Adjusted Exponential Smoothing

1
Adjusted Exponential Smoothing

• Paul Mendenhall
• BusM 361
• Professor Foster

2
Outline

• Tool defined
• Equation Explained
• Illustrated step by step problem
• Practice Problem
• Summary

3
Definition

• Times Series Forecasting model
• Adjusts for trends in information

4
Trends

• What are trends?
• Long term movements in a time series.
• Why are trends a problem?
• Cause lags in forecasts.

5
Smoothing and Alpha

• Alpha (a)
• If randomness is great than a is closer to 0.
• More weight on past data.
• If randomness is small than a is closer to 1.
• Greater weight on recent data.

6
Why the Model is Used

• Smoothes random information.
• Works with trends in information.
• Provides a more accurate forecast.

7
Equation

• The equation is
• AFt1 F t1 Tt1

8
Equation Explained

• The equation is AFt1 F t1 Tt1
• where
• F t1 aDt (1- a)Ft
• T t1 ß(F t1 -Ft) (1- ß)Tt
• Tt1 trend factor for the next
  period.
• Tt trend factor for the current period
• ß smoothing constant for the trend
  adjustment factor.

9
Equation Illustrated

• An electronics company is selling portable CD
  players and estimated the demand for the first
  period and forecasted the next three periods'
  adjusted demand using the Adjusted Exponential
  Smoothing model. The first periods demand is 50
  players and 54 players was used to start the
  forecast. ß 0.7 and a 0.2 (see Table 1)

10
Equation Illustrated cont
Period Demand Unadjusted Forecast Ft Trend Tt Adjusted Forecast AFt
1 54 50 - -
2 57 - - -
3 44 - - -

a value is 0.2 ß value is 0.7 a value is 0.2 ß value is 0.7
Table 1
11
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 Tt Adjusted Forecast AFt
1 54 50 - -
12
Step 2

• Calculate Ft1 for period 2
• F t1 aDt (1- a)Ft
• F2 0.257(1-0.2)50 50.8

Period Demand Unadjusted Forecast Ft Trend Tt Adjusted Forecast AFt
1 54 50 - -
2 57 50.8 - -
13
Step 3

• Calculate the trend adjustment factor for period
  2
• T t1 ß(F t1 -Ft) (1- ß)Tt
• T2 0.7(50.8-50)(1-0.7)0 0.56

Period Demand Unadjusted Forecast Ft Trend Tt Adjusted Forecast AFt
1 54 50 0 -
2 57 50.8 0.56 -
14
Step 4

• Calculate the Adjusted Forecast AFt
• AFt1 F t1 Tt1
• AF2 50.8 0.56 51.36

Period Demand Unadjusted Forecast Ft Trend Tt Adjusted Forecast AFt
1 54 50 0 -
2 57 50.8 0.56 51.36
15
Complete the table

• Now calculate the Adjusted Forecast for period 3.

Period Demand Unadjusted Forecast Ft Trend Tt Adjusted Forecast AFt
1 54 50 0 50
2 57 50.8 0.56 51.36
3 44 - - -
16
Steps 1-4 Completed

• Now calculate the Adjusted Forecast for period 3.
• Forecast table completed.

Period Demand Unadjusted Forecast Ft Trend Tt Adjusted Forecast AFt
1 54 50 0 50
2 57 50.8 0.56 51.36
3 44 52.04 1.036 53.08
17
Real World Example

• Concise Co. is considering purchasing new
  equipment to improve productivity, but must first
  do some financial analysis. To provide accurate
  information for the analysis, an accurate
  forecast of demand must be produced to determine
  the estimated profit and cash flows for the next
  year. Concise Co. is concerned about the
  accuracy of the forecast due to dramatic
  movements is demand the last few years. Top
  management has asked you, the financial analysis,
  to create the forecasted report for 2005.

18
Real World Ex. Continued

• You decide, after looking at the trends of the
  information, that the adjusted exponential
  smoothing model would work best for the forecast.
  Alpha is .3 and beta is .6. Use the last five
  years to create next years forecasted demand

19
Real World Ex. Continued

• Top management has asked you, the financial
  analysis, to create the forecasted report for
  2005. Use the last five years to create next
  years forecasted demand. The last five years
  demand is provided in the graph below.

Year Demand
2000 1376
2001 1189
2002 1122
2003 1306
2004 1213
20
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
21
Summary

• Times series
• Smoothing
• Trends
• Accurate forecasting

22
Additional Readings

• http//www.duke.edu/rnau/411outbd.htm
• Introduction to Operations and Supply Chain
  Management Bozarth, Cecil C., Handfield, Robert
  B. 1st ed. 2005