = β(Lt+1 - Lt) + (1-β)Tt
α = smoothing constant for levelβ = smoothing constant for trendExample 7.3, p. 188: Tahoe Salt demand data.
Forecast demand for period 1 using Holt’s model
(trend corrected exponential smoothing)Using linear regression,L0 = 12015 (linear intercept)
T0 = 1549 (linear slope)
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Quarter Demand Dt
II, 0000 1111
III, 0000 11111
IV, 0000 00000
I, 0000 11111
II, 0000 00000
III, 0000 00000
IV, 0000 00000
I, 0000 00000
II, 0000 00000III, 0000 00000
IV, 0000 00000
I, 0000 00000
Quarterly Demand for Tahoe SaltTable 7.1 (Chopra, p. 180)
Forecast demand
for the next four
quarters.
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Holt’s Model Example (continued)
Forecast for period 1:F1 = L0 + T0 = 12015 + 1549 = 13564Observed demand for period 1 = D1 = 8000E1 = F1 - D1 = 13564 - 8000 = 5564
Assume α = 0.1, β = 0.2L1 = αD1 + (1-α)(L0+T0) = (0.1)(8000) + (0.9)(13564) = 13008
T1 = β(L1 - L0) + (1-β)T0 = (0.2)(13008 - 12015) +
(0.8)(1549)= 1438F2 = L1 + T1 = 13008 + 1438 = 14446F5 = L1 + 4T1 = 13008 + (4)(1438) = 18760
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Trend- and Seasonality-CorrectedExponential Smoothing
• Appropriate when the systematic component of demand is assumed to have a level, trend, andseasonal factor (Winter’s model)
• Systematic component = (level+trend)(seasonal
factor)• Assume periodicity p
• Obtain initial estimates of level (L0), trend (T0),seasonal factors (S1,…,Sp) using procedure for static
forecasting• In period t, the forecast for future periods is given
by:Ft+1 = (Lt+Tt)(St+1) and Ft+n = (Lt + nTt)St+n
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Trend- and Seasonality-CorrectedExponential Smoothing (continued)
After observing demand for period t+1, revise estimates forlevel, trend, and seasonal factors as follows (Eq 7.18-7.20,p. 189):
Lt+1 = α(Dt+1 /St+1) + (1-α)(Lt+Tt)
Tt+1 = β(Lt+1 - Lt) + (1-β)Tt
St+p+1 = γ (Dt+1 /Lt+1) + (1-γ )St+1
α = smoothing constant for levelβ = smoothing constant for trend
γ = smoothing constant for seasonal factorExample 7.4, p. 189: Tahoe Salt data. Forecast demand for
period 1 using Winter’s model.Initial estimates of level, trend, and seasonal factors are
obtained as in the static forecasting case
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Trend- and Seasonality-Corrected ExponentialSmoothing Example (continued)
L0 = 18439 T0 = 524 S1=0.47, S2=0.68, S3=1.17, S4=1.67F1 = (L0 + T0)S1 = (18439+524)(0.47) = 8913
The observed demand for period 1 = D1 = 8000
Forecast error for period 1 = E1 = F1-D1 = 8913 - 8000 = 913
Assume α = 0.1, β=0.2, γ =0.1; revise estimates for level andtrend for period 1 and for seasonal factor for period 5
L1 = α(D1/S1)+(1-α)(L0+T0) = (0.1)(8000/0.47)+(0.9)(18439+524)=18769
T1 = β(L1-L0)+(1-β)T0 = (0.2)(18769-18439)+(0.8)(524) = 485S5 = γ (D1/L1)+(1-γ )S1 = (0.1)(8000/18769)+(0.9)(0.47) = 0.47
F2 = (L1+T1)S2 = (18769 + 485)(0.68) = 13093
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Evaluation Non Seasonal Models
• Naïve cenderung harus dihindari
• MA akan cenderung bisa dipergunakan untuk estimate sales harian,dimana efek trend ataupun seasonal tidak terlalu nampak Sales /Produksi Harian
• E.S memiliki hasil yang responsive atau smoothing terhadap actual data.Tapi masalahnya adalah :
– Hanya tepat untuk one periods ahead – Asumsi bahwa data mengikuti kecenderungan eksponensial,
sehingga seharusnya nilai foracast adalah nilai tertinggi dari nilainialai aktual sebelumnya
• Holt dan Winter memiliki output yang baik, tapi kurang aplikatif karena
kesulitan dalam mengkonversikan nilai aktual dari alpha, beta, dangamma dalam kondisi aktual
• Trend hanya tepat dipergunakan apabila tidak terlihat adanyaseasonal dan data aktual jelas terlihat pola nail turunnya
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• Mean Square Error – MSE / MSD
– Excel: =SUMSQ(error range)/COUNT(error range)
• Mean Absolute Percentage Error - MAPE
• R 2 - only for curve fitting model such as regression
• In general, the lower the error measure (BIAS, MAD, MSE) or the higherthe R 2, the better the forecasting model
n
(Error)
n
Forecast)-(Actual MSE
00
∑∑==
nActual
|Forecast-Actual|
MAPE∑
=
%000*
Evaluation of Forecasting Model
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Measuring Accuracy, Forecast Errors
To compare different time series techniques or to selectthe “best” set of initial values for the parameters, use acombination of the the following four metrics:
Mean Absolute Deviation Most popular but
Mean Absolut Percent Error Should be used in tandem with MAD
Mean Square Error
Root Mean Square Error
n
FA
=MAD1
∑=
−n
i
ii
∑=
−n
i i
ii
n 1 AFA100 =MAPE
( )
n
FA
=MSE 1
2
∑=
−n
i
ii
MSERMSE =
R2 - only for curve fitting model such as regression
In general, the lower the error measure (MAD, MAPE, MSE, RMSE) or
the higher the R2, the better the forecasting model
MAD P bl D
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MAD Problem Data
Question: What is the MAD value given
the forecast values in the table below?
Month Sales Forecast
1 220 n/a2 250 255
3 210 205
4 300 320
5 325 315
MAD P bl S l ti
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MAD Problem Solution
Month Sales Forecast Abs Error 1 220 n/a
2 250 255 5
3 210 205 5
4 300 320 20
5 325 315 10
40
MAD =
A - F
n=
00
0=0
t tt=0
n
∑Note that by itself, the MAD
only lets us know the mean
error in a set of forecasts.
T ki Si l
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Tracking Signal
The Tracking Signal or TS is a measure that
indicates whether the forecast average is keepingpace with any genuine upward or downwardchanges in demand.
Depending on the number of MAD’s selected, the TScan be used like a quality control chart indicating
when the model is generating too much error in itsforecasts.
TS is a monitoring system.
The TS formula is:
DeviationAbsoluteMean
ErrorsForecastof SumRunning=TS
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Confidence Interval for Forecast
• If normal, the error can provide aconfidence interval for the forecast. – The % confidence interval for the forecast
-Using the standard deviation of the
forecast:
0
)( 0
−
−
=∑
n
F A
S t
t t
F
F S Z Forecast Y (%)±=
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Example of Forecast Confidence Interval
• Using exponential smoothing in the previousexample, what is a 95% confidence interval forthe forecast for month 9?
alpha= .00
beta= .11
Month Demand
Excel exp
smooth
Text exp.
Smooth (A-F)^0
0 00 #N/A #N/A
0 11 .0000 .0000
0 00 .0000 .1111 00
0 11 .0000 .1111 0
0 00 .0000 .0000 .0000
0 00 .0000 .0000 .0000
0 00 .0000 .0000 .0000
0 00 .0000 .0000 .0000
0 00 .0000 .0000
sum= .00000
n= .000
n- =0 .000
Sf= .000
Start in month three to moreaccurately reflect the
exponential smoothing.
What is the interval
within which we are
95% confident that the
demand will be??
30.53+-1.96*5.11
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HOT ISSUE IN FORECASTING
• Agrregate Forecasting is more accurate than single
forecast• For MTS, Colllaboration idea has been developed tominimizing error and uncertainty
• Watch out with Bullwhip phenomenon, when all part inyour Supply Chain doing a forecast with same purposes !
• Forecasting can become an operational activity, or justcan become a strategic activity ! Clearly your forecastinggoals !
• Combination of subjective and objective methods is themost methods that implement by many company
nowadays• Forecasting not just a software !!!!!
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Final Thoughts- Big Picture
• Time is the enemy of the logistics plannerbecause time means uncertainty.
• Forecasting is often essential but think interms of reducing the importance / impact
of the forecast.• How ? Remember reduction in the cycle
time, demand management, Information
systems, and JIT ideas.
Types of Causal Forecasting
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Types of Causal Forecasting
• Regression
• Econometric models
• Input-Output Models:
Causal Methods
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Causal Methods
Linear Regression
• Causal methods are used when historical data areavailable and the relationship between the factor tobe forecasted and other external or internal factorscan be identified.
• Linear regression: A causal method in which onevariable (the dependent variable) is related to one ormore independent variables by a linear equation.
• Dependent variable: The variable that one wantsto forecast.
• Independent variables: Variables that areassumed to affect the dependent variable andthereby “cause” the results observed in the past.
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Y Y
XX
Linear Regression Model
Observed valueObserved value
Y Y aa bb X X i i i i + +
Y Y aa bb X X i i i i +
Error Error
Error Error
Regression lineRegression line
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Correlation
• Answers ‘how strong is the linearrelationship between 2 variables?’
• Coefficient of correlation used
• Used mainly for understanding
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Coefficient of Correlation Values
-1.0-1.0 +1.0+1.000
PerfectPerfect
PositivePositive
CorrelationCorrelation
Increasing degree of Increasing degree of
negative correlationnegative correlation
-.5-.5 +.5+.5
PerfectPerfect
NegativeNegative
CorrelationCorrelationNoNo
CorrelationCorrelation
Increasing degree of Increasing degree of
positive correlationpositive correlation
Linear Regression
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Line Formula
y = a + bx
y = the dependent variablea = the intercept
b = the slope of the line
x = the independent variable
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Linear Regression Formulas
a = Y – bX b = ∑xy – nXY
∑x² - nX²
a = intercept
b = slope of the line
X = ∑x = mean of x
n the x data
Y = ∑y = mean of yn the y data
n = number of periods
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Correlation
• Measures the strength of the relationshipbetween the dependent and independentvariable
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Correlation Coefficient Formula
r = ______n∑xy - ∑x∑y______
√[n∑x² - (∑x)²][n∑y² - (∑y)²]
______________________________________ r = correlation coefficient
n = number of periods
x = the independent variabley = the dependent variable
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Coefficient of Determination
• Another measure of the relationshipbetween the dependant and independentvariable
• Measures the percentage of variation in
the dependent (y) variable that isattributed to the independent (x) variabler = r²
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• Causal forecasting is accurate and efficient
• When strong correlation exists the modelis very effective
• No forecasting method is 100% effective
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Other Forecasting Methods
• Collaborative Planning Forecasting andReplenishment (CPFR)
– Establish collaborative relationships between buyers and sellers
– Create a joint business plan – Create a sales forecast
– Identify exceptions for sales forecast
– Resolve/collaborate on exception items
– Create order forecast – Identify exceptions for order forecast
– Resolve/collaborate on exception items
– Generate order
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Forecasting as a Process
The forecast process itself, typically done on a monthly
basis, consists of structured steps. They often are
facilitated by someone who might be called a demand
manager, forecast analyst, or demand/supply planner.
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