© 2006 Prentice Hall, Inc.4 – 1 Forcasting © 2006 Prentice Hall, Inc. Heizer/Render Principles...

© 2006 Prentice Hall, Inc. 4 – 1

ForcastingForcasting

© 2006 Prentice Hall, Inc.

Heizer/Render Heizer/Render Principles of Operations Management, 6ePrinciples of Operations Management, 6eOperations Management, 8e Operations Management, 8e


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

Reengineering Reengineering

InventoryInventory

PersonnelPersonnel

FacilitiesFacilities

Risk ManagementRisk Management

??


Trend

Seasonal

Cyclical

Random

Time Series ComponentsTime Series Components


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 Typically several years duration duration

Trend ComponentTrend Component


Regular pattern of up and Regular pattern of up and down fluctuationsdown fluctuations

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, ‘residual’ Erratic, unsystematic, ‘residual’ 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


Naive ApproachNaive Approach

Assumes demand in next period is Assumes demand in next period is the same as demand in most the same as demand in most recent periodrecent period e.g., If May sales were 48, then June e.g., If May sales were 48, then June

sales will be 48sales will be 48

Sometimes cost effective and Sometimes cost effective and efficientefficient


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 smoothingProvides overall impression of data Provides overall impression of data

over timeover time

Moving Average MethodMoving Average Method

Moving average =Moving average =∑∑ demand in previous n periodsdemand in previous n periods

nn


JanuaryJanuary 1010FebruaryFebruary 1212MarchMarch 1313AprilApril 1616MayMay 1919JuneJune 2323JulyJuly 2626

ActualActual 3-Month3-MonthMonthMonth Shed SalesShed Sales Moving AverageMoving Average

(12 + 13 + 16)/3 = 13 (12 + 13 + 16)/3 = 13 22//33

(13 + 16 + 19)/3 = 16(13 + 16 + 19)/3 = 16(16 + 19 + 23)/3 = 19 (16 + 19 + 23)/3 = 19 11//33

Moving Average ExampleMoving Average Example

101012121313

((1010 + + 1212 + + 1313)/3 = 11 )/3 = 11 22//33


Graph of Moving AverageGraph of Moving Average

| | | | | | | | | | | |

JJ FF MM AA MM JJ JJ AA SS OO NN DD

Sh

ed S

ales

Sh

ed S

ales

30 30 –28 28 –26 26 –24 24 –22 22 –20 20 –18 18 –16 16 –14 14 –12 12 –10 10 –

Actual Actual SalesSales

Moving Moving Average Average ForecastForecast


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

Weighted Moving AverageWeighted Moving Average

WeightedWeightedmoving averagemoving average ==

∑∑ ((weight for period nweight for period n)) x x ((demand in period ndemand in period n))

∑∑ weightsweights


JanuaryJanuary 1010FebruaryFebruary 1212MarchMarch 1313AprilApril 1616MayMay 1919JuneJune 2323JulyJuly 2626

ActualActual 3-Month Weighted3-Month 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

Weighted Moving AverageWeighted Moving Average

101012121313

[(3 x [(3 x 1313) + (2 x ) + (2 x 1212) + () + (1010)]/6 = 12)]/6 = 1211//66

Weights Applied Period

3 Last month2 Two months ago1 Three months ago6 Sum of weights


Moving Average And Moving Average And Weighted Moving AverageWeighted Moving Average

30 30 –

25 25 –

20 20 –

15 15 –

10 10 –

5 5 –

Sa

les

de

man

dS

ale

s d

em

and

| | | | | | | | | | | |

JJ FF MM AA MM JJ JJ AA SS OO NN DD

Actual Actual salessales

Moving Moving averageaverage

Weighted Weighted moving moving averageaverage

Figure 4.2Figure 4.2


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

Exponential SmoothingExponential Smoothing


Exponential SmoothingExponential Smoothing

New forecast =New forecast = last period’s forecastlast period’s forecast+ + ((last period’s actual demand last period’s actual demand

– – last period’s forecastlast period’s forecast))

FFtt = F = Ft t – 1– 1 + + ((AAt t – 1– 1 - - F Ft t – 1– 1))

wherewhere FFtt == new forecastnew forecast

FFt t – 1– 1 == 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 Mustangs Ford MustangsActual demand Actual demand = 153= 153Smoothing constant Smoothing constant = .20 = .20




New forecastNew forecast = 142 + .2(153 – 142)= 142 + .2(153 – 142)




New forecastNew forecast = 142 + .2(153 – 142)= 142 + .2(153 – 142)

= 142 + 2.2= 142 + 2.2

= 144.2 ≈ 144 cars= 144.2 ≈ 144 cars


Impact of Different Impact of Different

225 225 –

200 200 –

175 175 –

150 150 –| | | | | | | | |

11 22 33 44 55 66 77 88 99

QuarterQuarter

De

ma

nd

De

ma

nd

= .1= .1

Actual Actual demanddemand

= .5= .5


Choosing Choosing

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 - Forecast value= Actual demand - Forecast value

= A= Att - F - Ftt


Common Measures of ErrorCommon Measures of Error

Mean Absolute Deviation Mean Absolute Deviation ((MADMAD))

MAD =MAD =∑∑ |actual - forecast||actual - 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 =100 100 ∑∑ |actual |actualii - forecast - forecastii|/actual|/actualii

nn

nn

i i = 1= 1


Comparison of Forecast Comparison of Forecast Error 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 5522 168168 176176 88 178178 101033 159159 175175 1616 173173 141444 175175 173173 22 166166 9955 190190 173173 1717 170170 202066 205205 175175 3030 180180 252577 180180 178178 22 193193 131388 182182 178178 44 186186 44

8484 100100



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 5522 168168 176176 88 178178 101033 159159 175175 1616 173173 141444 175175 173173 22 166166 9955 190190 173173 1717 170170 202066 205205 175175 3030 180180 252577 180180 178178 22 193193 131388 182182 178178 44 186186 44

8484 100100

MAD =∑ |deviations|

n

= 84/8 = 10.50

For = .10

= 100/8 = 12.50

For = .50





11 180180 175175 55 175175 5522 168168 176176 88 178178 101033 159159 175175 1616 173173 141444 175175 173173 22 166166 9955 190190 173173 1717 170170 202066 205205 175175 3030 180180 252577 180180 178178 22 193193 131388 182182 178178 44 186186 44

8484 100100MADMAD 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





11 180180 175175 55 175175 5522 168168 176176 88 178178 101033 159159 175175 1616 173173 141444 175175 173173 22 166166 9955 190190 173173 1717 170170 202066 205205 175175 3030 180180 252577 180180 178178 22 193193 131388 182182 178178 44 186186 44

8484 100100MADMAD 10.5010.50 12.5012.50MSEMSE 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



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 5522 168168 176176 88 178178 101033 159159 175175 1616 173173 141444 175175 173173 22 166166 9955 190190 173173 1717 170170 202066 205205 175175 3030 180180 252577 180180 178178 22 193193 131388 182182 178178 44 186186 44

8484 100100MADMAD 10.5010.50 12.5012.50MSEMSE 194.75194.75 201.50201.50

MAPEMAPE 5.70%5.70% 6.85%6.85%


Trend ProjectionsTrend Projections

Fitting a trend line to historical data points Fitting a trend line to historical data points to project into the medium-to-long-rangeto project into the medium-to-long-range

Linear trends can be found using the least Linear trends can be found using the least squares techniquesquares technique

y y = = a a + + bxbx^̂

where ywhere y= computed value of the = computed value of the variable to be predicted (dependent variable to be predicted (dependent variable)variable)aa= y-axis intercept= y-axis 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

end

en

t V

ari

able


DeviationDeviation11







Actual observation Actual observation (y value)(y value)

Trend line, y = a + bxTrend line, y = a + bx^̂



Time periodTime period

Va

lue

s o

f D

ep

end

en

t V

ari

able









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)



Equations to calculate the regression variablesEquations to calculate the regression variables

b =b =xy - nxyxy - nxy

xx22 - nx - nx22

y y = = a a + + bxbx^̂

a = y - bxa = y - bx


Least Squares ExampleLeast Squares Example

b b = = = 10.54= = = 10.54∑∑xy - nxyxy - nxy

∑∑xx22 - nx - nx22

3,063 - (7)(4)(98.86)3,063 - (7)(4)(98.86)

140 - (7)(4140 - (7)(422))

aa = = yy - - bxbx = 98.86 - 10.54(4) = 56.70 = 98.86 - 10.54(4) = 56.70

TimeTime Electrical Power Electrical Power YearYear Period (x)Period (x) DemandDemand xx22 xyxy

19991999 11 7474 11 747420002000 22 7979 44 15815820012001 33 8080 99 24024020022002 44 9090 1616 36036020032003 55 105105 2525 52552520042004 66 142142 3636 85285220052005 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



b b = = = 10.54= = = 10.54xy - nxyxy - nxy

xx22 - nx - nx22

3,063 - (7)(4)(98.86)3,063 - (7)(4)(98.86)

140 - (7)(4140 - (7)(422))

aa = = yy - - bxbx = 98.86 - 10.54(4) = 56.70 = 98.86 - 10.54(4) = 56.70

TimeTime Electrical Power Electrical Power YearYear Period (x)Period (x) DemandDemand xx22 xyxy

19991999 11 7474 11 747420002000 22 7979 44 15815820012001 33 8080 99 24024020022002 44 9090 1616 36036020032003 55 105105 2525 52552520042004 66 142142 3636 85285220052005 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^



| | | | | | | | |19991999 20002000 20012001 20022002 20032003 20042004 20052005 20062006 20072007

160 160 –

150 150 –

140 140 –

130 130 –

120 120 –

110 110 –

100 100 –

90 90 –

80 80 –

70 70 –

60 60 –

50 50 –

YearYear

Po

wer

dem

and

Po

wer

dem

and

Trend line,Trend line,y y = 56.70 + 10.54x= 56.70 + 10.54x^̂


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 -1-1 to to +1+1

CorrelationCorrelation


Correlation CoefficientCorrelation Coefficient

r = r = nnxyxy - - xxy y

[[nnxx22 - ( - (xx))22][][nnyy22 - ( - (yy))22]]


Correlation CoefficientCorrelation Coefficient

r = r = nn∑∑xyxy - - ∑∑xx∑∑y y

[[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 to to 11

Easy to interpretEasy to interpret

CorrelationCorrelation

For the Nodel Construction example:For the Nodel Construction example:

r r = .901= .901

rr22 = .81 = .81

© 2006 Prentice Hall, Inc.4 – 1 Forcasting © 2006 Prentice Hall, Inc. Heizer/Render Principles...

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Transcript of © 2006 Prentice Hall, Inc.4 – 1 Forcasting © 2006 Prentice Hall, Inc. Heizer/Render Principles...