Forecasting

Chapter Objectives

Be able to: Discuss the importance of forecasting and

identify the most appropriate type of forecasting approach, given different forecasting situations.

Apply a variety of time series forecasting models, including moving average, exponential smoothing, and linear regression models.

Develop causal forecasting models using linear regression and multiple regression.

Calculate measures of forecasting accuracy and interpret the results.

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 (CPFR, discussed later)

Types of Forecasts

• Demand– Firm-level– Market-level

• Supply– Materials– Labor supply

• Price– Cost of supplies and services– Cost of money — interest rates, currency rates– Market price for firm’s product or service

Forecast Laws

Almost always wrong by some amount

More accurate for shorter time periods

More accurate for groups or families

No substitute for calculated values.

Qualitative Forecasting

• Executive opinions

• Sales force composite

• Consumer surveys

• Outside opinions

• Delphi method

• Life cycle analogy*

*See accompanying notes

Quantitative Methods • Used when situation is

‘stable’ and historical data exists– Existing products– Current technology

• Heavy use of mathematical techniques

*******************************• E.g., forecasting sales of

a mature product

Qualitative Methods• Used when situation is

vague and little data exists– New products– New technology

• Involves intuition, experience

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

to a new market

Forecasting Approaches

“Q2” Forecasting

Quantitative, then qualitative factors to “filter” the answer

Demand Forecasting

• Uses historical data

• Basic time series models

• Linear regression

– For time series or causal modeling

• Measuring forecast accuracy

Time Series Models

Period Demand1 122 153 114 95 106 87 148 12

What assumptionsmust we make touse this data toforecast?

Time Series Components of Demand . . .

Time

Demand

. . . randomness

Time Series with . . .

Time

Demand

. . . randomness and trend

Time series with . . .

Demand

. . . randomness, trend, and seasonality

May May May May

Idea Behind Time Series Models

Distinguish between random fluctuations and true changes in

underlying demand patterns.

Moving Average Models

Period Demand1 122 153 114 95 106 87 148 12

3-period moving averageforecast for Period 8:

= (14 + 8 + 10) / 3= 10.67

n

DF

n

iit

t

11

1

Weighted Moving Averages

Forecast for Period 8= [(0.5 14) + (0.3 8) + (0.2 10)] / (0.5 + 0.3 + 0.2)= 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

iit

n

iitit

tW

DWF

11

111

1

Table of Forecasts and Demand Values . . .

PeriodActual Demand

Two-Period Moving Average Forecast

Three-Period Weighted Moving Average

Forecast Weights = 0.5, 0.3, 0.2

1 12    

2 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

. . . and Resulting Graph

Note how the forecasts smooth out demand variations

0

5

10

15

20

1 2 3 4 5 6 7 8 9

Period

Volu

me Demand

2-Period Avg

3-Period Wt. Avg.

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

= Weight between 0 and 1

Exponential Smoothing II

Formula

Ft+1 = Ft + (Dt – Ft)

= ×Dt + (1 – × Ft

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

Exponential Smoothing Forecast with = 0.3

F2 = 0.3×12 + 0.7×11 = 3.6 + 7.7 = 11.3

F3 = 0.3×15 + 0.7×11.3 = 12.41

PeriodActual

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

Resulting Graph

0

2

4

6

8

10

12

14

16

1 2 3 4 5 6 7 8 9

Period

Dem

and

Demand

Forecast

Trends

What do you think will happen to a moving average or exponential smoothing model

when there is a trend in the data?

Same Exponential Smoothing Model as Before:

Since the modelis based onhistorical demand,it always lagsthe obviousupward trend

PeriodActual

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

Adjusting Exponential Smoothing for Trend

• Add trend factor and adjust using exponential smoothing

• 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

Simple Linear Regression

• Time series OR causal model

• Assumes a linear relationship: y = a + b(x)y

x

Definitions

Y = a + b(X)

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

X = predictor variable

“X” can be the time period or some other type of variable (examples?)

The Trick is Determining a and 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

)(

))((

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

1598

51520

98

515

55

5152015

5540

2

a

b

Column Sums

Resulting Regression Model:Forecast = 10 + 98×Period

0

100

200

300

400

500

600

1 2 3 4 5

X

Y

Demand

Regression

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

Example:Simplified Regression II

30450

985

1520

98

50

10

515200

980

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

Dealing with Seasonality

Quarter Period Demand

Winter 02 1 80Spring 2 240Summer 3 300Fall 4 440Winter 03 5 400Spring 6 720Summer 7 700Fall 8 880

What Do You Notice?

Forecasted Demand = –18.57 + 108.57 x Period

PeriodActual

DemandRegression

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

Regression picks up trend, butnot seasonality effect

0

200

400

600

800

1000

1 2 3 4 5 6 7 8

Demand

Forecast

Calculating Seasonal Index: Winter Quarter

(Actual / Forecast) for Winter Quarters:

Winter ‘02: (80 / 90) = 0.89Winter ‘03: (400 / 524.3) = 0.76

Average of these two = 0.83

Interpret!

Seasonally adjusted forecast model

For Winter Quarter

[ –18.57 + 108.57×Period ] × 0.83

Or more generally:

[ –18.57 + 108.57 × Period ] × Seasonal Index

Seasonally adjusted forecasts

Forecasted Demand = –18.57 + 108.57 x Period

PeriodActual

DemandRegression

ForecastDemand/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

Would You Expect the Forecast Model to Perform This Well With Future Data?

0

200

400

600

800

1000

1 2 3 4 5 6 7 8

Demand

forecast

More Regression Models I

Non-linear models

– Example: y = a + b × ln(x)

More Regression Models II

Multiple regression– More than one independent variable

y

x

z

y = a + b1 × x + b2 × z

Causal Models

Time series models 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.

Measuring Forecast Accuracy

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

Measures of Forecast Accuracy

Error = Actual demand – Forecast

or

Et = Dt – Ft

Mean Forecast Error (MFE)

For n time periods where we have actual demand and forecast values:

n

En

ii

MFE 1

Mean Absolute Deviation (MAD)

For n time periods where we have actual demand and forecast values:

What does this tell us that MFE doesn’t?

n

En

ii

MAD 1

Example

Period Demand Forecast Error AbsoluteError

3 11 13.5 -2.5 2.54 9 13 -4.0 4.05 10 10 0 0.06 8 9.5 -1.5 1.57 14 9 5.0 5.08 12 11 1.0 1.0

What is the MFE? The MAD? Interpret!

MFE and MAD:A Dartboard Analogy

Low MFE and MAD:

The forecast errorsare small and unbiased

An Analogy (continued)

Low MFE, but highMAD:

On average, thedarts hit thebulls eye (so muchfor averages!)

An Analogy (concluded)

High MFE and MAD:

The forecastsare inaccurate andbiased

Collaborative Planning, Forecasting, and Replenishment

(CPFR)

Supply chain partners, supported by information technology,

working together

CPFR Elements

• Mutual business objectives & measures

• Joint sales and operations plans

• Collaboration on sales forecasts & replenishment plans

• Electronic interchange of information

Case Study in Forecasting

Top-Slice Drivers