Vish A Viswanathan Director, Revenue Management April 27, 1999 Demand Forecasting.

Vish A Viswanathan

Director, Revenue Management

April 27, 1999

Demand Forecasting

2 Copyright © 1999 The SABRE GroupSABRE / AGIFORS 1999

Forecasting is fundamental for Airline & Transportation SolutionsForecasting is fundamental for Airline & Transportation Solutions

Forecasts of …

• Passengers bookings, by O&D, fare class, and # of days before departure

• Shipment weights

• Capacity

• Traffic

• Transaction volume

• Engine removals

Optimization and Analysis

Modules …

• Math programming

• Simulation

• Tabu Search

• Heuristics

• Constraint Logic Programming

• Network Algorithms

Recommendations

• YM availability

• Prices

• Routing plans

• Marketing

decisions

• Markets to serve

• Hardware

upgrades

• Manpower plans

areinput

to

to create


Yield Management Systems Are Driven by Forecasting and Optimization ModulesYield Management Systems Are Driven by Forecasting and Optimization Modules

Inventory ControlsInventory Controls

Optimization ModuleForecasting Module

DataData

DemandDemand

No-showNo-show

CancellationCancellation

OverbookingOverbooking

DiscountDiscountAllocationsAllocations

GroupGroupEvaluationEvaluation

Yield Management System


Forecasting Models operateby the GIGO rule (Garbage In/Garbage Out)

Time and resources should be allocatedfor data review and improvement

Screening methods should be used to eliminate bad information

Timely and Accurate Information Is Essential


What Are We Trying to Do WhenWe Forecast Demand?What Are We Trying to Do WhenWe Forecast Demand?

Evaluate the overall Evaluate the overall worth of an worth of an

“early, low-price” “early, low-price” booking in the booking in the

context of context of total demandtotal demand

Influence theInfluence the

kind ofkind of

passengerspassengers

acceptedaccepted


Forecasting Models Use Historical Behavior to Predict in a 2-Step ProcessForecasting Models Use Historical Behavior to Predict in a 2-Step Process

Step 1 Given Create

HistoricalHistoricalpassengerpassengerbehaviorbehavior

Assumptions aboutAssumptions aboutpassenger behaviorpassenger behavior

under different under different conditionsconditions

Step 2 Given

Assumptions aboutAssumptions aboutpassenger behaviorpassenger behavior

under different under different conditionsconditions

CurrentCurrentconditions forconditions forfuture flightsfuture flights

Create

Predictions ofPredictions ofpassenger behaviorpassenger behavior

for future flightsfor future flights+


DemandDemandForecastingForecasting

RevenueRevenueOpportunityOpportunity

Model Model

Historical BookingsHistorical BookingsCurrent BookingsCurrent BookingsBooking ProfilesBooking Profiles

Demand UntruncationDemand Untruncationbased on inventorybased on inventory

open/close dataopen/close data

Demand Forecasting Typical Methodology Demand Forecasting Typical Methodology


What Makes a Good Forecast Accuracy, Simplicity and Robustness

What Makes a Good Forecast Accuracy, Simplicity and Robustness

Accuracy Low mean absolute error (MAE) Low Mean Squared Error (MSE) Low Mean Error (bias)

Simplicity Explain the underlying forecast, easy of adjustment Ease of maintenance

Robustness Performs well under varying conditions Limited intervention and calibration


Demand Forecast AccuracyForecast Accuracy Impacts the Bottom LineDemand Forecast AccuracyForecast Accuracy Impacts the Bottom Line

Demand forecast accuracy results in aggressive inventory controls and minimizes revenue dilution A 10% improvement in forecast accuracy results in

1/2 % in incremental revenues

Forecast Accuracy Measurement can be based onthe following statistics

Mean Absolute Deviation (MAD) Mean Squared Error (MSE) Mean Absolute Percent Error (MAPE) Relative Deviation (RD) Bias (+/-)


Forecasts May Be Made UsingDifferent Types of ModelsForecasts May Be Made UsingDifferent Types of Models

Time Series Models

Regression Models

Neural Networks

Passenger Choice Models

Multivariate Models

Adaptive Models

Adaptive Transfer Function

Combinations

Each Technique May Be UsedTo Forecast a Variety of Behaviors


Demand Forecasting TechniquesDemand Forecasting Techniques



Time Series Models (TSM) Calibration based on historical data Exponential smoothing models

– Simple exponential, double exponential, additiveand multiplicative Holt Winters

Forecast parameters can be made adaptive basedon the magnitude of forecast errors


Time Series Models to Forecast Future Behavior Based on Time RelationshipsTime Series Models to Forecast Future Behavior Based on Time Relationships

Behavior of future flights is based upon historical information of flights, related by:

Day of week Time of day Time of year

New information is added via: Moving averages Exponential smoothing Other models



Regressions Models (REG) Causal model with one or more independent variables Calibration based on historical data with the method of

least squares Non-linearity can be introduced with a transformation of

variables to a linear model Requires sufficient data for calibration and requires

frequent calibration to sustain forecast accuracy


ForecastForecast

Other CausalOther CausalFactorsFactors

Regression Models Can IncorporateCausal FactorsRegression Models Can IncorporateCausal Factors

HistoricalHistoricalDataData

Current StatisticsRelating to Flight

Time toTime toDepartureDeparture

OA PricesOA Prices

GNPGNP

CausalFactors

FactorFactor

FactorFactor

FactorFactor

FactorFactor

+

+

+

+


DemandDemandForecastForecast

CapacityCapacity

Discount SalesDiscount Sales

Full Fare SalesFull Fare Sales

Days to DepartureDays to Departure


Neural Networks or Adaptive Networks (NN) Analogous to an electrical switching network which

responds to a set of inputs Neural networks learn through repeated trials “Degrades gracefully” when faced with insufficient data


Demand Forecasting TechniquesPassenger Choice Model (PCM)

Demand Forecasting TechniquesPassenger Choice Model (PCM)

Demand forecast model based on customer utilitycan be used to estimate

Demand for new markets Impact of schedule changes Recapture rates

Customer utility is a function of Market share, market size Departure time Service type (non-stop, through, connection) Fare Restrictions Carrier, turbo vs. jet Elapsed time Displacement time


Demand Forecasting TechniquesMultivariate Models


Principal Component Analysis (PCA) Uses reservations holding for all reading days and

fare classes for a segment. Computes the top 4-6 principal components that typically

accounts for 90% of the variation, which are uncorrelated linear combinations of the reservations holding values with maximal variance

To forecast, fit a regression on the componentsagainst reservations holding at departure




Canonical Variate Analysis (CVA) Uses reservations holding information for all reading days

and fare classes to create canonical variates which are uncorrelated with each other and have maximal correlation with the reservations holdingat departure


Demand Forecasting TechniquesAdaptive Models

Demand Forecasting TechniquesAdaptive Models

Kalman Filters (KF) Kalman filtering combines information on current forecast

error, measurement noise variance and process noise variance to update parameters

A Kalman Filter resembles a exponential smoother,but the weight (gains) changes with time

Primary benefits are– self-calibrating

– no initialization

– easy to implement

– fast to compute

– robust


CombinedCombinedForecastForecast

Base ForecastingBase Forecasting ModuleModule

Exponential smoothingExponential smoothingon pre-departureon pre-departure

changes in bookings changes in bookings with parameters with parameters updated onlineupdated online

with Kalman Filteringwith Kalman Filtering

Kalman FilteringKalman Filteringcombines information combines information on current forecaston current forecasterror, measurement error, measurement noise variance andnoise variance andprocess noise process noise variance tovariance toupdate parametersupdate parameters

Benefits areBenefits are•Self calibratingSelf calibrating•No initializationNo initialization

Update weightsUpdate weightswith Kalman with Kalman

FilteringFiltering

The Kalman FilterTypical Approach The Kalman FilterTypical Approach

Kalman Filter Bias Kalman Filter Bias AdjustmentAdjustment

Kalman Filter Bias Kalman Filter Bias AdjustmentAdjustment


Demand Forecasting TechniquesSABRE Evaluation Summary


Time Series Models Additive time series Multiplicative time series Adaptive time series

Regression Models Linear regression Bias adjustment technique

Neural Networks Combine regression

and time series in an integrated framework

Traditional technique Does not respond to

changes quickly

Requires frequentrecalibration

Only valid over thecalibration range

Does not work well Calibration takes time Forecasts are not intuitive

(cause / effect relationship)

TechniqueTechnique ResultsResults




Passenger Choice Model Market share and size Competitive schedules Quality of Service Index

Schedule sensitive Forecasts are routinely

generated for Airline Profitability Model at the macro level

Considers competitive schedules Promising, but detailed forecasts

requires calibration Research is ongoing to integrate

Capacity Planning and YM applications and business processes





Multivariate Models Principal component

analysis Canonical variate analysis

Adaptive Models Combine current model

with a Kalman Filter model Bias adjustment technique

Did not perform well Both PC and CV techniques

are linear combinations Components can be unstable

Good results that use current models as a foundation

Improves forecast accuracy



Advances in Demand Forecasting at Advances in Demand Forecasting at SABRESABRE

The Process of Continuous ImprovementThe Process of Continuous Improvement


Advances in Forecasting Advances in Forecasting

New Technique -- developed from econometric theories The new forecasting process based on a combination

of time series and causal models (Kalman Filtering is a special case)

Primary objectives are to improve forecasting accuracy and reduce calibration and support costs

The new forecasting model was tested against published forecasting benchmark problems -- it consistently outperformed the best published results


Advances in Forecasting Advances in Forecasting

Improves on simple regression models (e.g. Y = a0 + a1x by reading day) by handling:

Information from related entities (to use all possible data) Data transformations (to handle non-linear effects) Automatic choice of variables (to create accurate and

robust models) like stepwise regression Auto-correlation of errors in regression (to prevent bias that

typically occurs in regression)


Forecasting Framework: Data Collection and AnalysisForecasting Framework: Data Collection and AnalysisRaw Data

Preprocess Data

MergingMissing DataOutliers

Create pool of variables

Exploratory Data Analysis and Visualization

Collection

Clean data

Report on relationships among variables and patterns over timeCollect additional data


Forecasting Framework: Develop models and monitor resultsForecasting Framework: Develop models and monitor results

Create forecast equations

Forecast calibration

Parse equations and build database tables

Implement forecasts

Forecast Engine

Recommend actions

Decision Support System

Monitor

Quality control, tracking, error analysis

Deliverforecasts

Requestforecasts

Results

Actions

Recalibrate


Textbook Problems BenchmarksTextbook Problems Benchmarks

Case Other Improvement%

Modeling Approach MAE (%) MAE (%)

a) Sales based on advertising (Makridakis,Wheelwright, McGee, 1983 text)

Transfer function(manual calibration)

12% 0.3% 98

b) Improvement on (a)(Bowerman, O’Connell, 1993 text)

More sophisticatedARIMA error term

11.6% 0.3% 97

c) Sales based on advertising (the famousLydia Pinkham data, Vandaele, 1983 text)

Transfer function(manual calibration)

4.4% 4.1% 7

d) T-bill interest rate based on moneysupply, inflation, industry production(Pindyck, Rubinfeld, 1998 text)

Regression withARIMA error (liketransfer function)

5.3% 3.6% 33

e) Advertising time-series, with noindependent variables (Vandaele, 1983)

ARIMA manualcalibration

11.2% 9% 20

f) Housing starts time-series (Johnston, 1997text)

manual seasonalARIMA

19.1% 15.5% 19

g) Electricity demand time-series (NorthAmerican Electric Reliability Council, 1991)

Exponential smoothing 138% 14% 90

SABRE


Future Direction and ResearchFuture Direction and Research

Detailed Passenger Choice Model Market size, passenger preference and QSI

Wavelets Analyzing data in frequency domain. Instead of operating

globally (e.g. Fourier transforms), operate locally Multivariate Adaptive Regression Splines

An enhancement over Classification and Regression Trees by smoothing out discrete jumps in forecasts

Variations on Neural Networks To better handle non-linearities without the inability

to explain results in traditional neural networks

Discussion

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Vish A Viswanathan Director, Revenue Management April 27, 1999 Demand Forecasting.

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