Adjusted Exponential Smoothing
Paul Mendenhall
BusM 361
Professor Foster

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

Definition
• Times Series Forecasting model
• Adjusts for trends in information

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

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

Why the Model is Used
• Smoothes random information.
• Works with trends in information.
• Provides a more accurate forecast.

Equation
The equation is:
AF t+1
= F t+1
+ T t+1

Equation Explained
The equation is: AF t+1 where:
= F t+1
+ T t+1
F t+1
T t+1
= αD t
+ (1- α)F t
= β(F t+1
-F t
) + (1- β)T t
T t=1
= trend factor for the next period.
T t
= trend factor for the current period
β = smoothing constant for the trend adjustment factor.

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. β = 0.7 and
α= 0.2 (see Table 1)

Equation Illustrated cont…
Period
1
2
3
Demand
54
57
44
Unadjusted
Forecast F t
50
-
-
Trend T t
-
-
-
Adjusted
Forecast AF t
-
-
-
* α value is 0.2
** β value is 0.7
Table 1

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
1
Demand
54
Unadjusted
Forecast F t
50
Trend T t
-
Adjusted Forecast
AF t
-

Step 2
Calculate F t+1 for period 2:
F t+1
= αD t
+ (1- α)F t
F2 = 0.2*57+(1-0.2)*50 = 50.8
Period
1
2
Demand
54
57
Unadjusted
Forecast F t
50
50.8
Trend T t
-
-
Adjusted Forecast
AF t
-
-

Step 3
Calculate the trend adjustment factor for period 2:
T t+1
= β(F t+1
-F t
) + (1- β)T t
T2 = 0.7(50.8-50)+(1-0.7)*0 = 0.56
Period
1
2
Demand
54
57
Unadjusted
Forecast F t
50
50.8
Trend T t
0
0.56
Adjusted Forecast
AF t
-
-

Step 4
Calculate the Adjusted Forecast AF t
:
AF t+1
= F t+1
+ T t+1
AF
2
= 50.8 + 0.56 = 51.36
Period
1
2
Demand
54
57
Unadjusted
Forecast F t
50
50.8
Trend T t
0
0.56
Adjusted Forecast
AF t
-
51.36

Complete the table
Now calculate the Adjusted Forecast for period 3.
Period
1
2
3
Demand
54
57
44
Unadjusted
Forecast F t
50
50.8
-
Trend T t
0
0.56
-
Adjusted Forecast
AF t
50
51.36
-

Steps 1-4 Completed
• Now calculate the Adjusted Forecast for period 3.
• Forecast table completed.
Period
1
2
3
Demand
54
57
44
Unadjusted
Forecast F t
50
50.8
52.04
Trend T t
0
0.56
1.036
Adjusted Forecast
AF t
50
51.36
53.08

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.

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 year’s forecasted demand…

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 year’s forecasted demand. The last five years demand is provided in the graph below.
Year
2000
2001
2002
2003
2004
Demand
1376
1189
1122
1306
1213

Practice Problem Answer
Year
2000
2001
2002
2003
2004
Demand
1376
1189
1122
1306
1213
Unadjusted
Forecast F t
1200
1253
1234
1200
1232
Trend Tt
0
32
1
-20
11
Adjusted Forecast
AFt
1200
1284
1235
1181

Summary
• Times series
• Smoothing
• Trends
• Accurate forecasting

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