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ForecastingForecasting
13
ForFor Operations Management, 9eOperations Management, 9ebyby
Krajewski/Ritzman/MalhotraKrajewski/Ritzman/Malhotra 2010 Pearson Eduation 2010 Pearson Eduation
!omework" 2# 12#!omework" 2# 12#
1$# 1% &omit a'(1$# 1% &omit a'(
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ForecastingForecasting
Forecasts are critical inputs to business plans,annual plans, and budgets
Finance, human resources, marketing, operations,and supply chain managers need forecasts to
plan: output levels, purchases of services andmaterials, workforce and output schedules,inventories, and long-term capacities
Forecasts are made on many different variables
Forecasts are important to managing bothprocesses and managing supply chains
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ForecastingForecasting
arely perfect because of randomness
Forecasts more accurate for groups vs!individuals
"ccuracy decreases as time hori#on increases
I see that you will
get an A this seester.
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Demand PatternsDemand Patterns
" time seriesis the repeated observationsof demand for a service or product in theirorder of occurrence
%here are five basic time series patterns&ori#ontal
%rend
'easonal
(yclical
andom
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Demand PatternsDemand Patterns
*uantity
%ime
+a &ori#ontal: ata cluster about a hori#ontal line
Figure 13!1 .atterns of emand
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Demand PatternsDemand Patterns
*uantity
%ime
+b %rend: ata consistently increase or decrease
Figure 13!1 .atterns of emand
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Demand PatternsDemand Patterns
*uant
ity
onths
+c 'easonal: ata consistently show peaks and valleys
ear 1
ear 2
Figure 13!1 .atterns of emand
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Demand PatternsDemand Patterns
*uant
ity
ears
+d (yclical: ata reveal gradual increases anddecreases over e5tended periods
Figure 13!1 .atterns of emand
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Types of ForecastsTypes of Forecasts
7udgmental8ses sub9ective inputs
%ime series8ses historical data assuming the future will be like the past
"ssociative models8ses e5planatory variable+s to make a forecast regarding a dependent variable
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Judgment MethodsJudgment Methods
;ther methods +casual and time-series re
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Judgment MethodsJudgment Methods
arket research is a systematic approach todetermine e5ternal customer interest throughdata-gathering surveys
elphi method is a process of gaining consensus
from a group of e5perts while maintaining theiranonymity
8seful when no historical data are available
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Linear RegressionLinear Regression
" dependent variable is related to one or moreindependent variables by a linear ecause? the results observed in the past
'imple linear regression model is a straight line
Y@ aA bX
where
Y@ dependent variableX@ independent variablea @ Y-intercept of the lineb @ slope of the line
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Linear RegressionLinear Regression
-ependentva
riable
Bndependent variable
X
Y
=stimate ofY fromregressione
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Linear RegressionLinear Regression
%he sample correlation coefficient, r easures the direction and strength of the relationship
between the independent variable and the dependentvariable!
%he value of rcan range from 1! E rE 1!
%he sample coefficient of determination, r2
easures the amount of variation in the dependentvariable about its mean that is e5plained by theregression line
%he values of r2range from ! E r2E 1!
%he standard error of the estimate, syx easures how closely the data on the dependent variable
cluster around the regression line
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Using Linear RegressionUsing Linear Regression
=".D= 13!1%he supply chain manager seeks a better way to forecast thedemand for door hinges and believes that the demand is relatedto advertising e5penditures! %he following are sales andadvertising data for the past ) months:
onth 'ales +thousands of units "dvertising +thousands of G
1 2/$ 2!)
2 11/ 1!3
3 1/) 1!$
$ 11 1!
) 26 2!
%he company will spend G1,0) ne5t month on advertising forthe product! 8se linear regression to develop an e
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Using Linear RegressionUsing Linear Regression
';D8%B;HIe used .; for Iindows to determine the best values of a, b,the correlation coefficient, the coefficient of determination, andthe standard error of the estimate
a@
b@r@
r2@
syx@
%he regression e
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Using Linear RegressionUsing Linear Regression
%he regression line is shown in Figure 13!3! %he rof !64suggests an unusually strong positive relationship betweensales and advertising e5penditures! %he coefficient ofdetermination,r2, implies that 6/ percent of the variation insales is e5plained by advertising e5penditures!
1! 2!
"dvertising +G
2)
2
1)
1
)
'ales+:::units,
Jrass oor &inge
ata
Forecasts
Figure 13!3 Dinear egression Dine for the 'ales and "dvertising ata
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Linear Regression OutputLinear Regression Output
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Linear Regression AssumptionsLinear Regression Assumptions
!ariations around the line are rando "e#iations around the line norally
distributed
Predictions are being ade only within therange o$ obser#ed #alues
%or best results&
Always plot the data to #eri$y linearity Chec' $or data being tie(dependent
)all correlation ay iply that other #ariables
are iportant
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Time Series MethodsTime Series Methods
Bn a naive forecast the forecast for the ne5tperiod e
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Simple Moing AeragesSimple Moing Aerages
t@ actual demand in period t
Ft@ forecast for period t
=t@ forecast error in period t
n @ total number of periods in the average
t Ft =t
Ieek ate .i##as 3-wk " "bs
1 2(*un +0
2 (*un -+
1-(*un +2/ 2(*un +- ++.- 0.
+ 0(*un ++ +.- 2.-
- (*ul -0 +/. +.-
+.00
ean 2.
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!eighted Moing Aerages!eighted Moing Aerages
Ieights are givenK e5ample +!), !3, !2
t Ft =t
Ieek ate .i##as 3-wk wt! " "bs
1 2(*un +0
2 (*un -+
1-(*un +2
/ 2(*un +- ++.+0 0.+0
+ 0(*un ++ +-.-0 1.-0
- (*ul -0 +/.0 +.0 +.0
ean 2./
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"#ponential Smoothing"#ponential Smoothing
Ft= Ft1
+(Dt1
Ft1)
Ft+1 = Ft + (Dt1 Ft1)
Ft+1 = Dt +(1 )Ft
t =t
Ieek ate .i##as Ft "bs
1 2(*un +0 +0.00
2 (*un -+ +0.00
1-(*un +2 -.+0
/ 2(*un +- +.1+ 2.+
+ 0(*un ++ ++.2 0.2
- (*ul -0 ++.0 /.
+.+1
ean 2.
alpha 0.
t =t
Ieek ate .i##as Ft "bs
1 2(*un +0 +0.00
2 (*un -+ +0.00
1-(*un +2 +.00
/ 2(*un +- +2.0 .20
+ 0(*un ++ +.// 1.+-
- (*ul -0 +.+ -.2+
++.00
ean .-
alpha 0.2
3 Premise((4he ost recent obser#ations ight ha#e the highest predicti#e#alue.
4here$ore, we should gi#e ore weight to the ore recent tie periods when$orecasting.
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"#ponential Smoothing"#ponential Smoothing
%he emphasis given to the most recent demandlevels can be ad9usted by changing the smoothingparameter
Darger $values emphasi#e recent levels of
demand and result in forecasts more responsiveto changes in the underlying average
'maller $values treat past demand moreuniformly and result in more stable forecasts
=5ponential smoothing is simple and re
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%ncluding a Trend%ncluding a Trend
" trend in a time series is a systematicincrease or decrease in the average of theseries over time
%he forecast can be improved bycalculating an estimate of the trend
%rend-ad9usted e5ponential smoothingre
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%ncluding a Trend%ncluding a Trend
For each period, we calculate the average and thetrend:
At@ $+emand this period
A +1 L+"verage A %rend estimate last period
@ $DtA +1 $+At1A Tt1
Tt@&+"verage this period "verage last period
A +1 &+%rend estimate last period
@&+AtAt1 A +1 &Tt1
FtA1@AtA Tt
whereAt@ e5ponentially smoothed average of the series in periodtTt@ e5ponentially smoothed average of the trend in period t
@ smoothing parameter for the average, with a value between and 1@ smoothing parameter for the trend, with a value between
and 1FtA1@ forecast for period tA 1
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Using Trend'Ad(usted "#ponentialUsing Trend'Ad(usted "#ponentialSmoothingSmoothing
=".D= 13!$ edanalysis, Bnc!, provides medical laboratory services
anagers are interested in forecasting the number of bloodanalysis re
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3!2 A 2!4 @ 33 blood tests
Using Trend'Ad(usted "#ponentialUsing Trend'Ad(usted "#ponentialSmoothingSmoothing
';D8%B;H
Bf the actual number of blood tests re
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Using Trend'Ad(usted "#ponentialUsing Trend'Ad(usted "#ponentialSmoothingSmoothing
3!2 A 2!4$ @ 33!$
$3!2
3)!23
2!4$
3!24
24! A 3! @ 31!
3)!23 A 3!24 @ 34!)1
34!21 A 3!22 @ $1!$3
$!1$ A 2!6/ @ $3!1
$)!4 A 3!3/ @ $4!$$
$/!3) A 2!6$ @ $6!26
)!43 A 3!2) @ )$!4
))!$/ A 3!)2 @ )4!64
)$!66 A 2!02 @ )0!01
)0!10 A 2!/2 @ )6!06
)4!/3 A 2!34 @ /1!1
)6!21 A 2!2 @ /1!23
/!66 A 1!60 @ /2!6/
/2!30 A 1!4/ @ /$!23
1!6/
1!)1
/!$3
6!6
1!$$
0!01
/!62
16!64
2!01
)!06
6!1
1!23
2!6/
1!00
34!21
$!1$
$)!4
$/!3)
)!43
))!$/
)$!66
)0!10
)4!/3
)6!21
/!66
/2!30
//!34
3!22
2!6/
3!3/
2!6$
3!2)
3!)2
2!02
2!/2
2!34
2!2
1!60
1!4/
2!26
%"JD= 13!1 F;=("'%' F; ="H"D'B' 8'BHN %&= %=H-"78'%= =.;H=H%B"D ';;%&BHN ;=D
(alculations to Forecast "rrivals for He5t Ieek
Ieek "rrivals'moothed"verage
%rend"verage
Forecast for %his Ieek Forecast =rror
24 24! 3!
1 20
2 $$
3 30
$ 3)
) )3
/ 34
0 )0
4 /1
6 36
1 ))
11 )$
12 )2
13 /
1$ /1) 0)
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Using Trend'Ad(usted "#ponentialUsing Trend'Ad(usted "#ponentialSmoothingSmoothing
Week (t) Dt Change At Tt Ft
0 28 28.00 3.00
1 27 -1 30.20 2.84 31.00
2 44 17 35.23 3.28 33.04
3 37 -7 38.21 3.22 38.51
4 35 -2 40.14 2.96 41.43
5 53 18 45.08 3.36 43.10
6 38 -15 46.35 2.94 48.44
7 57 19 50.83 3.25 49.29
8 61 4 55.46 3.52 54.08
9 39 -22 54.99 2.72 58.9910 55 16 57.17 2.62 57.72
11 54 -1 58.63 2.38 59.79
12 52 -2 59.21 2.02 61.02
13 60 8 60.99 1.97 61.24
14 60 0 62.37 1.86 62.96
15 75 15 66.38 2.29 64.23
Smoothing
Parameters
Alpha 0.2 3.13
Beta 0.2
Smoothing Constants
Tt=estimate of the trend for period t
At=expoetiall! smoothed average of the series i period t
expoetiall! smoothed fore"ast
#t=TA-$% #ore"ast for period t
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1 2 3 $ ) / 0 4 6 1 11 12 13 1$ 1)
4
0
/
)
$
3 .atientar
rivals
Ieek
"ctual bloodtest re
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Application )*+,Application )*+,
%he forecaster for (anine Nourmet dog breath freshenersestimated +in arch the sales average to be 3, cases soldper month and the trend to be A4, per month! %he actualsales for "pril were 33, cases! Ihat is the forecast for ay,assuming $@ !2 and&@ !1O
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Seasonal PatternsSeasonal Patterns
'easonal patterns are regularly repeatedupward or downward movements indemand measured in periods of less thanone year
"ccount for seasonal effects by using oneof the techni
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1! For each year, calculate the average demand for
each season by dividing annual demand by thenumber of seasons per year
2! For each year, divide the actual demand for eachseason by the average demand per season,resulting in a seasonal inde5 for each season
3! (alculate the average seasonal inde5 for eachseason using the results from 'tep 2
$! (alculate each seasonMs forecast for ne5t year
Multiplicatie Seasonal MethodMultiplicatie Seasonal Method
ultiplicative seasonal method, whereby seasonalfactors are multiplied by an estimate of the averagedemand to arrive at a seasonal forecast
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%he manager wants to forecast customer demand for each
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Using the Multiplicatie SeasonalUsing the Multiplicatie SeasonalMethodMethod
U i h M l i li i S l
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Using the Multiplicatie SeasonalUsing the Multiplicatie SeasonalMethodMethod
Year1 Year2 Year3 Year4 Yr5Foreast
&1 45 70 100 100 132.82
&2 335 370 585 725 843.62
&3 520 590 830 1160 1300.03
&4 100 170 285 215 323.52
Totals 1000 1200 1800 2200 2600A'era(e 250 300 450 550 650
SFYr1 SFYr2 SFYr3 SFYr4 AvgSF
&1 0.18 0.23 0.22 0.18 0.20
&2 1.34 1.23 1.30 1.32 1.30
&3 2.08 1.97 1.84 2.11 2.00
&4 0.40 0.57 0.63 0.39 0.50
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Measures of Forecast "rrorMeasures of Forecast "rror
Et2
n'= @
Et
n" @
+EtPDt+1n".= @
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Measures of Forecast "rrorMeasures of Forecast "rror
Simple Moving Average Weighted Moving Average
Exponential Smoothing Exponential Smoothing
MAD Results
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Measures of Forecast "rrorMeasures of Forecast "rror
Simple Moving Average Weighted Moving Average
MSE Results
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Measures of Forecast "rrorMeasures of Forecast "rror
MAPE Results
Simple Moving Average Weighted Moving Average