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Forecasting


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2006 Pearson Prentice Hall

Introduction to Operations and Supply ChainManagement Bozarth & Handfield Chapter 9, Slide 2

Why Forecast?

Assess long-term capacity needs

Develop budgets, hiring plans, etc.

Plan production or order materials

Get agreement within firm and

across supply chain partners


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Forecast Characteristics

Almost always wrong by some amount

More accurate for groups or families

More accurate for shorter time periods

No substitute for calculated demand.


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Quantitative Methods Used when situation is

stable and historicaldata exists Existing products Current technology

Heavy use ofmathematicaltechniques

******************************* E.g., forecasting sales

of a mature product

Qualitative Methods Used when situation

is vague and littledata exists New products New technology

Involves intuition,experience

***************************** E.g., forecasting sales

to a new market

Forecasting Approaches


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Q2 Forecasting

Quantitative, then qualitative factors

to filter the answer


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Qualitative Forecasting

Executive opinions

Sales force composite

Consumer surveys

Outside opinions

Delphi method


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Demand Forecasting

Basic time series models

Linear regression

For time series or causalmodeling

Measuring forecast accuracy

Mini-case: Northcutt Bikes (A)


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Time Series Models

Period Demand

1 12

2 153 11

4 9

5 10

6 8

7 14

8 12

What assumptionsmust we make touse this data to

forecast?


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Time Series Components ofDemand . . .

Time

Demand

.. . randomness


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Time Series with . . .

Time

Demand

. . . randomness and trend


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Time series with . . .

Demand

. . . randomness, trend and seasonality

May May May May


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Idea Behind Time SeriesModels

Distinguish between random

fluctuations and true changesin underlying demand patterns.


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Moving Average Models

Period Demand

1 12

2 153 11

4 9

5 10

6 8

7 14

8 12

3-period moving average

forecast for Period 8:

= (14 + 8 + 10) / 3

= 10.67

n

D

F

n

iit

t

1

1

1


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Weighted MovingAverages

Forecast for Period 8

= [(0.5 14) + (0.3 8) + (0.2 10)] / (0.5 + 0.3 + 0.1)= 11.4

What are the advantages?What do the weights add up to?

Could we use different weights?

Compare with a simple 3-period moving average.

n

i it

n

iitit

t

W

DW

F

1 1

111

1


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Table of Forecasts andDemand Values . . .

Period

Actual

Demand

Two-Period

Moving

Average

Forecast

Three-Period Weighted Moving

Average Forecast Weights =

0.5, 0.3, 0.2

1 122 15

3 11 13.5

4 9 13 12.4

5 10 10 10.8

6 8 9.5 9.9

7 14 9 8.8

8 12 11 11.4

9 13 11.8


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. . . and Resulting Graph

Note how the forecasts smooth out variations

0

5

10

15

20

1 2 3 4 5 6 7 8 9

Period

Volume Demand

2-Period Avg

3-Period Wt. Avg.


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Exponential Smoothing I

Sophisticated weight averaging model

Needs only three numbers:

Ft = Forecast for the current period t

Dt = Actual demand for the current period t

a = Weight between 0 and 1


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Exponential Smoothing II

Formula

Ft+1 = Ft + a(DtFt)=a Dt + (1a) Ft

Where did the current forecast come from?

What happens as a gets closer to 0 or 1? Where does the very first forecast come from?


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Exponential SmoothingForecast with a = 0.3

F2 = 0.312 + 0.711

= 3.6 + 7.7= 11.3

F3 = 0.315 + 0.711.3= 12.41

Period

Actual

Demand

Exponential

Smoothing

Forecast

1 12 11.00

2 15 11.30

3 11 12.41

4 9 11.99

5 10 11.09

6 8 10.76

7 14 9.93

8 12 11.15

9 11.41


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Resulting Graph

0

2

4

6

8

10

12

14

16

1 2 3 4 5 6 7 8 9

Period

Demand

Demand

Forecast


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Trends

What do you think will happen to a

moving average or exponential

smoothing model when there is a trendin the data?


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Same ExponentialSmoothing Model as Before:

Since the modelis based on

historical demand,

it always lags

the obviousupward trend

Period

Actual

Demand

Exponential

Smoothing

Forecast

1 11 11.00

2 12 11.00

3 13 11.30

4 14 11.81

5 15 12.47

6 16 13.23

7 17 14.06

8 18 14.94

9 15.86


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Adjusting ExponentialSmoothing for Trend

Add trend factor and adjust using exponentialsmoothing

Needs only two more numbers:

Tt = Trend factor for the current period t = Weight between 0 and 1 Then: Tt+1 = (Ft+1 Ft) + (1) Tt And the Ft+1 adjusted for trend is = Ft+1 + Tt+1


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SimpleLinear Regression

Time series OR causal model

Assumes a linear relationship:

y = a + b(x)

y

x


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Definitions

Y = a + b(X)

Y = predicted variable (i.e., demand)

X = predictor variable

X can be the time period or some other typeof variable (examples?)


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The Trick is Determining aand b:

xbya

n

xx

n

yxyx

bn

i

n

ii

i

n

i

n

i

n

iii

ii

1

1

2

2

1

1 1

)(

)((


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2006 Pearson Prentice Hall Introduction to Operations and Supply Chain

Management Bozarth & Handfield Chapter 9, Slide 27

Example:Regression Used for Time Series

Period (X) Demand (Y) X2 XY

1 110 1 110

2 190 4 380

3 320 9 960

4 410 16 1640

5 490 25 2450

15 1520 55 5540

105

15

985

1520

98

5

1555

5

1520155540

2

a

b

Column Sums


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Resulting Regression Model:Forecast = 10 + 98Period

0

100

200

300

400

500

600

1 2 3 4 5

X

YDemand

Regression


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Example:Simplified Regression I

If we redefine the X values so that their

sum adds up to zero, regression

becomes much simpler

a now equals the average of the y values

b simplifies to the sum of the xy products

divided by the sum of the x2 values


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Example:Simplified Regression II

3045

0

985

1520

98

5

010

5

15200980

2

a

b

Period

(X)

Period

(X)'

Demand

(Y) X2 XY

1 -2 110 4 -220

2 -1 190 1 -190

3 0 320 0 0

4 1 410 1 410

5 2 490 4 980

0 1520 10 980


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Dealing with Seasonality

Quarter Period Demand

Winter 02 1 80

Spring 2 240Summer 3 300

Fall 4 440

Winter 03 5 400

Spring 6 720Summer 7 700

Fall 8 880


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What Do You Notice?

Forecasted Demand =18.57 + 108.57 x Period

Period

Actual

Demand

Regression

Forecast

Forecast

Error

Winter 02 1 80 90 -10

Spring 2 240 198.6 41.4

Summer 3 300 307.1 -7.1

Fall 4 440 415.7 24.3

Winter 03 5 400 524.3 -124.3

Spring 6 720 632.9 87.2

Summer 7 700 741.4 -41.4

Fall 8 880 850 30


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Regression picks up trend, butnot seasonality effect

0

200

400

600

800

1000

1 2 3 4 5 6 7 8

Demand

Forecast


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Calculating SeasonalIndex: Winter Quarter

(Actual / Forecast) for Winter Quarters:

Winter 02: (80 / 90) = 0.89

Winter 03: (400 / 524.3) = 0.76

Average of these two = 0.83

Interpret!


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Seasonally adjusted forecastmodel

For Winter Quarter

[18.57 + 108.57Period ] 0.83

Or more generally:

[18.57 + 108.57 Period ] Seasonal Index


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Seasonally adjustedforecasts

Forecasted Demand =18.57 + 108.57 x Period

Period

Actual

Demand

Regression

Forecast

Demand/

Forecast

Seasonal

Index

Seasonally

Adjusted

Forecast

Forecast

Error

Winter 02 1 80 90 0.89 0.83 74.33 5.67

Spring 2 240 198.6 1.21 1.17 232.97 7.03

Summer 3 300 307.1 0.98 0.96 294.98 5.02

Fall 4 440 415.7 1.06 1.05 435.19 4.81

Winter 03 5 400 524.3 0.76 0.83 433.02 -33.02

Spring 6 720 632.9 1.14 1.17 742.42 -22.42

Summer 7 700 741.4 0.94 0.96 712.13 -12.13

Fall 8 880 850 1.04 1.05 889.84 -9.84

W ld Y E t th F t


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Would You Expect the ForecastModel to Perform This Well With

Future Data?

0

200

400

600

800

1000

1 2 3 4 5 6 7 8

Demand

forecast


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More Regression Models I

Non-linear models

Example: y = a + b ln(x)


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More Regression Models II

Multiple regression

More than one independent variable

y

x

z

y = a + b1 x + b2 z


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Causal Models

Time series assume that demand is a

function of time. This is not always true.

1. Pounds of BBQ eaten at party.

2. Dollars spent on drought relief.

3. Lumber sales.

Linear regression can be used in these

situations as well.

M i F t


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Measuring ForecastAccuracy

How do we know:

If a forecast model is best?

If a forecast model is still working?

What types of errors a particular

forecasting model is prone to make?

Need measures of forecast accuracy

M f F t


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Management Bozarth & HandfieldChapter 9, Slide 42

Measures of ForecastAccuracy

Error = Actual demand Forecast

orEt = DtFt


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Mean Forecast Error (MFE)

For n time periods where we have actual

demand and forecast values:

)

n

En

ii

MFE 1

M Ab l t D i ti


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Mean Absolute Deviation(MAD)

For n time periods where we have actual

demand and forecast values:

What does this tell us that MFE doesnt?

n

En

ii

MAD 1


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Example

Period Demand Forecast Error Absolute

Error

3 11 13.5 -2.5 2.5

4 9 13 -4.0 4.05 10 10 0 0.0

6 8 9.5 -1.5 1.5

7 14 9 5.0 5.0

8 12 11 1.0 1.0

What is the MFE? The MAD? Interpret!

MFE d MAD


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MFE and MAD:A Dartboard Analogy

Low MFE and MAD:

The forecast errors

are small and unbiased


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An Analogy (continued)

Low MFE, but high

MAD:

On average, the

arrows hit the

bulls eye (so much

for averages!)


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2006 Pearson Prentice Hall Introduction to Operations and Supply Chain Chapter 9, Slide 48

An Analogy (concluded)

High MFE and MAD:

The forecasts

are inaccurate and

biased

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