Ch 13 Student Krajewski

7/25/2019 Ch 13 Student Krajewski

1/41

13 1Copyright 2010 Pearson Education, Inc. Publishing as Prentice Hall.

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'(


2/41



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


3/41



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.


4/41

13 $Copyright 2010 Pearson Education, Inc. Publishing as Prentice Hall.

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


5/41

13 )Copyright 2010 Pearson Education, Inc. Publishing as Prentice Hall.


*uantity

%ime

+a &ori#ontal: ata cluster about a hori#ontal line

Figure 13!1 .atterns of emand


6/41

13 /Copyright 2010 Pearson Education, Inc. Publishing as Prentice Hall.


*uantity

%ime

+b %rend: ata consistently increase or decrease



7/4113 0Copyright 2010 Pearson Education, Inc. Publishing as Prentice Hall.


*uant

ity

onths

+c 'easonal: ata consistently show peaks and valleys

ear 1

ear 2





*uant

ity

ears

+d (yclical: ata reveal gradual increases anddecreases over e5tended periods




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



Judgment MethodsJudgment Methods

;ther methods +casual and time-series re



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



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




-ependentva

riable

Bndependent variable

X

Y

=stimate ofY fromregressione


14/4113 1$Copyright 2010 Pearson Education, Inc. Publishing as Prentice Hall.


%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


15/4113 1)Copyright 2010 Pearson Education, Inc. Publishing as Prentice Hall.

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


16/4113 1/Copyright 2010 Pearson Education, Inc. Publishing as Prentice Hall.


';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




%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



Linear Regression OutputLinear Regression Output



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



Time Series MethodsTime Series Methods

Bn a naive forecast the forecast for the ne5tperiod e



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.



!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./



"#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.


24/41

13 2$Copyright 2010 Pearson Education, Inc. Publishing as Prentice Hall.

"#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


25/41

13 2)Copyright 2010 Pearson Education, Inc. Publishing as Prentice Hall.

%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


26/41

13 2/Copyright 2010 Pearson Education, Inc. Publishing as Prentice Hall.

%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


27/41


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


28/41


3!2 A 2!4 @ 33 blood tests


';D8%B;H

Bf the actual number of blood tests re


29/41



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)


30/41



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


31/41


1 2 3 $ ) / 0 4 6 1 11 12 13 1$ 1)

4

0

/

)

$

3 .atientar

rivals

Ieek

"ctual bloodtest re


32/41


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


33/41


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


34/41

13 3$Copyright 2010 Pearson Education, Inc. Publishing as Prentice Hall.

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


35/41

13 3)Copyright 2010 Pearson Education, Inc. Publishing as Prentice Hall.

%he manager wants to forecast customer demand for each


36/41

13 3/Copyright 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Using the Multiplicatie SeasonalUsing the Multiplicatie SeasonalMethodMethod

U i h M l i li i S l


37/41


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


38/41


Measures of Forecast "rrorMeasures of Forecast "rror

Et2

n'= @

Et

n" @

+EtPDt+1n".= @


39/41



Simple Moving Average Weighted Moving Average

Exponential Smoothing Exponential Smoothing

MAD Results


40/41

13 $Copyright 2010 Pearson Education, Inc. Publishing as Prentice Hall.



MSE Results


41/41


MAPE Results


Documents

Ch 13 Student Krajewski