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Exponential Smoothing 1 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Chapter 7 Demand Forecasting in a Supply Chain Forecasting -2 Exponential Smoothing Ardavan Asef-Vaziri Based on Operations management: Stevenson Operations Management: Jacobs and Chase Supply Chain Management: Chopra and Meindl

Exponential Smoothing 1 Ardavan Asef-Vaziri 6/4/2009 Forecasting-2 Chapter 7 Demand Forecasting in a Supply Chain Forecasting -2 Exponential Smoothing

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Exponential Smoothing 1Ardavan Asef-Vaziri 6/4/2009

Forecasting-2

Chapter 7Demand Forecastingin a Supply Chain

Forecasting -2Exponential Smoothing

Ardavan Asef-Vaziri

Based on Operations management: Stevenson

Operations Management: Jacobs and ChaseSupply Chain Management: Chopra and Meindl

Exponential Smoothing 2Ardavan Asef-Vaziri 6/4/2009

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Time Series Methods

Moving Average Discard old records

Assign same weight for recent records

Assign different weights Weighted moving average

3211 ttttt AAAAF 3211 1.02.03.04.0 ttttt AAAAF

Exponential Smoothing

Exponential Smoothing 3Ardavan Asef-Vaziri 6/4/2009

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Exponential Smoothing

)(α1 tttt FAFF

ttt AFF α)α1(1

tttt FAFF αα1

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Exponential Smoothing

α=0.2 tAtFt

1100100

A1 F2

2

100

Since I have no information for F1, I just enter A1 which is 100. Alternatively we may assume the average of all available data as our forecast for period 1.

150

F3 =(1-α)F2 + α A2

F3 =0.8(100) + 0.2(150)

F3 =80 + 30 = 110

3

110

F2 & A2 F3

A1 F2 A1 & A2 F3

F3 =(1-α)F2 + α A2

Exponential Smoothing 5Ardavan Asef-Vaziri 6/4/2009

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Exponential Smoothing

α=0.2

tAtFt

1100100

F4 =(1-α)F3 + α A3

F4 =0.8(110) + 0.2(120)

F4 =88 + 24 = 112

A3 & F3 F4

A1 & A2 F3 A1& A2 & A3 F4

2150100

3

110

4

112120

F4 =(1-α)F3 + α A3

Exponential Smoothing 6Ardavan Asef-Vaziri 6/4/2009

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Example: Forecast for week 9 using a = 0.1

Week Demand Forecast

1 200

2 250 200

3 175

4 186

5 225

6 285

7 305

8 190

205250*1.0200*9.01 223 AFF

Exponential Smoothing 7Ardavan Asef-Vaziri 6/4/2009

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Week 4

Week Demand Forecast

1 200

2 250 200

3 175 205

4 186

5 225

6 285

7 305

8 190

202175*1.0205*9.01 334 AFF

Exponential Smoothing 8Ardavan Asef-Vaziri 6/4/2009

Forecasting-2

Exponential Smoothing

Week Demand Forecast

1 200

2 250 200

3 175 205

4 186 202

5 225 200

6 285 203

7 305 211

8 190 220

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Two important questions

How to choose a? Large or Small When does it work? When does it not?

What is better exponential smoothing

OR moving average?

Exponential Smoothing 10Ardavan Asef-Vaziri 6/4/2009

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The Same Example: a = 0.4

Week Demand Forecast

1 200

2 250 200

3 175 220

4 186 202

5 225 196

6 285 207

7 305 238

8 190 265

Exponential Smoothing 11Ardavan Asef-Vaziri 6/4/2009

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Comparison

0

50

100

150

200

250

300

350

1 2 3 4 5 6 7 8

week

Demand

alpha = 0.1

alpha = 0.4

Exponential Smoothing 12Ardavan Asef-Vaziri 6/4/2009

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Comparison

As a becomes larger, the predicted values

exhibit more variation, because they are

more responsive to the demand in the

previous period. A large a seems to track the series better.

Value of stability

This parallels our observation regarding MA:

there is a trade-off between responsiveness

and smoothing out demand fluctuations.

Exponential Smoothing 13Ardavan Asef-Vaziri 6/4/2009

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Comparison

Week DemandForecast for

0.1 alpha ADForecast for 0.4

alpha AD

1 200

2 250 200.00 50.00 200.00 50.00

3 175 205.00 30.00 220.00 45.00

4 186 202.00 16.00 202.00 16.00

5 225 200.40 24.60 195.60 29.40

6 285 202.86 82.14 207.36 77.64

7 305 211.07 93.93 238.42 66.58

8 190 220.47 30.47 265.05 75.05

46.73 51.38

Choose the forecast with lower MAD.

Exponential Smoothing 14Ardavan Asef-Vaziri 6/4/2009

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Which a to choose?

In general want to calculate MAD for many

different values of a and choose the one

with the lowest MAD.

Same idea to determine if Exponential

Smoothing or Moving Average is preferred.

Note that one advantage of exponential

smoothing requires less data storage to

implement.

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All Pieces of Data are Taken into Account in ES

Ft = a At–1 + (1 – a) Ft–1

Ft–1 = a At–2 + (1 – a) Ft–2

Ft = aAt–1+(1–a)aAt–2+(1–a)2Ft–2

Ft–2 = a At–3 + (1 – a) Ft–3

Ft = aAt–1+(1–a)aAt–2+(1–a)2a At–3 + (1 – a) 3 Ft–3

= aAt–1+(1–a)aAt–2+(1–a)2aAt–3 +(1–a)3aAt–4

+(1–a)4aAt–5+(1–a)5aAt–6 +(1–a)6aAt–7+…

A large number of data are taken into account– All data are taken

into account in ES.

Exponential Smoothing 16Ardavan Asef-Vaziri 6/4/2009

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What is better? Exponential Smoothing or Moving Average

Age of data in moving average is (1+ n)/2 .Age of data in exponential smoothing is about 1/

a.1n)/2 = 1/ a a = 2/(n+1)If we set a = 2/(n +1) , then moving average and

exponential smoothing are approximately equivalent. It does not mean that the two models have

the same forecasts. The variances of the errors are identical.

Exponential Smoothing 17Ardavan Asef-Vaziri 6/4/2009

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Compute MAD & TS

Alpha = 0.50 MAD = 927

Period At Ft Dev AD MAD Sum Dev TS1 13400 13912 -512 512 512 -512 -1.0002 14100 13656 444 444 478 -68 -0.1423 14700 13878 822 822 593 754 1.2724 15100 14289 811 811 647 1565 2.4185 13400 14695 -1295 1295 777 271 0.3486 16000 14047 1953 1953 973 2223 2.2867 12700 15024 -2324 2324 1166 -100 -0.0868 15400 13862 1538 1538 1212 1438 1.1869 13000 14631 -1631 1631 1259 -193 -0.15310 16200 13815 2385 2385 1371 2191 1.59811 16100 15008 1092 1092 1346 3284 2.44012 13500 15554 -2054 2054 1405 1230 0.87513 14900 14527 373 373 1326 1603 1.20914 15200 14713 487 487 1266 2089 1.65115 15200 14957 243 243 1198 2333 1.94816 15800 15078 722 722 1168 3054 2.61617 16100 15439 661 661 1138 3715 3.26518 16400 15770 630 630 1110 4346 3.91619 15300 16085 -785 785 1093 3561 3.25920 15900 15692 208 208 1048 3768 3.59421 16300 15796 504 504 1022 4272 4.17822 15500 16048 -548 548 1001 3724 3.72123 15800 15774 26 26 959 3750 3.91224 16000 15787 213 213 927 3963 4.273

Exponential Smoothing 18Ardavan Asef-Vaziri 6/4/2009

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Data Table Excel

9270.1 10170.2 8970.3 8860.4 9010.5 9270.6 9600.7 9970.8 10360.9 1078

1 1130

9270.1 10170.2 8970.3 8860.4 9010.5 9270.6 9600.7 9970.8 10360.9 1078

1 1130 886

Data, what if, Data table

Min, conditional formatting

Alpha = 0.50 MAD = 927

Period At Ft Dev AD MAD Sum Dev TS1 13400 13912 -512 512 512 -512 -1.0002 14100 13656 444 444 478 -68 -0.1423 14700 13878 822 822 593 754 1.2724 15100 14289 811 811 647 1565 2.4185 13400 14695 -1295 1295 777 271 0.3486 16000 14047 1953 1953 973 2223 2.2867 12700 15024 -2324 2324 1166 -100 -0.0868 15400 13862 1538 1538 1212 1438 1.1869 13000 14631 -1631 1631 1259 -193 -0.15310 16200 13815 2385 2385 1371 2191 1.59811 16100 15008 1092 1092 1346 3284 2.44012 13500 15554 -2054 2054 1405 1230 0.87513 14900 14527 373 373 1326 1603 1.20914 15200 14713 487 487 1266 2089 1.65115 15200 14957 243 243 1198 2333 1.94816 15800 15078 722 722 1168 3054 2.61617 16100 15439 661 661 1138 3715 3.26518 16400 15770 630 630 1110 4346 3.91619 15300 16085 -785 785 1093 3561 3.25920 15900 15692 208 208 1048 3768 3.59421 16300 15796 504 504 1022 4272 4.17822 15500 16048 -548 548 1001 3724 3.72123 15800 15774 26 26 959 3750 3.91224 16000 15787 213 213 927 3963 4.273

9270.10.20.30.40.50.60.70.80.9

1 This is a one variable Data Table

Exponential Smoothing 19Ardavan Asef-Vaziri 6/4/2009

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Office Button

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Add-Inns

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Not OK, but GO, then Check Mark Solver

Exponential Smoothing 22Ardavan Asef-Vaziri 6/4/2009

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Data Tab/ Solver

Exponential Smoothing 23Ardavan Asef-Vaziri 6/4/2009

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Target Cell/Changing Cells

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Optimal a Minimal MAD

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NOTE – The following pages are not recorded

Note: The following discussion – from the next

page up to the end of this set of slides – are

not recorded.

Exponential Smoothing 26Ardavan Asef-Vaziri 6/4/2009

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Measures of Forecast Error; Additional Indices

Error: difference between predicted value

and actual value (E)

Mean Absolute Deviation (MAD)

Tracking Signal (TS)

Mean Square Error (MSE)

Mean Absolute Percentage Error (MAPE)

Exponential Smoothing 27Ardavan Asef-Vaziri 6/4/2009

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7-1-27

Measures of Forecast Error

nsObservatio of # (MAD)Deviation AbsoluteMean tE

nsObservatio of # (MSE)Error SquaredMean

2 tE

nsObservatio of #

100

)Error(MAPE Percentage AbsoluteMean

t

t

A

E

Error ofDeviation Standard estimatean is 1.25MAD

Error ofDeviation Standard estimateanother also is MSE