10 forecasting

8/3/2019 10 Forecasting

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Demand Management

and

FORECASTING

Operations Management

Dr. Ron Tibben-Lembke


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Demand Management Coordinate sources of demand for supply chain

to run efficiently, deliver on time

Independent Demand Things demanded by end users

Dependent Demand

Demand known, once demand for end items is

known


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Affecting Demand Increasing demand

Marketing campaigns

Sales force efforts, cut prices Changing Timing of demand

Incentives for earlier or later delivery

At capacity, dont actively pursue more


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Predicting the Futu

re

We know the forecast will be wrong.

Try to make the best forecast we can,

Given the time we want to invest Given the available data


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Time Horizons

Different decisions require projections aboutdifferent time periods:

Short-range: who works when, what to make eachday (weeks to months) Medium-range: when to hire, lay off (months toyears)

Long-range: where to build plants, enter newmarkets, products (years to decades)


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Forecast Impact

Finance & Accounting: budget planningHuman Resources: hiring, training, laying off

employeesCapacity: not enough, customers go away angry,

too much, costs are too highSupply-Chain Management: bringing in newvendors takes time, and rushing it can lead to

quality problems later


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Qualitative Methods Sales force composite / Grass Roots Market Research / Consumer market surveys &

interviews Jury of Executive Opinion / Panel Consensus Delphi Method Historical Analogy - DVDs like VCRs Nave approach


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Quantitative MethodsTime Series Methods

0. All-Time Average

1. Simple Moving Average2. Weighted Moving Average

3. Exponential Smoothing

4. Exponential smoothing with trend

5. Linear regressionCausal Methods

Linear Regression


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Time Series Fo

recasting

Assume patterns in data will continue, including:

Trend (T)Seasonality (S)

Cycles (C)

Random

Variations


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All-Time Average

To forecast next period, take the average of allprevious periods

Advantages: Simple to use

Disadvantages: Ends up with a lot of data

Gives equal importance to very old data


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Moving Average

Compute forecast using n most recent periods

Jan Feb Mar Apr May Jun Jul

3 month Moving Avg:

June forecast:

FJun = (AMar + AApr + AMay)/3If no cycles to demand, quite a bit of freedom to

choose n


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Moving Average

Advantages:

Ignores data that is too old

Requires less data than simple average More responsive than simple average

Disadvantages:

Still lacks behind trend like simple average,

(though not as badly) The larger n is, more smoothing, but the more it

will lag

The smaller n is, the more over-reaction


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Simple and Moving Averages

Period Demand All-Time 3MA

1 10

2 12 10

3 14 11.0

4 15 12.0 12.0

5 16 12.8 13.7

6 17 13.4 15.0

7 19 14.0 16.08 21 14.7 17.3

9 23 15.5 19.0

10 16.3 21.0


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Centered Moving Ave

rage

Take average of n periods,

Plot the average in the middle period

Not useful for forecasting

More stable than actuals If seasonality, n = season length (4wks, 12 mo, etc.)


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CMA - #Periods to Ave

rage

What if data has 12-month cycle?

Ja F M Ap My Jn Jl Au S O N D Ja F M

Avg of Jan-Dec gives average of month 6.5:

(1+2+3+4+5+6+7+8+9+10+11+12)/12=6.5Avg of Feb-Jan gives average of month 6.5:(2+3+4+5+6+7+8+9+10+11+12+13)/12=7.5

How get a July average? Average of other two averages


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Centered Moving Ave

rage

To center even-number of periods

12: take half each of 1 and 13, plus sum of 2-12.

F14 = 0.5 A1 + A2 + A3 + A4 + A5 + A6 + A7 +A8 + A9 + A10 + A11 + A12 + 0.5A13

This is exactly the same as what you get bytaking the average of the averages from previous

slide


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Old DataComparison of simple, moving averages clearly

shows that getting rid of old data makes forecastrespond to trends faster

Moving average still lags the trend, but it suggeststo us we give newer data more weight, older dataless weight.


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Weighted Moving Average

FJun = (AMar + AApr + AMay)/3= (3AMar + 3DApr + 3AMay)/9

Why not consider:

FJun = (2AMar + 3AApr + 4AMay)/9FJun = 2/9 AMar + 3/9 AApr + 4/9 AMayFt = w1At-3 + w2At-2 + w3At-1

Complicated:

Have to decide number of periods, and weights for each Weights have to add up to 1.0 Most recent probably most relevant, gets most weight Carry around n periods of data to make new forecast


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Period Demand 3WMA

1 10

2 12

3 144 15 12.6

5 16 14.1

6 17 15.3

7 19 16.3

8 21 17.89 23 19.6

10 21.6

Wts = 0.5, 0.3, 0.2


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Exponential Smoothing

At-1 Actual demand in period t-1Ft-1 Forecast for period t-1E Smoothing constant >0,


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Exponential Smoothing Smoothing Constant between 0.1-0.3

Easier to compute than moving average

Most widely used forecasting method, because ofits easy use

F1 = 1,050, E = 0.05, A1 = 1,000

F2 = F1 + E(A1 - F1)

= 1,050 + 0.05(1,000 1,050) = 1,050 + 0.05(-50) = 1,047.5 units

BTW, we have to make a starting forecast to getstarted. Often, use actual A1


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Period Demand ES

1 10 10.0

2 12 10.0

3 14 10.64 15 11.6

5 16 12.6

6 17 13.6

7 19 14.7

8 21 16.09 23 17.5

10 19.1

Alpha = 0.3


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Period Demand ES

1 10 10.0

2 12 10.0

3 14 11.04 15 12.5

5 16 13.8

6 17 14.9

7 19 15.9

8 21 17.59 23 19.2

10 21.1

Alpha = 0.5


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Exponential Smoothing

11 1 ! ttt FAF EE

221 1 ! ttt FAF EE

We take:

And substitute in

to get:

and if we continue doing this, we get:

Older demands get exponentially less weight

22

21 11 ! tttt FAAF EEEE

...1111 34

3

3

3

2

21 ! tttttt AAAAAF EEEEEEEEE


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Choosing E LowE: if demand is stable, we dont want to get

thrown into a wild-goose chase, over-reacting to

trends that are really just short-term variation High E: If demand really is changing rapidly, wewant to react as quickly as possible


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Averaging Methods

Simple Average

Moving Average

Weighted Moving Average ExponentiallyWeighted Moving Average

(Exponential Smoothing)

They ALL take an average of the past

With a trend, all do badly Average must be in-between

302010


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Trend-Adjusted Ex. Smoothing

TrendIncludingForecastttt TFFIT !

EstimateTrendSmoothedExp.forforecastSmoothedExp.

!

!

t

t

T

tF

11

11

111

)1(

!

!

!

tttt

tt

tttt

FITFTT

AFIT

FITAFITF

H

EE

E

constantssmoothingareandwhere HE


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3.103.010)110111(*30.010

121112

!!!

!!

FITFTFITFTT ttt HH

F1 !100

T1 !10

E ! 0.20

H ! 0.30Forecast including trend for period 1 is

FIT1! F

1T

1!10010 !110

F2 ! FITt1 E At1 FITt1 ! FIT1 E A1 FIT1

!110 0.2*(115 110) !1101!111.0

Suppose actual demand is 115, A1=115

FIT2! F

2T

2!11110.3 !121.3


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22.10078.03.10)3.12104.121(*30.03.10

2323

!!!

! FITFTT H

0.1112 !F 3.102 !T

E ! 0.20

H ! 0.30Forecast including trend for period 1 is

3.1213.10111222!!!

TFFIT

04.1213.1*2.03.121)3.121120(*2.03.121

2223

!!!

! FITAFITF E

Suppose actual demand is 120, A2=120

26.13122.1004.121333

!!! TFFIT


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Selecting E andH

You could: Try an initial value for each parameter.

Try lots of combinations and see what looks best.

But how do we decide what looks best?

Lets measure the amount of forecast error.

Then, try lots of combinations of parameters in a

methodical way. Let E = 0 to 1, increasing by 0.1x For each Evalue, tryH = 0 to 1, increasing by 0.1


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Evaluating Forecasts

How far off is the forecast?

What do we do with this information?

Forecasts

Demands


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Evaluating Forecasts

Mean Absolute

Deviation

Mean SquaredError

Mean AbsolutePercent Error

MAD ! (1/n) At Fti!1

n

MSE! (1/n) At Ft 2

i!1

n

MAPE! (1/n)At FtDii!1

n

-

v100


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Tr

acking Signal To monitor, compute tracking signal

If >4 or


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Monitoring Fo

recast Accu

racy

Monitor forecast error each period, to see if itbecomes too great

0

-10

10

Fore

castError

Forecast PeriodLower Limit

Upper Limit


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Updating MAD

Simplified calculation avoids keepingrunning total of all errors and demands:

Standard Deviation can be estimatedfrom MAD:

MAD! 25.1W

11 ! tttt MADForecastActualMADMAD E


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Techniques for

Trend

Determine how demand increases as a functionof time

t = periods since beginning of data

b = Slope of the line

a = Value of yt at t = 0

btayt !


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Computing Values

2

)(1

2

22

!

!

!

!

!

n

YyS

xbyn

xbya

xnx

yxnxyb

n

i ii

yx


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Linea

rReg

ression

Three methods Type in formulas for trend, intercept Tools | Data Analysis | Regression

Graph, and R click on data, add a trendline, anddisplay the equation. Use intercept(Y,X) and slope(Y,X) commands

Fits a trend and intercept to the data. Gives all data equal weight.

Exp. smoothing with a trend gives more weightto recent, less to old.


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Causal Forecasting

Linear regression seeks a linear relationshipbetween the input variable and the outputquantity.

R2 measures the percentage of change in y thatcan be explained by changes in x.

bxayc

!


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Video sales of Shrek 2?

Box Office $ Millions

0

100

200

300

400

500

600700

800

900

1000

Shrek Shrek2

Shrek did $500m at the box office, and soldalmost 50 million DVDs & videos

Shrek2 did $920m at the box office


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Video sales of Shrek 2?

Assume 1-1 ratio: 920/500 = 1.84 1.84 * 50 million = 92 million videos?

F

ortunately, not that dumb. January 3, 2005: 37 million sold! March analyst call: 40m by end Q1 March SEC filing: 33.7 million sold. Oops. May 10 Announcement:

In 2nd public Q, missed earnings targets by 25%. May 9, word started leaking Stock dropped 16.7%


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Lessons

Lea

r

ned Flooded market with DVDs Guaranteed Sales

Promised the retailer they would sell them, or else the

retailer could return them Didnt know how many would come back

5 years ago Typical movie 30% of sales in first week

Animated movies even lower than that 2004/5 50-70% in first week

Shrek 2: 12.1m in first 3 days American Idol ending, had to vote in first week


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Washoe Gaming

Win, 1993-96

180

200

220

240

260

280

300

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

What did they

mean when they

said it was downthree quarters

in a row?

1993 1994 1995 1996


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Seasonality Seasonality is regular up or down

movements in the data

Can be hourly, daily, weekly, yearly Nave method

N1: Assume January sales will be same asDecember

N2: Assume this Fridays ticket sales will besame as last


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Seasonal Factor

s Seasonal factor for May is 1.20, means May sales

are typically 20% above the average

F

actor forJ

uly is 0.90, meaningJ

uly sales aretypically 10% below the average


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Seasonality & No Tr

endSales Factor

Spring 200 200/250 = 0.8

Summer 350 350/250 = 1.4Fall 300 300/250 = 1.2

Winter 150 150/250 = 0.6

Total 1,000Avg 1,000/4=250


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Seasonality & No Tr

endIf we expected total demand for the next year to be

1,100, the average per quarter would be1,100/4=275

ForecastSpring 275 * 0.8 = 220Summer 275 * 1.4 = 385Fall 275 * 1.2 = 330

Winter 275 * 0.6 = 165Total 1,100


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Tr

end & Seasonality Deseasonalize to find the trend

1. Calculate seasonal factors

2. Deseasonalize the demand

3. Find trend of deseasonalized line

Project trend into the future4. Project trend line into future

5. Multiply trend line by seasonal component.


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Washoe Gaming

Win, 1993-96

180

200

220

240

260

280

300

1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4

Looks like a

downhill slide

-SilverLegacyopened 95Q3

-Otherwise,

upward trend

1993 1994 1995 1996

Source: Comstock Bank, Survey of Nevada Business & Economics


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Washoe

Win 1989-1996

150000

170000

190000

210000

230000

250000

270000

290000

1989 1990 1991 1992 1993 1994 1995 1996

Definitely a general upward trend, slowed 93-94


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1989-2007


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1989-2007


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1998-2007

CacheCreek

ThunderValley

CC

Expands9/11


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2003Q3 - 2007Q3


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2003Q2 - 2007Q3


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2003-2007

Date Quarter Win

59 276,371

60 235,766

2004 61 240,22162 259,350

63 279,758

64 245,811

2005 65 231,608

66 259,687

67 297,414

68 260,149

2006 69 245,775

70 269,670

71 294,839

72 257,015

2007 73 244,643

74 273,116

75 284,734

Q Avg Index

1 240,562 0.9168

2 265,456 1.0117

3 289,187 1.1022

4 254,325 0.9693

Total Avg. 262,382

For each Q:

C

ompute Indexes

Deseasonalize: Divide Win by Index276,371 / 1.1022 = 250,755

Compute Avg Win for each Q

Divide Avg by Total Avg to get Index:240,562/262,382 = 0.9168


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2003-2007

period Win Deseasonalized

59 276,371 250,755

60 235,766 243,236

2004 61 240,221 262,010

62 259,350 256,347

63 279,758 253,828

64 245,811 253,598

2005 65 231,608 252,616

66 259,687 256,681

67 297,414 269,847

68 260,149 268,391

2006 69 245,775 268,069

70 269,670 266,548

71 294,839 267,511

72 257,015 265,157

2007 73 244,643 266,834

74 273,116 269,954

75 284,734 258,343

Do LR on deseasonalized dataintercept 185,538.00

slope 1,119.91

rsq 0.497

Create Linear ForecastsInt + slope * period

Linear

251,613

252,733

253,853

254,972

256,092

257,212

258,332

259,452

260,572

261,692

262,812

263,932

265,052

266,172

267,291

268,411

269,531

270,651

271,771

272,891

274,011


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Seasonal Forecast

58 257,062 Deseasonalized Linear Forecast

59 276,371 250,755 251,613 277,317

60 235,766 243,236 252,733 244,972

2004 61 240,221 262,010 253,853 232,741

62 259,350 256,347 254,972 257,959

63 279,758 253,828 256,092 282,254

64 245,811 253,598 257,212 249,314

2005 65 231,608 252,616 258,332 236,848

66 259,687 256,681 259,452 262,491

67 297,414 269,847 260,572 287,191

68 260,149 268,391 261,692 253,656

2006 69 245,775 268,069 262,812 240,956

70 269,670 266,548 263,932 267,023

71 294,839 267,511 265,052 292,129

72 257,015 265,157 266,172 257,998

2007 73 244,643 266,834 267,291 245,063

74 273,116 269,954 268,411 271,556

75 284,734 258,343 269,531 297,066

76 270,651 262,340

2008 77 271,771 263,425

78 272,891 264,511

79 274,011 265,596

Multiply Linearforecast by

indexes251,613 * 1.1022= 277,317

267,291 * 0.9168= 245,063

Q Index

1 0.9168

2 1.0117

3 1.1022

4 0.9693

10 forecasting

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