Adj Exp Smoothing

7/31/2019 Adj Exp Smoothing

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Adjusted Exponential Smoothing

Paul Mendenhall

BusM 361Professor Foster


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Outline

Tool defined

Equation Explained

Illustrated step by step problem

Practice Problem

Summary


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Definition

Times Series Forecasting model

Adjusts for trends in information


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Trends

What are trends?

Long term movements in a time series.

Why are trends a problem?

Cause lags in forecasts.


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Smoothing and Alpha

Alpha ()

If randomness is great than is closer to 0.

More weight on past data.

If randomness is small than is closer to 1.

Greater weight on recent data.


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Why the Model is Used

Smoothes random information.

Works with trends in information.

Provides a more accurate forecast.


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Equation

The equation is:

AFt+1 = F t+1 + Tt+1


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Equation Explained

The equation is: AFt+1 = F t+1 + Tt+1where:

F t+1 = Dt + (1- )Ft

T t+1 = (F t+1 -Ft) + (1- )Tt

Tt=1 = trend factor for the nextperiod.

Tt = trend factor for the current period

= smoothing constant for the trendadjustment factor.


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Equation Illustrated

An electronics company is selling portable

CD players and estimated the demand forthe first period and forecasted the next threeperiods' adjusted demand using theAdjusted Exponential Smoothing model.

The first periods demand is 50 players and54 players was used to start the forecast. = 0.7 and = 0.2 (see Table 1)


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Equation Illustrated cont

Period Demand

Unadjusted

Forecast Ft Trend T

t

Adjusted

Forecast AFt

1 54 50 - -

2 57 - - -

3 44 - - -

* value is 0.2

** value is 0.7

Table 1


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Step 1

Create a table in Excel and enter the figures for

the first period. Demand was 54.

Unadjusted Forecast is any reasonable starting

figure to start the process, in this case 50 players.

Period Demand

Unadjusted

Forecast Ft Trend T

t

Adjusted Forecast

AFt

1 54 50 - -


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Step 2

Calculate Ft+1 for period 2:

F t+1 = Dt + (1- )FtF2 = 0.2*57+(1-0.2)*50 = 50.8

Period Demand

Unadjusted

Forecast Ft Trend T

t

Adjusted Forecast

AFt

1 54 50 - -

2 57 50.8 - -


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Step 3

Calculate the trend adjustment factor for period 2:

T t+1 = (F t+1 -Ft) + (1- )Tt

T2 = 0.7(50.8-50)+(1-0.7)*0 = 0.56

Period Demand

Unadjusted

Forecast Ft Trend T

t

Adjusted Forecast

AFt

1 54 50 0 -

2 57 50.8 0.56 -


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Step 4

Calculate the Adjusted Forecast AFt:

AFt+1 = F t+1 + Tt+1

AF2 = 50.8 + 0.56 = 51.36

Period Demand

Unadjusted

Forecast Ft Trend T

t

Adjusted Forecast

AFt

1 54 50 0 -

2 57 50.8 0.56 51.36


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Complete the table

Now calculate the Adjusted Forecast for period 3.

Period Demand

Unadjusted

Forecast Ft Trend T

t

Adjusted Forecast

AFt

1 54 50 0 50

2 57 50.8 0.56 51.36

3 44 - - -


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Steps 1-4 Completed

Now calculate the Adjusted Forecast for period 3.

Forecast table completed.

Period Demand

Unadjusted

Forecast Ft Trend T

t

Adjusted Forecast

AFt

1 54 50 0 50

2 57 50.8 0.56 51.36

3 44 52.04 1.036 53.08


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Real World Example

Concise Co. is considering purchasing new equipment toimprove productivity, but must first do some financialanalysis. To provide accurate information for the analysis,an accurate forecast of demand must be produced todetermine the estimated profit and cash flows for the nextyear. Concise Co. is concerned about the accuracy of theforecast due to dramatic movements is demand the last fewyears. Top management has asked you, the financialanalysis, to create the forecasted report for 2005.


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Real World Ex. Continued

You decide, after looking at the trends of the information,

that the adjusted exponential smoothing model would workbest for the forecast. Alpha is .3 and beta is .6. Use the

last five years to create next years forecasted demand


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Real World Ex. Continued

Top management has asked you, the financial analysis, tocreate the forecasted report for 2005. Use the last five

years to create next years forecasted demand. The lastfive years demand is provided in the graph below.

Year Demand

2000 1376

2001 1189

2002 1122

2003 1306

2004 1213


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Practice Problem Answer

Year Demand

Unadjusted

Forecast Ft Trend Tt

Adjusted Forecast

AFt

2000 1376 1200 0 1200

2001 1189 1253 32 1284

2002 1122 1234 1 1235

2003 1306 1200 -20 1181

2004 1213 1232 11


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Summary

Times series

Smoothing

Trends

Accurate forecasting


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Additional Readings

http://www.duke.edu/~rnau/411outbd.htm

Introduction to Operations and SupplyChain Management Bozarth, Cecil C.,

Handfield, Robert B. 1st ed. 2005
http://www.duke.edu/~rnau/411outbd.htmhttp://www.duke.edu/~rnau/411outbd.htm

Adj Exp Smoothing

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