Chapter 7 Demand Forecasting in a Supply Chain

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

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Chapter 7Demand Forecastingin a Supply Chain

Forecasting -2Exponential Smoothing

Ardavan Asef-Vaziri

Based on Operations management: Stevenson

Operations Management: Jacobs, Chase, and AquilanoSupply Chain Management: Chopra and Meindl


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Time Series Methods

Moving Average

Exponential Smoothing

More sophisticated techniques available


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How did we use data

Moving average Discard old records

Assign same weight for recent records

Advantage? Disadvantage?

Assign different weights Weighted moving average

For example

4321 ttttt AAAAF 4321 1.02.03.04.0 ttttt AAAAF


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)(α1 tttt FAFF

ttt AFF α)α1(1

tttt FAFF αα1


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α=0.2 tAtFt

1100100

A1 F2

2

100

Since I have no information for F2, I just enter A1 which is 100. Alternatively we may assume the average of all available data as our forecast for period 2.

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


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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


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How do we pick ?

Large When does it work? When does it not?

Small When does it work? When does it not?


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Given a = 0.1. What is the forecast for week 9?

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


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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


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1 200

2 250 200

3 175 205

4 186 202

5 225

6 285

7 305

8 190


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1 200

2 250 200

3 175 205

4 186 202

5 225 200

6 285 203

7 305 211

8 190 220

Similarly we get:


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Two important questions

How to choose a?

What is better exponential smoothing

OR moving average?


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Exponential Smoothing: a = 0.4


1 200

2 250 200

3 175 220

4 186 202

5 225 196

6 285 207

7 305 238

8 190 265


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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


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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.


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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.


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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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Pieces of Data and Age of Data in Exponential Smoothing

Ft = a At–1 + (1 – a) Ft–1

Ft–1 = a At–2 + (1 – a) Ft–2, etc

Ft = aAt–1+(1–a)aAt–2+(1–a)2Ft–2

= 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.

“Age” of data is about 1/ a periods .


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What is better? Exponential Smoothing or Moving Average

If we set a = 2/(N+1), then MA and ES are approximately equivalent.

What does it mean that the two systems are equivalent? The variances of the errors are identical. Does it mean that the two systems have the

same forecasts?

Exponential smoothing requires less data storage to implement.


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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


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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


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Office Buttton


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Add-Inns


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Not OK, but GO, then Check Mark Solver


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Data Tab/ Solver


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Target Cell/Changing Cells


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Optimal a Minimal MAD


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Associative (Causal) Forecasting

The primary method for associative forecasting is Regression Analysis.

The relationship between a dependent variable and one or more independent variables.

The independent variables are also referred to as predictor variables.

We only discuss linear regression between two variables.

We consider the relationship between the dependent variable (demand) and the independent variable (time).


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Regression Method

0

10

20

30

40

50

0 5 10 15 20 25

tbbFt 10

Least Squares Line

minimizes sum of squared deviations around the line

Computedrelationship


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Regression: Chart the Data

Period Demand1 1172 1263 2104 2225 2626 3107 2788 3389 37910 388

0 2 4 6 8 10 120

50

100

150

200

250

300

350

400

450

Demand

Demand


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Regression: The Same as Solver but This Time Data Analysis


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Data/Data Analysis/ Regression


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Regression: Tools / Data Analysis / Regression


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Regression Output

Ft = 94.13 +30.71tForecast for the next period.F11 = 94.13 +30.71(11) = 431.7

SUMMARY OUTPUT

Regression StatisticsMultiple R 0.98R Square 0.95Adjusted R Square 0.95Standard Error 22.21Observations 10

ANOVAdf SS MS F Significance F

Regression 1 77771 77771 158 1.51524E-06Residual 8 3945 493Total 9 81716

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%Intercept 94.13 15.17 6.21 0.000258 59.15 129.12X Variable 1 30.70 2.44 12.56 0.000002 25.07 36.34


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Assignment ….. Due at the beginning of the next class

Month Sales (1000)

Feb 19

Mar 18

Apr 15

May 20

Jun 18

Jul 22

Aug 20

• Linear regression• 5 period moving average• Exponential smoothing.

α=.2 March forecast=19• Naive method• Compute MAD for naive method

and exponential smoothing. Which one is preferred? NM or ES?

Based on the data below forecast the demand for September using the listed techniques:


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Assignment ….. Due at the beginning of the next class

(a) Exponential smoothing is being used to forecast demand. The previous forecast of 66 turned out to be 5 units larger than actual demand. The next forecast is 65. Compute ?

(b) The 5-period moving average in month 6 was 150 units. Actual demand in month 7 is 180 units. What is the 6 period moving average in month 7?

(c) Tickets numbered from 100 to 200 have been sold. Using the random number rand() = 0.35 identify the winner.


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Practice

The president of State University wants to forecast student

enrollments for this academic year based on the following

historical data:

5 years ago 15,0004 years ago 16,0003 years ago 18,0002 years ago 20,000Last year 21,000

What is the forecast for this year using exponential smoothing with α = 0.4, if the forecast for two

years agowas 16,000?


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Practice

t 1 2 3 4 5

At 15000 16000 18000 20000 21000

Ft 16000

Forecast for last year

F5 = (1-α)F4+ α(A4)

F5 = .6(16000)+.4(20000)=17600

Forecast for this year

F6 = (1-α)F5+ α(A5)

F6 = .6(17600)+.4(21000)=18960

17600


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Practice ……… For your own practice

Based on the data below forecast the total number of new customers in year 9. Use the listed techniques:

• Linear regression (show equation)

• 4 period moving average• Exponential Smoothing.

α=.3 Year 3 forecast=43• Naive method• Compute MAD for naive

method and exponential smoothing. Which one is preferred? NM or ES?

Year Customers1 352 433 414 465 486 637 678 79

Chapter 7 Demand Forecasting in a Supply Chain

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