Forecasting

Anticipating service requirements over the short term

Operational purposesPlanning and scheduling resourcesExamples:

Manufacturing and distributing printers at HP Staffing levels (NS) etc.

Objectives

What is forecastingWhat are the issuesWhat are the tools

Forecasting

Developing predictions or estimates of future values Demand volume Price levels Lead times Resource availability ...

Taco Bell

Labor is 30% of revenueMake to order environmentSignificant “seasonality”

52% of days sales during lunch 25% of days sales during busiest hour

Balance staff with demand

Feed the dog

Value Meals

Drove demand Forecasting system in each store

forecasts arrivals within 15 minute intervals Simulation system

“predicts” congestion and lost salesOptimization system

Finds the minimum cost allocation of workers

Forecasting System

Customer arrivals by 15-minute interval of day (e.g., 11:15-11:30 am Friday)

Fed by in-store computer system6-week moving averageEstimated savings: Over $40 Million

in 3 years.

Independent vs Dependent

Independent Exogenously controlled Subject to random or unpredictable changes What we forecast

Dependent or Derived Calculated or derived from other sources Bill of Materials Related activity like packaging

Phenomena To Capture

RandomnessTrend

Linear Exponential

Seasonality

RandomnessMonthly Returns from The Dow

-15%

-10%

-5%

0%

5%

10%

15%

Feb

-47

Feb

-49

Feb

-51

Feb

-53

Feb

-55

Feb

-57

Feb

-59

Feb

-61

Feb

-63

Feb

-65

Feb

-67

Feb

-69

Feb

-71

Feb

-73

Feb

-75

Feb

-77

Feb

-79

Feb

-81

Feb

-83

Feb

-85

Feb

-87

Feb

-89

Feb

-91

Linear TrendDow Jones Monthly Average

1500

1700

1900

2100

2300

2500

2700

2900

3100

3300

3500

Jan-88 Jul-88 Feb-89 Aug-89 Mar-90 Oct-90 Apr-91 Nov-91

Exponential TrendIntel Quarterly Sales in Millions of Dollars

$0

$500

$1,000

$1,500

$2,000

$2,500

$3,000

$3,500

$4,000

$4,500

$5,000

12/19/85 5/3/87 9/14/88 1/27/90 6/11/91 10/23/92 3/7/94 7/20/95

SeasonalityCoca Cola Quarterly Sales in Millions of Dollars

$1,000

$1,500

$2,000

$2,500

$3,000

$3,500

$4,000

$4,500

$5,000

$5,500

Q1-

86

Q3-

86

Q1-

87

Q3-

87

Q1-

88

Q3-

88

Q1-

89

Q3-

89

Q1-

90

Q3-

90

Q1-

91

Q3-

91

Q1-

92

Q3-

92

Q1-

93

Q3-

93

Q1-

94

Q3-

94

Q1-

95

Q3-

95

Q1-

96

SeasonalityToys "R" Us Quarterly Revenues in Millions of Dollars

$500

$1,000

$1,500

$2,000

$2,500

$3,000

$3,500

$4,000

$4,500

Q1-92 Q2-92 Q3-92 Q4-92 Q1-93 Q2-93 Q3-93 Q4-93 Q1-94 Q2-94 Q3-94 Q4-94 Q1-95 Q2-95 Q3-95 Q4-95

Forecasting MethodsQualitative or Judgemental

Ask people who ought to knowHistorical Projection or Extrapolation

Moving Averages Exponential Smoothing Regression based methods Neural Networks

Econometric or Causal Regression Simulation

Moving Averages

Simple, ubiquitousReduce random noiseOne Extreme

Predict next period = This periodAnother Extreme

Predict next period = Long run averageIntermediate View: K period moving avg.

Predict next period = Average of last K periods

The Dow

1500

1700

1900

2100

2300

2500

2700

2900

3100

3300

3500

Jan-

88

Mar

-88

May

-88

Jul-8

8

Sep-8

8

Nov-8

8

Jan-

89

Mar

-89

May

-89

Jul-8

9

Sep-8

9

Nov-8

9

Jan-

90

Mar

-90

May

-90

Jul-9

0

Sep-9

0

Nov-9

0

Jan-

91

Mar

-91

May

-91

Jul-9

1

Sep-9

1

Nov-9

1

Jan-

92

Mar

-92

Questions

1500

1700

1900

2100

2300

2500

2700

2900

3100

3300

3500

Jan-

88

Mar

-88

May

-88

Jul-8

8

Sep-8

8

Nov-8

8

Jan-

89

Mar

-89

May

-89

Jul-8

9

Sep-8

9

Nov-8

9

Jan-

90

Mar

-90

May

-90

Jul-9

0

Sep-9

0

Nov-9

0

Jan-

91

Mar

-91

May

-91

Jul-9

1

Sep-9

1

Nov-9

1

Jan-

92

Mar

-92

What’s the forecast for 6 months out?

Will a shorter span always be better?

Is moving average a good method here? Which will handle this

better?

Which is better?Monthly Dow Returns

-8%

-6%

-4%

-2%

0%

2%

4%

6%

8%

May-50 Jun-50 Jul-50 Aug-50 Sep-50 Oct-50 Nov-50 Dec-50 Jan-51 Feb-51 Mar-51 Apr-51 May-51

Average Error 3-month 1490% 6-month 619%

Exponential Smoothing

Moving Averages Equal weight to older observations

Exponential Smoothing More weight to more recent observations

Forecast for next period is a weighted average of Observation for this period Forecast for this period

Alpha*Observation + (1-Alpha)*Past Forecast

Initial Values

First ObservationAverage of previous observationsetc.

Which is which?Monthly Dow Returns

-10%

-8%

-6%

-4%

-2%

0%

2%

4%

6%

Sep-89 Oct-89 Nov-89 Dec-89 Jan-90 Feb-90 Mar-90 Apr-90 May-90 Jun-90 Jul-90 Aug-90 Sep-90

Alpha = .01 or Alpha = .2

Modeling Trend

Holt’s Method Forecast is weighted combination of

Current ObservationCurrent Forecast for Next Period

Forecast Trend as weighted combination of Current Trend in Forecasts

• (our estimate of trend)

Current Forecast for Trend • (differences in successive forecasts)

Why this way?

With and Without TrendDow Monthly Averages

1500

1700

1900

2100

2300

2500

2700

2900

3100

3300

3500

Jan-

88

Mar

-88

May

-88

Jul-8

8

Sep-8

8

Nov-8

8

Jan-

89

Mar

-89

May

-89

Jul-8

9

Sep-8

9

Nov-8

9

Jan-

90

Mar

-90

May

-90

Jul-9

0

Sep-9

0

Nov-9

0

Jan-

91

Mar

-91

May

-91

Jul-9

1

Sep-9

1

Nov-9

1

Jan-

92

Mar

-92

Intel’s TrendIntel Quarterly Sales in Millions of Dollars

$0

$500

$1,000

$1,500

$2,000

$2,500

$3,000

$3,500

$4,000

$4,500

$5,000

12/19/85 5/3/87 9/14/88 1/27/90 6/11/91 10/23/92 3/7/94 7/20/95

Exponential Growth

Forecasted Sales = et

Natural Log of Forecasted Sales Ln + t That’s linear growth

Take Natural Log of observationsForecast Natural Log of Sales Convert back to Forecast of Sales

Seasonality

Deseasonalize the dataForecastSeasonalize the forecastSeasonal Factors

Ratio of Actual to “Average” Updated with Exp. Smooth. Weighted combination of

Actual/Deseasonalized ForecastCurrent Forecast of seasonal factor

Seasonality

Deseasonalized Forecast Alpha*(Actual/Seasonal Factor)+ (1-Alpha)*(Past Deseasonalized Forecast)

Seasonalized Forecast Deseasonalized Forecast * Seasonal Factor

Updating the seasonal factors Gamma * (Actual/Deseasonalized Forecast) + (1- Gamma) * Previous estimate of seasonal

factor

Initialization and Factors

LevelTrendSeasonality

Coca Cola Quarterly Sales in Millions of Dollars

$0

$1,000

$2,000

$3,000

$4,000

$5,000

$6,000

Q3-87

Q4-87

Q1-88

Q2-88

Q3-88

Q4-88

Q1-89

Q2-89

Q3-89

Q4-89

Q1-90

Q2-90

Q3-90

Q4-90

Q1-91

Q2-91

Q3-91

Q4-91

Q1-92

Q2-92

Q3-92

Q4-92

Q1-93

Q2-93

Q3-93

Q4-93

Q1-94

Q2-94

Q3-94

Q4-94

Q1-95

Q2-95

Q3-95

Q4-95

Q1-96

Q2-96

Trend in Model of Coca Cola Quarterly Sales

-$600

-$500

-$400

-$300

-$200

-$100

$0

$100

$200

$300

$400

Q3-877

Q1-889

Q3-8811

Q1-8913

Q3-8915

Q1-9017

Q3-9019

Q1-9121

Q3-9123

Q1-9225

Q3-9227

Q1-9329

Q3-9331

Q1-9433

Q3-9435

Q1-9537

Q3-9539

Q1-9641

Seasonal Factors in Model of Coca Cola Quarterly Sales

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Q3-877

Q1-889

Q3-8811

Q1-8913

Q3-8915

Q1-9017

Q3-9019

Q1-9121

Q3-9123

Q1-9225

Q3-9227

Q1-9329

Q3-9331

Q1-9433

Q3-9435

Q1-9537

Q3-9539

Q1-9641

Seasonalized and Deseasonalized Forecasts of Coca Cola Quarterly Sales in Millions of Dollars

0.00

1,000.00

2,000.00

3,000.00

4,000.00

5,000.00

6,000.00

Q3-877

Q1-889

Q3-8811

Q1-8913

Q3-8915

Q1-9017

Q3-9019

Q1-9121

Q3-9123

Q1-9225

Q3-9227

Q1-9329

Q3-9331

Q1-9433

Q3-9435

Q1-9537

Q3-9539

Q1-9641

Regression-Based Models

Time Series Find best fit of proposed model to past data Project that fit forward

Econometric Find exogenous factors driving value

WeatherEconomic factorsRainfall

Develop formula for (future) values based on these factors

Example

Locating a new retail storeBuild a model of sales volume (profitability)

based on existing stores Population Wealth Competitors Access …

Predict sales for new store with this model

Forecast Error

Building a Forecast Fit to historical data Project future data

Forecast Error How well does model fit historical data Do we need to tune or refine the model Can we offer confidence intervals about

our predictions

Measuring Forecast Error

MAD or MAE average of the absolute errors

RMSE (root mean square error) Square root of average squared error

Sample std deviation Differs by 1 degree of freedom (N-1)

MAPE (mean absolute percentage error) Average absolute ratio of error to actual

Forecasting is a necessary evil, try to reduce the need for it.

Complexity costs money, does it provide better forecasts?

Aggregation provides accuracy, but precludes local information

Forecast the right thing

Issues

What about HP?

Why are forecasts bad in Europe?