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The Art of Forecasting

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Costs of ForecastingIBM continues to struggle with shortages in the Think Pad line. WSJ 5/2/94IBM sells out new Aptiva PC. Shortage may cost millions… WSJ 10/7/94Dell … stock plunges. Dell…was sharply off in its forecast of demand… WSJ 8/93Liz Claiborne said … earnings decline is consequence of [unanticipated] excess inventories. WSJ 7/15/93Toyota believes it can save $100M/3a … [with] accurate ordering and inventory management. “It’s unbelievable the number of (after market) parts that are thrown away each year.” Automotive News 2/26/01

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Store Mark-Downs

6%

10%

14%

18%

22%

26%

1970 1975 1980 1985 1990

% o

f Dol

lar

Sale

s

Source: Fisher, Marshall L. et al. “Making Supply Meet Demand in an Uncertain World.” Boston, MA: Harvard Business Review, 1994. Reprint No. 94302. and National Retail Federation

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Forecasting Basics…

Forecasts are usually wrongForecasts should contain error measure.

Aggregate Forecasts are more accurateThe longer the horizon, the lower the accuracyCommon Sense Compatibility

Include other known Information

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Basic TaxonomyQualitative(subjective)

Expertise BasedDelphi MethodThe “Sage”Sales ForceCustomer SurveysLong TermComplex Scenarios

Quantitative(objective)

Causal ModelsY=f(X1, X2, …, Xn)

Time Series ModelsYt =f(Yt-1, Yt-2,…, Yt-n)

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Causal Models

Use Data other than the Series predictedPrincipal Tool: Regression Analysis

Y = a0 + a1X1 + a2X2+ … anXn

Estimates ai to minimize “Sum of Least Squares”

Y

X

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Time Series Models

Prediction based exclusively on previously observed ValuesGeneral Idea: Detect Patterns!Short Term Demand PredictionPrevalent Tool In Operations

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Time Series PatternsRandom

No PatternTrend

Linear (default) or Nonlinear Seasonality

Repetition at Fixed IntervalsCyclic

Long Term Economy

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The Basic Concept

Question: How to assign Weights?

iatiD

t-tF

DaF

i

i

t

nntnt

Period with associated Weights: Periodin Demand Observed :

Periodin made , Periodfor Forecast :<

=∑∞

=−

11

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Stationary Series

Moving Averages &

Exponential Smoothing

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Moving Averages

Simple Average of Last N PeriodsNo PatternLarge N ⇒ Stability upSmall N ⇒ Responsiveness up

elsewhere 0 ,for

...

=<=

+++== −−−

=−∑

iNi

NtttN

nntt

a NiaN

DDDDN

F

1

11

1

1

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Exponential Smoothing

New Forecast = Weighted Average of Last Demand and Last Forecast

( )111 −−− −⋅−= ttt DFaF

Errorlast The 111 ≅⋅−= −−− ttt eeaF

Small a ⇒ Stability upLarge a ⇒ Responsiveness up

( ) 11 1 −− ⋅−+⋅= ttt FaDaF

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Moving Average vs. Exponential Smoothing

CommonalitiesStationary Process1 Parameter (a or N)Lag behind Trend

DifferencesES: All past dataMA: Last N periods

Outliers washed out

ES: Less dataLast Forecast * Demand

MA: Last N data

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Trends

Exponential Smoothing with Linear Trend

Regression Analysis

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tF=

Exponential Smoothing with Linear Trend

St ≅ The “Intercept” or “Status Quo”Gt ≅ The “Trend”

( ) [ ]( ) ( ) 11

11

11

−−

−−

⋅−+−⋅=+⋅−+⋅=

tttt

tttt

GbSSbGGSaDaS

ttt GSF +=+1

ttt GSF ⋅+=+ ττ

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Regression Analysis

Min Sum of 2

Y = a0 + a1*XY

X

a0

Sum of Least Squares

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Regression in Excel

“Formal Regression Analysis”1. Tools, Data Analysis, Regression2. Input Y Range: Dependent Variable3. Input X Range: Independent Variable4. Specify where you want Output5. Output is Table with Regression Statistics

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Trend Tool

=Trend(y-range,x-range,x-value) Output: Trend Estimate for “x-value”Y-range: Observed Data (Demand)X-range: Independent Variable (Time)X-value: Value (Date) for which to estimate Y (Demand)

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Non Linear Trend

RegressionSame Procedure as Linear RegressionDifference:Change Time to Time2 ln(Time) etc..

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Seasonal PatternsBasic Idea:

Assign Weights cn to the N PeriodsΣcn = NAdjust Forecast by Weights

Caution:A Season is the time until a Pattern repeats

I.e. a week is a Season with 7 PeriodsA year is a Season with 4 Periods…

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Error Measures

∑=

−=n

ittn DF

1

21MSD

Mean Square Deviation MSD

( )∑=

−=n

ittn DF

1

1Bias

∑=

−=n

ittn DF

1

1MAD

Mean Absolute Deviation MAD

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How to choose the right forecasting technique?

Chambers, Mullick & Smith

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Demand and Product Life Cycles

Demand Predictions are dependent on Life Cycle

Time

Dem

and

DeclineSteadyStateIntroduction

Growth

Product Develop-ment

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Decisions Made During PLC

Product Development AnalysisDevelopment Effort delphi / expertMarket Entry ComparisonsProduct Specs QFD

Product Introduction Analysisfacility size market testssupply chain design consumer survey

life cycle analysis

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Decision Made During PLC

Growth Analysiscapacity expansion Causal Modelsstatistical tech

production planning Simulationpromotions

Steady State Analysisproduction planning time seriesinventory models causal models

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Next Week

MondayVoluntary Lead-OffsDownload Inventory Problems from SloanSpace in Handouts folder

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Sale of SKU 367890,a seasonal product

PREDICTED

ACTUAL

Sale

s

OBSERVED

Feb Apr Jun Aug Oct Dec

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Random PatternsD

eman

d

Time

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Increasing Linear TrendD

eman

d

Time

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Curve Linear TrendD

eman

d

Time

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Seasonal & Linear TrendD

eman

d

Time