mg t 303 lecture notes 3

7/25/2019 Mg t 303 Lecture Notes 3

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Operations

Management

Operations

ManagementForecasting

Murat ErkocMGT303University of Miami

4 2

What is Forecasting?

Process ofpredicting a futureevent

Underlying basis o fall businessdecisions

Production

Inventory

Personnel

Facilities

??

4 3

Short-range forecast

Up to 1 year, generally less th an 3 months

Purchasing, job scheduling, workforcelevels, job assignments, production levels

Medium-range forecast

3 months t o 3 years

Sales and production planning, budgeting

Long-range forecast

3+ years

New product planning, facility location,research and development

Forecasting Time Horizons


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Product Life Cycle

Best period toincrease marketshare

R&D engineering iscritical

Practical to changeprice or qualityimage

Strengthen niche

Poor time tochange image,price, or quality

Competitive costsbecome criticalDefend marketposition

Cost controlcritical

Introduction Growth Maturity Decline

CompanyStrategy/Issues

Internet search engines

Sales

Xbox 360

Drive-throughrestaurants

CD-ROMs

3 1/2Floppydisks

LCD & plasma TVsAnal og TVs

iPods

4 5

Types of Forecasts

Economic f orecasts

Address business c yc le inflati on rate,money supply, housing starts, etc.

Technological forecasts

Predict rate of technological progress

Impacts development of new products

Demand forecasts

Predict sales of existing pro ducts andservices

4 6

Seven Steps in Forecasting

Determine the use of the fo recast

Select the items to be forecasted

Determine the time horizon of theforecast

Select the forecasting model(s)

Gather the data

Make the forecast

Validate and implement results


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The Realities!

Forecasts are seldom perfect

Most techniques assume anunderlying stability in the system

Product family and aggregatedforecasts are more accurate thanindividual product forecasts

4 8

Forecasting Approaches

Used when situation is vagueand littl e data exist

New products

New technology

Involves intuition, experience

e.g., forecasting sales on Internet

Qualitative Methods

4 9

Forecasting Approaches

Used when situation is stable and

historical data exist Existing products

Current technology

Involves mathematical techniques

e.g., forecasting sales of colortelevisions

Quantitative Methods


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Overview of QualitativeMethods

Jury of executive opinion Pool opinions of high-level experts,

sometimes augment by statisticalmodels

Delphi method

Panel of experts , queried iteratively

4 11

Overview of QualitativeMethods

Sales force composite

Estimates from individualsalespersons are reviewed forreasonableness, then aggregated

Consumer Market Survey

Ask the customer

4 12

Overview of QuantitativeApproaches

1. Naive approach

2. Moving averages3. Exponential

smoothing

4. Trend projection

5. Linear regression

Time-SeriesModels

Associati veModel


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Set of evenly spaced numerical data

Obtained by observing responsevariable at regular time periods

Forecast based only on past values,no other variables important

Assumes that f actors inf luencingpast and present will continueinfluence in future

Time Series Forecasting

4 14

Trend

Seasonal

Cyclical

Random

Time Series Components

4 15

Components of Demand

Demandforproduc

torservice

| | | |1 2 3 4

Year

Aver agedemand overfour years

Seasonal peaks

Trendcomponent

Act ualdemand

Randomvariation

Figure 4.1


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Persistent, overall upward or

downward pattern Changes due to popu lation,

technology, age, cultu re, etc.

Typically several yearsduration

Trend Component

4 17

Regular pattern of up anddown fluctuations

Due to weather, customs, etc.

Occurs wit hin a single year

Seasonal Component

Number ofPeriod Length Seasons

Week Day 7Month Week 4-4.5Month Day 28-31Year Quarter 4Year Month 12Year Week 52

4 18

Repeating up and down movements

Af fec ted by business cyc le, pol it ical,

and economic factors Multiple years duration

Often causal orassociativerelationships

Cyclical Component

0 5 10 15 20


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Erratic, unsystematic, residual

fluctuations

Due to random variation orunforeseen events

Short duration andnonrepeating

Random Component

M T W T F

4 20

Naive Approach

Assumes demand in nex tperiod is the same asdemand in most recent period

e.g., If January sales were 68, thenFebruary sales will be 68

Sometimes cost effective andefficient

Can be good starting point

4 21

MA is a series of arithmetic means

Used if little or no trend

Used often for smoothingProvides overall impression of data

over time

Moving Average Method

Moving average = demand in previous n periods

n


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January 10February 12March 13Apri l 16May 19June 23July 26

Actual 3-Month

Month Shed Sales Moving Average

(12 + 13 + 16)/3 = 13 2/3(13 + 16 + 19)/3 = 16(16 + 19 + 23)/3 = 19 1/3

Moving Average Example

101213

(10 + 12 + 13)/3 = 11 2/3

4 23

Graph of Moving Average

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

J F M A M J J A S O N D

ShedSales

30

28

26

24

22

20

18

16

14

12

10

ActualSales

MovingAverageForecast

4 24

Used when trend is present

Older data usually less important

Weights based on experience andintuition

Weighted Moving Average

Weightedmoving average =

(weight for period n)x (demand in period n)

weights


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January 10February 12March 13

Apr il 16May 19June 23July 26

Ac tual 3-Month WeightedMonth Shed Sales Moving Average

[(3 x 16) + (2 x 13) + (12)]/6 = 141/3[(3 x 19) + (2 x 16) + (13)]/6 = 17[(3 x 23) + (2 x 19) + (16)]/6 = 201/2

Weighted Moving Average

101213

[(3 x 13) + (2 x 12) + (10)]/6 = 121/6

Weights Applied Period

3 Last month2 Two months ago1 Three months ago

6 Sum of weights

4 26

Increasing n smooths the forecastbut makes it less sensitive tochanges

Do not forecast trends well

Require extensive historical data

Potential Problems WithMoving Average

4 27

Moving Average AndWeighted Moving Average

30

25

20

15

10

5

Salesdeman

d

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

J F M A M J J A S O N D

Actualsales

Movingaverage

Weightedmovingaverage

Figure 4.2


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Form of weighted moving average

Weights decline exponentially

Most recent data weighted most

Requires smoothing constant ()

Ranges from 0 to 1

Subjectively chosen

Involves little record keeping of pastdata

Exponential Smoothing

4 29

Exponential Smoothing

New forecast = Last periods forecast+ (Last periods actual demand

Last periods forecast)

Ft = Ft 1 +(At 1 - Ft 1)

where Ft = new forecast

Ft 1 = previous forecast

= smoothing (or weighting)constant (0 1)

4 30

Exponential SmoothingExample

Predicted demand = 142 Ford MustangsActual demand = 153

Smoothing constant = .20


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Predicted demand = 142 Ford MustangsActual demand = 153Smoothing constant = .20

New forecast = 142 + .2(153 142)

4 32


Predicted demand = 142 Ford MustangsActual demand = 153Smoothing constant = .20

New forecast = 142 + .2(153 142)

= 142 + 2.2

= 144.2 144 cars

4 33

Effect ofSmoothing Constants

Weight Assigned to

Mo st 2nd Mo st 3r d Mo st 4t h Mo st 5t h Mo stRecent Recent Recent Recent RecentSmoothing Period Period Period Period PeriodConstant () (1 -) (1 -)2 (1 -)3 (1 -)4

= .1 .1 .09 .081 .073 .066

= .5 .5 .25 .125 .063 .031


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Impact of Different

225

200

175

150 | | | | | | | | |

1 2 3 4 5 6 7 8 9

Quarter

Demand

= .1

Actualdemand

= .5

4 35

Impact of Different

225

200

175

150 | | | | | | | | |

1 2 3 4 5 6 7 8 9

Quarter

Demand

= .1

Actualdemand

= .5Chose high values of

when underlying averageis likely to change

Choose low values ofwhen underlying averageis stable

4 36

Choosing

The objective is to obtain the mostaccurate forecast no matter the

techniqueWe generally do this by selecting themodel that gives us the lowest forecasterror

Forecast error = Actual demand - Forecast value

= At - Ft


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Common Measures of Error

Mean Absolute Deviation (MAD)

MAD = |Actual - Forecast|

n

Mean Squared Error (MSE)

MSE = (Forecast Errors)2

n

4 38

Common Measures of Error

Mean Absolu te Percent Error (MAPE)

MAPE =100|Actual i - Forecast i|/Actuali

n

n

i = 1

4 39

Comparison of ForecastError

Rounded Absolute Rounded AbsoluteActual Forecas t Deviat ion Forecas t Deviati onTonnage with for with for

Quarter Un loaded

= .10

= .10

= .50

= .50

1 180 175 5.00 175 5.00

2 168 175.5 7.50 177.50 9.503 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.30

82.45 98.62


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Rounded Absolute Rounded AbsoluteActual Forecas t Deviat ion Forecas t Deviati on

Tonnage with for with for Quarter Un loaded = .10 = .10 = .50 = .50

1 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.503 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.30

82.45 98.62

MAD = |deviations|

n

= 82.45/8 = 10.31

For = .10

= 98.62/8 = 12.33

For = .50

4 41



Quarter Un loaded = .10 = .10 = .50 = .50

1 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.503 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.30

82.45 98.62MAD 10.31 12.33

= 1,526.54/8 = 190.82

For = .10

= 1,561.91/8 = 195.24

For = .50

MSE = (forecast errors)2

n

4 42



Quarter Un loaded

= .10

= .10

= .50

= .50

1 180 175 5.00 175 5.00

2 168 175.5 7.50 177.50 9.503 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.30

82.45 98.62MAD 10.31 12.33MSE 190.82 195.24

= 44.75/8 = 5.59%

For = .10

= 54.05/8 = 6.76%

For = .50

MAPE =100|deviation i|/actual i

n

n

i = 1


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Rounded Absolute Rounded AbsoluteActual Forecas t Deviat ion Forecas t Deviati on

Tonnage with for with for Quarter Un loaded = .10 = .10 = .50 = .50

1 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.503 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.30

82.45 98.62MAD 10.31 12.33MSE 190.82 195.24MAPE 5.59% 6.76%

4 44

Exponential Smoothing withTrend Adjustment

When a trend is present, exponentialsmoothing must be modified

Forecastincluding (FITt) =trend

Exponentially Exponentiallysmoothed (Ft) + (Tt) smoothedforecast trend

4 45

Exponential Smoothing withTrend Adjustment

Ft = (At - 1) + (1 -)(Ft - 1 + Tt - 1)

Tt = (Ft - Ft - 1) + (1 -)Tt - 1

Step 1: Compute FtStep 2: Compute Tt

Step 3: Calculate the forecast FITt = Ft + Tt


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Exponential Smoothing withTrend Adjustment Example

Forecast

Actual Smoot hed Smoothed Includi ngMonth(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt1 12 11 2 13.002 173 204 195 246 217 318 289 36

10

Table 4.1

4 47


ForecastActual Smoot hed Smoothed Includi ng

Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt1 12 11 2 13.002 173 204 195 246 217 318 289 36

10

Table 4.1

F2 = A1 + (1 -)(F1 + T1)

F2 = (.2)(12) + (1 - .2)(11 + 2)

= 2.4 + 10.4 = 12.8 units

Step 1: Forecast for Month 2

4 48



Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt1 12 11 2 13.00

2 17 12.803 204 195 246 217 318 289 36

10

Table 4.1

T2 = (F2 - F1) + (1 -)T1

T2 = (.4)(12.8 - 11) + (1 - .4)(2)

= .72 + 1.2 = 1.92 units

Step 2: Trend for Month 2


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Forecast

Actual Smoot hed Smoothed Includi ngMonth(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt1 12 11 2 13.002 17 12.80 1.923 204 195 246 217 318 289 36

10

Table 4.1

FIT2 = F2 + T1

FIT2 = 12.8 + 1.92

= 14.72 units

Step 3: Calculate FIT for Month 2

4 50



Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt1 12 11 2 13.002 17 12.80 1.92 14.723 204 195 246 217 318 289 36

10

Table 4.1

15.18 2.10 17.2817.82 2.32 20.1419.91 2.23 22.1422.51 2.38 24.8924.11 2.07 26.1827.14 2.45 29.5929.28 2.32 31.6032.48 2.68 35.16

4 51


Figure 4.3

| | | | | | | | |

1 2 3 4 5 6 7 8 9

Time (month)

Productdema

nd

35

30

25

20

15

10

5

0

Actual demand (At)

Forecast i ncluding trend (FITt)with= .2 and= .4


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Trend Projections

Fitting a trend line to histori cal data points

to project into the medium to long-range

Linear trends can be found using the leastsquares technique

y = a + bx^

where y = computed value of the variable tobe predicted (dependent variable)

a = y-axis interceptb = slope of the regression linex = the independent variable

^

4 53

Least Squares Method

Time period

ValuesofDependentVariable

Figure 4.4

Deviation1(error)

Deviation5

Deviation7

Deviation2

Deviation6

Deviation4

Deviation3

Actual observ ation(y value)

Trend line, y = a + bx^

4 54


Time period

ValuesofDependen

tVariable

Figure 4.4

Deviation1

Deviation5

Deviation7

Deviation2

Deviation6

Deviation4

Deviation3

Actual observ ation(y value)

Trend line, y = a + bx^

Least squares methodminimizes the sum of the

squared errors (deviations)


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Equations to calculate the regression variables

b =xy - nxy

x2 - nx2

y = a + bx^

a = y - bx

4 56

Least Squares Example

b = = = 10.54xy -nxy

x2

- nx2

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

140 - (7)(42

)

a = y - bx = 98.86 - 10.54(4) = 56.70

Ti me El ec tr ic al Po werYear Period (x) Demand x2 xy

2001 1 74 1 742002 2 79 4 1582003 3 80 9 2402004 4 90 16 3602005 5 105 25 5252005 6 142 36 8522007 7 122 49 854

x = 28 y = 692 x2 = 140 xy = 3,063x = 4 y = 98.86

4 57


b = = = 10.54xy -nxy

x2 - nx2

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

140 - (7)(42)

a = y - bx = 98.86 - 10.54(4) = 56.70

Ti me El ec tr ic al Po werYear Period (x) Demand x2 xy

1999 1 74 1 742000 2 79 4 1582001 3 80 9 2402002 4 90 16 3602003 5 105 25 5252004 6 142 36 8522005 7 122 49 854

x = 28 y = 692 x2 = 140 xy = 3,063x = 4 y = 98.86

The trend line is

y = 56.70 + 10.54x^


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| | | | | | | | |2001 2002 2003 2004 2005 2006 2007 2008 2009

160

150 140

130

120

110

100

90

80

70

60

50

Year

Powerdemand

Trend line,

y = 56.70 + 10.54x

^

4 59

Seasonal Variations In Data

The multiplicativeseasonal modelcan adjust trenddata for seasonalvariations indemand

4 60

Seasonal Variations In Data

1. Find average historical demand for eachseason

2. Compute the average demand over allseasons

3. Compute a seasonal index for each season

4. Estimate next years total demand

5. Divide this estimate of total demand by thenumber of seasons, then multiply it by theseasonal index for that season

Steps in the process:


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Seasonal Index Example

Jan 80 85 105 90 94 0.957

Feb 70 85 85 80 94 0.851

Mar 80 93 82 85 94 0.904

Apr 90 95 115 100 94 1.064

May 113 125 131 123 94 1.309

Jun 110 115 120 115 94 1.223

Jul 100 102 113 105 94 1.117

Aug 88 102 110 100 94 1.064

Sept 85 90 95 90 94 0.957

Oct 77 78 85 80 94 0.851

Nov 75 72 83 80 94 0.851

Dec 82 78 80 80 94 0.851

Demand Average Average SeasonalMonth 2005 2006 2007 2005-2007 Monthly Index

Expected annual demand = 1,200

Jan x .957 = 961,200

12

Feb x .851 = 851,200

12

Forecast for 2008

4 65

Seasonal Index Example

140

130

120

110

100

90

80

70 | | | | | | | | | | | |

J F M A M J J A S O N DTime

Demand

2008 Forecast

2007 Demand

2006 Demand

2005 Demand

4 66

San Diego Hospital

10,200

10,000

9,800

9,600

9,400

9,200

9,000 | | | | | | | | | | | |Jan Feb Mar Apr May Jun e Jul y Aug Sept Oct Nov Dec67 68 69 70 71 72 73 74 75 76 77 78

Month

InpatientDays

9530

9551

9573

9594

9616

9637

9659

9680

9702

9724

9745

9766

Figure 4.6

Trend Data


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San Diego Hospital

1.06

1.04

1.02

1.00

0.98

0.96

0.94

0.92 | | | | | | | | | | | |

Jan Feb Mar Apr May Jun e Jul y Aug Sept Oct Nov Dec67 68 69 70 71 72 73 74 75 76 77 78

Month

IndexforInpatientDays 1.04

1.021.01

0.99

1.031.04

1.00

0.98

0.97

0.99

0.970.96

Figure 4.7

Seasonal Indices

4 68

San Diego Hospital

10,200

10,000

9,800

9,600

9,400

9,200

9,000 | | | | | | | | | | | |

Jan Feb Mar Apr May Jun e Jul y Aug Sept Oct Nov Dec67 68 69 70 71 72 73 74 75 76 77 78

Month

InpatientDays

Figure 4.8

9911

9265

9764

9520

9691

9411

9949

9724

9542

9355

10068

9572

Combined Trend and Seasonal Forecast

4 69

Associative Forecast ing

Used when changes in one or moreindependent variables can be used to predict

the changes in the dependent variable

Most common technique is linearregression analysis

We apply this technique just as we didin the time series example


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Associative Forecast ing

Forecasting an outcome based on

predictor variables using the least squarestechnique

y = a + bx^

where y = computed value of the variable tobe predicted (dependent variable)

a = y-axis interceptb = slope of the regression linex = the independent variable though to

predict the value of the dependentvariable

^

4 71

Associative Forecast ingExample

Sales Local Payroll($ mi ll ions ), y ($ bi ll ions ), x

2.0 13.0 32.5 42.0 22.0 13.5 7

4.0

3.0

2.0

1.0

| | | | | | |

0 1 2 3 4 5 6 7

Sales

Area pay rol l

4 72


Sales, y Payroll, x x2 xy

2.0 1 1 2.03.0 3 9 9.0

2.5 4 16 10.02.0 2 4 4.02.0 1 1 2.03.5 7 49 24.5

y = 15.0 x = 18 x2 = 80 xy = 51.5

x = x/6 = 18/6 = 3

y = y/6 = 15/6 = 2.5

b = = = .25xy -nxy

x2 - nx2

51.5 - (6)(3)(2.5)

80 - (6)(32)

a = y - bx = 2.5 - (.25)(3) = 1.75


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4.0

3.0

2.0

1.0

| | | | | | |0 1 2 3 4 5 6 7

Sales

Area pay rol l

y = 1.75 + .25x^ Sales = 1.75 + .25(payroll)

If payroll next yearis estimated to be$6 billion, then:

Sales = 1.75 + .25(6)Sales = $3,250,000

3.25

4 74

Measures how well the forecast ispredicting actual values

Ratio of running sum of forecast errors(RSFE) to mean absolu te deviation (MAD)

Good tracking signal has low values

If forecasts are continually high or low, theforecast has a bias error

Monitoring and ControllingForecasts

Tracking Signal

4 75

Monitoring and ControllingForecasts

Tracking

signal

RSFE

MAD

=

Trackingsignal =

(Actual demand inperiod i -

Forecast demandin period i)

|Actual - Forecast|/n)


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Tracking Signal

Tracking signal

+

0 MADs

Upper control l imit

Lower control limit

Time

Signal exceeding limit

Acceptabl erange

4 77

Adaptive Forecasting

Its possible to use the computer tocontinually monitor forecast error andadjust the values of the and coefficients used in exponentialsmoothing to continually minimizeforecast error

This technique is called adaptivesmoothing

4 78

Forecasting in the ServiceSector

Presents unusual challenges

Special need for short term records

Needs differ greatly as function ofindustry and product

Holidays and other calendar events

Unusual events


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Fast Food RestaurantForecast

20%

15%

10%

5%

11-12 1-2 3-4 5-6 7-8 9-1012-1 2-3 4-5 6-7 8-9 10-11

(Lunchtime) (Dinnertime)

Hour of day

Percentageofsales

Figure 4.12

4 80

FedEx Call Center Forecast

Figure 4.12

12%

10%

8%

6%

4%

2%

0%

Hour of dayA.M. P.M.

2 4 6 8 10 12 2 4 6 8 10 12

mg t 303 lecture notes 3

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