05 Forecasting.pptx

8/13/2019 05 Forecasting.pptx

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2008 Prentice-Hall, Inc.

Chapter 5

To accompanyQuantitative Analysis for Management, Tenth Edition,by Render, Stair, and HannaPower Point slides created by Jeff Heyl

Forecasting

2009 Prentice-Hall, Inc.

2009 Prentice-Hall, Inc. 5 2

Introduction

! Managers are always trying to reduceuncertainty and make better estimates of whatwill happen in the future

! This is the main purpose of forecasting! Some firms use subjective methods

! Seat-of-the pants methods, intuition,experience

! There are also several quantitative techniques! Moving averages, exponential smoothing,

trend projections, least squares regressionanalysis


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Introduction

! Eight steps to forecasting :1. Determine the use of the forecastwhat

objective are we trying to obtain?

2. Select the items or quantities that are to beforecasted

3. Determine the time horizon of the forecast

4. Select the forecasting model or models

5. Gather the data needed to make theforecast

6. Validate the forecasting model7. Make the forecast

8. Implement the results


Introduction! These steps are a systematic way of initiating,

designing, and implementing a forecastingsystem

! When used regularly over time, data iscollected routinely and calculations performedautomatically

! There is seldom one superior forecastingsystem

! Different organizations may use differenttechniques

! Whatever tool works best for a firm is the onethey should use


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RegressionAnalysis

MultipleRegression

MovingAverage

ExponentialSmoothing

TrendProjections

Decomposition

DelphiMethods

Jury of ExecutiveOpinion

Sales ForceComposite

ConsumerMarket Survey

Time-SeriesMethods

QualitativeModels

CausalMethods

Forecasting Models

ForecastingTechniques

Figure 5.1


Time-Series Models

! Time-series modelsattempt to predict thefuture based on the past

! Common time-series models are! Nave! Simple moving average and weighted moving

average

! Exponential smoothing!

Trend projections! Decomposition

! Regression analysis is used in trendprojections and one type of decompositionmodel


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Causal Models

! Causal modelsuse variables or factorsthat might influence the quantity beingforecasted

! The objective is to build a model withthe best statistical relationship betweenthe variable being forecast and theindependent variables

! Regression analysis is the mostcommon technique used in causalmodeling


Qualitative Models

! Qualitative modelsincorporate judgmentalor subjective factors

! Useful when subjective factors arethought to be important or when accuratequantitative data is difficult to obtain

! Common qualitative techniques are! Delphi method! Jury of executive opinion! Sales force composite! Consumer market surveys


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Qualitative Models

! Delphi Method an iterative group process where(possibly geographically dispersed) respondentsprovide input to decision makers

! Jury of Executive Opinion collects opinions of asmall group of high-level managers, possiblyusing statistical models for analysis

! Sales Force Composite individual salespersonsestimate the sales in their region and the data iscompiled at a district or national level

! Consumer Market Survey input is solicited fromcustomers or potential customers regarding theirpurchasing plans


Scatter Diagrams

0

50

100

150

200

250

300

350

400

450

0 2 4 6 8 10 12

Time (Years)

AnnualSales

Radios

Televisions

CompactDiscs

Scatter diagrams are helpful when forecasting time-seriesdata because they depict the relationship between variables.


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Scatter Diagrams

! Wacker Distributors wants to forecast sales forthree different products

YEAR TELEVISION SETS RADIOS COMPACT DISC PLAYERS

1 250 300 110

2 250 310 100

3 250 320 120

4 250 330 140

5 250 340 170

6 250 350 150

7 250 360 1608 250 370 190

9 250 380 200

10 250 390 190

Table 5.1


Scatter Diagrams

Figure 5.2

330

250

200

150

100

50

| | | | | | | | | |

0 1 2 3 4 5 6 7 8 9 10

Time (Years)

AnnualSalesofTelevisions

(a)

! Sales appear to beconstant over time

Sales = 250

! A good estimate ofsales in year 11 is250 televisions


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Scatter Diagrams

! Sales appear to beincreasing at aconstant rate of 10radios per year

Sales = 290 + 10(Year)

! A reasonableestimate of sales inyear 11 is 400

televisions

420

400

380

360

340

320

300

280

| | | | | | | | | |

0 1 2 3 4 5 6 7 8 9 10

Time (Years)

AnnualSalesofRadios

(b)

Figure 5.2


Scatter Diagrams! This trend line may

not be perfectlyaccurate becauseof variation fromyear to year

! Sales appear to beincreasing

! A forecast wouldprobably be a

larger figure eachyear

200

180

160

140

120

100

| | | | | | | | | |

0 1 2 3 4 5 6 7 8 9 10

Time (Years)

AnnualSalesofCDPlayers

(c)

Figure 5.2


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Measures of Forecast Accuracy

! Using a naveforecasting modelYEAR

ACTUALSALES OF CD

PLAYERS FORECAST SALES

ABSOLUTE VALUE OFERRORS (DEVIATION),(ACTUAL FORECAST)

1 110

2 100 110 |100 110| = 10

3 120 100 |120 110| = 20

4 140 120 |140 120| = 20

5 170 140 |170 140| = 30

6 150 170 |150 170| = 20

7 160 150 |160 150| = 10

8 190 160 |190 160| = 30

9 200 190 |200 190| = 1010 190 200 |190 200| = 10

11 190

Sum of |errors| = 160

MAD = 160/9 = 17.8

Table 5.2

8179

160errorforecast.MAD

n



! There are other popular measures of forecastaccuracy

! The mean squared error

n

2error)(MSE

! The mean absolute percent error

%MAPE 100actual

error

n

! And biasis the average error and tells whether the

forecast tends to be too high or too low and byhow much. Thus, it can be negative or positive.


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Year Actual CD Sales Forecast Sales |Actual -Forecast|

1 110

2 100 110 10

3 120 100 20

4 140 120 20

5 170 140 30

6 150 170 20

7 160 150 10

8 190 160 30

9 200 190 10

10 190 200 10

11 190

Sum of |errors| 160

MAD 17.8


Hospital Days Forecast Error

Example

Ms. Smith forecastedtotal hospital inpatientdays last year. Nowthat the actual data areknown, she isreevaluating herforecasting model.

Compute the MAD,

MSE, and MAPE for herforecast.

Month Forecast ActualJAN 250 243

FEB 320 315

MAR 275 286

APR 260 256

MAY 250 241

JUN 275 298

JUL 300 292

AUG 325 333

SEP 320 326

OCT 350 378

NOV 365 382

DEC 380 396


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Decomposition of a Time-Series

! A time series typically has four components1.Trend(T) is the gradual upward or

downward movement of the data over time

2.Seasonality(S) is a pattern of demandfluctuations above or below trend line thatrepeats at regular intervals

3.Cycles(C) are patterns in annual data thatoccur every several years

4.Random variations(R) are blips in thedata caused by chance and unusualsituations



Average Demandover 4 Years

TrendComponent

ActualDemand

Line

Time

DemandforProductorService

| | | |

Year Year Year Year1 2 3 4

Seasonal Peaks

Figure 5.3


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! There are two general forms of time-seriesmodels

! The multiplicative modelDemand = TxSx CxR

! The additive modelDemand = T+S+ C+R

! Models may be combinations of these twoforms

! Forecasters often assume errors arenormally distributed with a mean of zero


Nave Forecast *

! Nave forecast is the simplest technique. Ituses the actual demand for the past period asthe forecasted demand for the next period

! This makes the theory that the past will repeat.! Also assumes that any time series

components are either reflected in theprevious periods demand or do not exist.

Nave forecast, Ft+1 = Yt


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Nave Forecast *

Period Actual Demand Forecast

1 35

2 40 35

3 55 40

4 65 55

5 60 65

6 - 60


Moving Averages

! Moving averagescan be used when demand isrelatively steady over time

! The next forecast is the average of the mostrecent ndata values from the time series

! The most recent period of data is added andthe oldest is dropped!This methods tends to smooth out short-termirregularities in the data series

n

nperiodspreviousindemandsofSumforecastaverageMoving


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Moving Averages

! Mathematically

n

YYYF

nttt

t

11

1

...

where

= forecast for time period t+ 1

= actual value in time period t

n = number of periods to average

tY

1tF


Wallace Garden Supply Example

! Wallace Garden Supply wants toforecast demand for its Storage Shed

! They have collected data for the pastyear

! They are using a three-month movingaverage to forecast demand (n= 3)


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Table 5.3

MONTH ACTUAL SHED SALES THREE-MONTH MOVING AVERAGE

January 10

February 12

March 13

April 16

May 19

June 23

July 26

August 30

September 28

October 18November 16

December 14

January

(12 + 13 + 16)/3 = 13.67

(13 + 16 + 19)/3 = 16.00

(16 + 19 + 23)/3 = 19.33

(19 + 23 + 26)/3 = 22.67

(23 + 26 + 30)/3 = 26.33

(26 + 30 + 28)/3 = 28.00(30 + 28 + 18)/3 = 25.33

(28 + 18 + 16)/3 = 20.67

(18 + 16 + 14)/3 = 16.00

(10 + 12 + 13)/3 = 11.67


Weighted Moving Averages! Weighted moving averagesuse weights to put

more emphasis on recent periods

! Often used when a trend or other pattern isemerging

)(

))((

Weights

periodinvalueActualperiodinWeight1

iF

t

! Mathematically

n

ntntt

t

www

YwYwYwF

......

21

1121

1

where

wi= weight for the ithobservation


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Weighted Moving Averages

! Both simple and weighted averages areeffective in smoothing out fluctuations inthe demand pattern in order to providestable estimates

! Problems!Increasing the size of nsmoothes outfluctuations better, but makes the methodless sensitive to real changes in the data

!Moving averages can not pick up trendsvery well they will always stay within pastlevels and not predict a change to a higher orlower level



! Wallace Garden Supply decides to try aweighted moving average model to forecastdemand for its Storage Shed

! They decide on the following weightingscheme

WEIGHTS APPLIED PERIOD

3 Last month

2 Two months ago

1 Three months ago

6

3 x Sales last month + 2 x Sales two months ago + 1 X Sales three months ago

Sum of the weights


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Table 5.4

MONTH ACTUAL SHED SALESTHREE-MONTH WEIGHTED

MOVING AVERAGE

January 10

February 12

March 13

April 16

May 19

June 23

July 26

August 30

September 28

October 18November 16

December 14

January

[(3 X 13) + (2 X 12) + (10)]/6 = 12.17

[(3 X 16) + (2 X 13) + (12)]/6 = 14.33

[(3 X 19) + (2 X 16) + (13)]/6 = 17.00

[(3 X 23) + (2 X 19) + (16)]/6 = 20.50

[(3 X 26) + (2 X 23) + (19)]/6 = 23.83

[(3 X 30) + (2 X 26) + (23)]/6 = 27.50

[(3 X 28) + (2 X 30) + (26)]/6 = 28.33[(3 X 18) + (2 X 28) + (30)]/6 = 23.33

[(3 X 16) + (2 X 18) + (28)]/6 = 18.67

[(3 X 14) + (2 X 16) + (18)]/6 = 15.33



Program 5.1A


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Program 5.1B


Exponential Smoothing

! Exponential smoothingis easy to use andrequires little record keeping of data

! It is a type of moving averageNew forecast = Last periods forecast

+ (Last periods actual demand Last periods forecast)

Where is a weight (or smoothing constant)with a value between 0 and 1 inclusive

A larger gives more importance to recentdata while a smaller value gives moreimportance to past data


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Exponential Smoothing

! Mathematically)(

tttt FYFF

1

where

Ft+1= new forecast (for time period t+ 1)

Ft= previous forecast (for time period t)

= smoothing constant (0 ! !1)

Yt= previous periods actual demand

! The idea is simple the new estimate is theold estimate plus some fraction of the error inthe last period


Exponential Smoothing Example! In January, Februarys demand for a certain

car model was predicted to be 142

! Actual February demand was 153 autos! Using a smoothing constant of = 0.20, what

is the forecast for March?

New forecast (for March demand) = 142 + 0.2(153 142)= 144.2 or 144 autos

!If actual demand in March was 136 autos, theApril forecast would be

New forecast (for April demand) = 144.2 + 0.2(136 144.2)= 142.6 or 143 autos


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Selecting the Smoothing Constant

! Selecting the appropriate value for iskey to obtaining a good forecast

! The objective is always to generate anaccurate forecast

! The general approach is to develop trialforecasts with different values of andselect the that results in the lowestMAD


Port of Baltimore Example

QUARTER

ACTUALTONNAGE

UNLOADEDFORECAST

USING =0.10FORECAST

USING =0.50

1 180 175 175

2 168 175.5 = 175.00 + 0.10(180 175) 177.5

3 159 174.75 = 175.50 + 0.10(168 175.50) 172.75

4 175 173.18 = 174.75 + 0.10(159 174.75) 165.88

5 190 173.36 = 173.18 + 0.10(175 173.18) 170.44

6 205 175.02 = 173.36 + 0.10(190 173.36) 180.227 180 178.02 = 175.02 + 0.10(205 175.02) 192.61

8 182 178.22 = 178.02 + 0.10(180 178.02) 186.30

9 ? 178.60 = 178.22 + 0.10(182 178.22) 184.15

Table 5.5

! Exponential smoothing forecast for two values of


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Selecting the Best Value of

QUARTER

ACTUALTONNAGE

UNLOADEDFORECAST

WITH = 0.10

ABSOLUTEDEVIATIONSFOR = 0.10

FORECASTWITH = 0.50

ABSOLUTEDEVIATIONSFOR = 0.50

1 180 1755"..

1755".

2 168 175.57.5..

177.59.5..

3 159 174.7515.75

172.7513.75

4 175 173.181.82

165.889.12

5 190 173.3616.64

170.4419.56

6 205 175.0229.98

180.2224.78

7 180 178.021.98

192.6112.61

8 182 178.223.78

186.304.3..

Sum of absolute deviations 82.45 98.63

MAD=!|deviations|

= 10.31 MAD= 12.33n

Table 5.6

Best choice



Program 5.2A


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Program 5.2B


PM Computer: Moving Average

Example! PM Computer assembles customized personal

computers from generic parts

! The owners purchase generic computer partsin volume at a discount from a variety ofsources whenever they see a good deal.

! It is important that they develop a goodforecast of demand for their computers sothey can purchase component partsefficiently.


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PM Computers: Data

Period Month Actual Demand

1 Jan 37

2 Feb 40

3 Mar 41

4 Apr 37

5 May 45

6 June 50

7 July 43

8 Aug 47

9 Sept 56

! Compute a 2-month moving average! Compute a 3-month weighted average using weights of

4,2,1 for the past three months of data

! Compute an exponential smoothing forecast using =0.7, previous forecast of 40

! Using MAD, what forecast is most accurate?


PM Computers: Moving Average

Solution2 month

MA Abs. Dev 3 month WMA Abs. Dev Exp.Sm. Abs. Dev

37.00

37.00 3.00

38.50 2.50 39.10 1.90

40.50 3.50 40.14 3.14 40.43 3.43

39.00 6.00 38.57 6.43 38.03 6.97

41.00 9.00 42.14 7.86 42.91 7.09

47.50 4.50 46.71 3.71 47.87 4.87

46.50 0.50 45.29 1.71 44.46 2.54

45.00 11.00 46.29 9.71 46.24 9.76

51.50 51.57 53.07

5.29 5.43 4.95

MADExponential smoothing resulted in the lowest MAD.


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Exponential Smoothing with

Trend Adjustment! Like all averaging techniques, exponential

smoothing does not respond to trends

! A more complex model can be used thatadjusts for trends

! The basic approach is to develop anexponential smoothing forecast then adjust itfor the trend

Forecast including trend (FITt) = New forecast (Ft)

+ Trend correction (Tt)


Exponential Smoothing with

Trend Adjustment

! The equation for the trend correction uses anew smoothing constant

! Ttis computed by)()1( 11 tttt FFTT !+!= ++ ""

where

Tt+1= smoothed trend for period t+ 1

Tt= smoothed trend for preceding period

= trend smooth constant that we select

Ft+1= simple exponential smoothed forecast forperiod t+ 1

Ft= forecast for pervious period


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Selecting a Smoothing Constant

! As with exponential smoothing, a high value ofmakes the forecast more responsive to changesin trend

! A low value of gives less weight to the recenttrend and tends to smooth out the trend

! Values are generally selected using a trial-and-error approach based on the value of theMADfordifferent values of

! Simple exponential smoothing is often referred toas first-order smoothing

! Trend-adjusted smoothing is called second-order,double smoothing, or Holts method


Trend Projection

! Trend projection fits a trend line to aseries of historical data points

! The line is projected into the future formedium- to long-range forecasts

! Several trend equations can bedeveloped based on exponential orquadratic models

! The simplest is a linear model developedusing regression analysis


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Trend Projection

Valu

eofDependentVariable

Time

*

*

*

*

*

*

*Dist2

Dist4

Dist6

Dist1

Dist3

Dist5

Dist7

Figure 5.4


Midwestern Manufacturing

Company Example

! Midwestern Manufacturing Company hasexperienced the following demand for its electricalgenerators over the period of 2001 2007

YEAR ELECTRICAL GENERATORS SOLD

2001 74

2002 79

2003 80

2004 90

2005 1052006 142

2007 122

Table 5.7Determine the forecast for 2008 and 2009, andplot a time series.


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Company Example

Program 5.3A

Notice codeinstead of

actual years



Company Example

Program 5.3B

r2says model predictsabout 80% of the

variability in demand

Significance level forF-test indicates a

definite relationship


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Company Example! The forecast equation is

XY 54107156 ..

! To project demand for 2008, we use the codingsystem to defineX= 8

(sales in 2008) = 56.71 + 10.54(8)= 141.03, or 141 generators

! Likewise forX= 9(sales in 2009) = 56.71 + 10.54(9)

= 151.57, or 152 generators



Company Example

GeneratorDemand

Year

160

150

140

130

120

110

100

90

80

70 60

50

| | | | | | | | |

2001 2002 2003 2004 2005 2006 2007 2008 2009

Actual Demand Line

Trend LineXY 54107156 ..

Figure 5.5


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Company Example

Program 5.4A



Company Example

Program 5.4B


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Seasonal Variations

! Recurring variations over time mayindicate the need for seasonaladjustments in the trend line

! A seasonal index indicates how aparticular season compares with anaverage season

! When no trend is present, the seasonalindex can be found by dividing the

average value for a particular season bythe average of all the data


Seasonal Variations

! Eichler Supplies sells telephoneanswering machines

! Data has been collected for the past twoyears sales of one particular model

! They want to create a forecast thatincludes seasonality


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Seasonal Variations

MONTH

SALES DEMANDAVERAGE TWO- YEAR

DEMANDMONTHLYDEMAND

AVERAGESEASONAL INDEXYEAR 1 YEAR 2

January 80 10090

94 0.957

February 85 7580

94 0.851

March 80 9085

94 0.904

April 110 90100

94 1.064

May 115 131123

94 1.309

June 120 110115

94 1.223

July 100 110105

94 1.117

August 110 90100

94 1.064

September 85 9590

94 0.957

October 75 8580

94 0.851

November 85 7580

94 0.851

December 80 8080

94 0.851

Total average demand = 1,128

Seasonal index =Average two-year demand

Average monthly demandAverage monthly demand = = 94

1,128

12 months

Table 5.8


Seasonal Variations! The calculations for the seasonal indices are

Jan. July96957012

2001.

,

112117112

2001.

,

Feb. Aug.85851012

2001.

,

106064112

2001.

,

Mar. Sept.90904012

2001.

,

96957012

2001.

,

Apr. Oct.106064112

2001.

,

858510

12

2001.

,

May Nov.131309112

2001.

,

85851012

2001.

,

June Dec.122223112

2001.

,

85851012

2001.

,


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Seasonal Variations with Trends

! When both trend and seasonal componentsare present in a time series, a change fromone month to the next could be due to a trend,to a seasonal variation, or simply to randomfluctuations.

! To help with this problem, the seasonalindices should be computed using centeredmoving averageapproach whenever trend is

present.! Using this approach prevents a variation due

to trend from being incorrectly interpreted asa variation due to the season.


Steps Used to Compute Seasonal

Indices based on CMAs

I

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.

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1. Compute a CMA for each observation (wherepossible)

2. Compute seasonal ratio = Observation/CMA forthat observation.

3. Average seasonal ratios to get seasonal indices.(This eliminates as much randomness aspossible.)

4. If seasonal indices do not add to the number of

seasons, multiply each index by (Number ofseasons)/(Sum of the indices).


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Turner Industries Example


Turner Industries Example

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Scatter Plot of Turner

Industries Sales and CMA


The Decomposition Method with

Trend and Seasonal Components

! Decomposition is the process of isolating lineartrend and seasonal factors to develop moreaccurate forecasts

! The first step is to compute seasonal indices foreach season, then the data are deseasonalizedby dividing each number by its seasonal index

! A trend line is then found using thedeseasonalized data.


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Steps to Develop a Forecast Using

the Decomposition Method

:

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..

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1. Compute seasonal indices using CMAs.

2. Deseasonalize the data by dividing each numberby its seasonal index.

3. Find the equation of a trend line using thedeseasonalized data.

4. Forecast the future periods using the trend line.

5. Multiply the trend line forecast by theappropriate seasonal index


Deseasonalized Data for

Turner Industries

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Finding the Trend Line of

Deseasonalized Data

:

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b1= 2.34, b0= 124.78

Y = 124.78 + 2.34X where X = time

This equation is used to develop the forecast based on

trend, and the result is multiplied by the appropriate seasonalindex to make a seasonal adjustment.

The forecast for the first quarter of year 4 (time period = 13and seasonal index I1= 0.85)

Y = 124.78 + 2.34X = 124.78 + 2.34(13)

= 155.2 (forecast before adjustment for seasonality)Multiply this by the seasonal index for quarter 1:

Y x I1= 155.2 x 0.85 = 131.92

Find the forecast for quarters 2, 3 and 4 of the next year.


Regression with Trend and

Seasonal Components

! Multiple regressioncan be used to forecast bothtrend and seasonal components in a time series! One independent variable is time! Dummy independent variables are used to represent the

seasons

! The model is an additive decomposition model

where

X1 = time periodX2 = 1 if quarter 2, 0 otherwiseX3 = 1 if quarter 3, 0 otherwiseX4 = 1 if quarter 4, 0 otherwise

44332211 XbXbXbXbaY


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Seasonal Components

Program 5.6A



Seasonal Components

Program 5.6B (partial)


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Seasonal Components! The resulting regression equation is

4321 130738715321104 XXXXY .....

! Using the model to forecast sales for the first twoquarters of next year

! These are different from the results obtainedusing the multiplicative decomposition method

! Use MADand MSEto determine the best model

13401300738071513321104 )(.)(.)(.)(..Y

15201300738171514321104 )(.)(.)(.)(..Y



Seasonal Components

! American Airlines original spare parts inventorysystem used only time-series methods toforecast the demand for spare parts! This method was slow to responds to even moderate

changes in aircraft utilization let alone major fleetexpansions

! They developed a PC-based system named RAPSwhich uses linear regression to establish arelationship between monthly part removals andvarious functions of monthly flying hours! The computation now takes only one hour instead of

the days the old system needed

! Using RAPS provided a one time savings of $7 millionand a recurring annual savings of nearly $1 million


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Monitoring and Controlling Forecasts

! Tracking signalscan be used to monitorthe performance of a forecast

! Tracking signals are computed using thefollowing equation

MAD

RSFEsignalTracking

n

errorforecastMADwhere



AcceptableRange

Signal Tripped

Upper Control Limit

Lower Control Limit

0MADs

+

Time

Figure 5.7

Tracking Signal


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! Positive tracking signals indicate demand isgreater than forecast

! Negative tracking signals indicate demand is lessthan forecast

! Some variation is expected, but a good forecastwill have about as much positive error asnegative error

! Problems are indicated when the signal tripseither the upper or lower predetermined limits

! This indicates there has been an unacceptableamount of variation

! Limits should be reasonable and may vary fromitem to item



Seasonal Components

! How do you decide on the upper and lower limits?! Too small a value will trip the signal too often and

too large will cause a bad forecast

! Plossl & Wight use maximums of 4 MADs forhigh volume stock items and 8 MADs for lowervolume items! One MAD is equivalent to approximately 0.8

standard deviation so that 4 MADs =3.2 s.d.

!For a forecast to be in control, 89% of the errorsare expected to fall within 2 MADs, 98% with 3MADs or 99.9% within 4 MADs whenever theerrors are approximately normally distributed


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Kimballs Bakery Example

! Tracking signal for quarterly sales of croissantsTIME

PERIODFORECAST

DEMANDACTUALDEMAND ERROR RSFE

|FORECAST || ERROR |

CUMULATIVEERROR MAD

TRACKINGSIGNAL

1 100 90 10 10 10 10 10.0 1

2 100 95 5 15 5 15 7.5 2

3 100 115 +15 0 15 30 10.0 0

4 110 100 10 10 10 40 10.0 1

5 110 125 +15 +5 15 55 11.0 +0.5

6 110 140 +30 +35 30 85 14.2 +2.5

214685

errorforecast.MAD

n

sMAD..MAD

RSFE52

214

35signalTracking


Forecasting at Disney

! The Disney chairman receives a dailyreport from his main theme parks thatcontains only two numbers the forecastof yesterdays attendance at the parks andthe actual attendance! An error close to zero (using MAPE as the

measure) is expected

! The annual forecast of total volumeconducted in 1999 for the year 2000resulted in a MAPE of 0


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