extended log it

8/4/2019 Extended Log It

1/23

The Art and Science of Marketshare Models:

How to forecast passenger demand in acompetitive environment ?


2/23

Presentation

Chart 2

May 30th, 2004

Agenda

Marketshare Models for Travel Demand Forecasting

Correlations: Red and Blue Busses

A Practical Example

Summary and Outlook


3/23

PresentationMay 30th, 2004

Marketshare models: Forecasting marketshares

JFK

LHR

TXL

FRA

...

NYC

BERMUC

15%

18%

20%

x%

EWR


4/23

Presentation

Chart 4

May 30th, 2004

Marketshare Models Why ?

n Support for Scheduling and Network Decisions in its own right

Scenario studies for

Re-timings

Frequency changes

Equipment changes

Codeshares and Alliances ...

ZRH

ORD

VEN

SVO

LED

FRA


5/23

Presentation

Chart 5

May 30th, 2004

Marketshare Models in Scheduling and Strategic Planning

n Goal function for Optimizers, such as ...

... Timing Optimization

... Fleet Assignment

... Codeshare Assignment

n Why:

One model throughout the company!

Consistent evaluation fore.g., re-fleeting and and re-timing

scenarios ! Save calibration and data preparation efforts

CodeshareAssignerHubOptimizer

Route

Optimizer

Fleet

Assigner

Passenger Demand Forecast


6/23

Presentation

Chart 6

May 30th, 2004

Requirements

n Reliability

Accuracy of Forecasts Taking into account all relevant effects appropriately

n Scenario capability

account for all relevant business cases(re-timings, equipment changes, codeshares, ...)

n Speed

Optimizers require lots of evaluations

Convenience for users(spend time on analysis rather than generating numbers)


7/23

Presentation

Chart 7

May 30th, 2004

Marketshare Models How do they work ?

n Mathematical measure for itinerary quality, for example:

n Account for all relevant effects that have an impact on passengers choice

Departure/arrival time preference

Airline preferences

Connect type

Elapsed time

...

...***)( .. +++= efPrAirlineAirlinetimeelTimeelConTypeConType xxxiu

ZRH

ORD

VEN

SVO

LED

FRA


8/23

Presentation

Chart 8

May 30th, 2004

QSI models

Mathematical measure for itinerary quality, for example:

...***)( .. +++= efPrAirlineAirlinetimeelTimeelConTypeConType xxxiu

( )( )

=

j

ju

iuishare )(

Is related to marketshare for itinerary i:


9/23

Presentation

Chart 9

May 30th, 2004

Random utility theory Logit and Probit

nUtility maximisation theory:

Decisions are made such, that the utility for the decision-making individual ismaximised.

nHow to measure utility ?

non-rational/non-parametrisable influences

non-observable influence

taste variations

...

( ) ( )

( ) ( )iixix

iiuiV

+++=

+=

...*)(*

)(

2211


10/23

Presentation

Chart 10

May 30th, 2004

Parametrisation of the stochastic term

n Logit:

Gumbel distribution

Independent alternatives

Analytical integration possible

n Probit:

Gau distribution

Correlated alternatives

numerical solutions only time consuming !

( ) [ ] ))(exp(*))(exp(exp~ iii

[ ] exp~


11/23

Presentation

Chart 11

May 30th, 2004

Stochastic contribution to the utility

-5 -4 -3 -2 -1 0 1 2 3 4 5

0.0

0.1

0.2

0.3

0.4

Gumbel

Gauss

density

( ) ( )( ) ( )iixix

iiuiV

+++=

+=

...*)(*

)(

2211


12/23

Presentation

Chart 12

May 30th, 2004

Agenda



A Practical Example

Summary and Outlook


13/23

Presentation

Chart 13

May 30th, 2004

Correlation effects: Red Bus-Blue Bus paradox

OOO DDD

Car

Bus

Introducing Blue Bus with identical attributes as Red Bus

model forecast: decreasing marketshare for Car


14/23

Presentation

Chart 14

May 30th, 2004

Correlation effects: Timings

OOO DDD

Introducing blue serviceaffects marketshare of redservice differently dependingon timing !

25%25%0%Add.

service

25%50 %50 %Afternoon

service

50%25 %50 %Morning

service

Add. afternoon

service

Add. morning

service

No add.

service


15/23

Presentation

Chart 15

May 30th, 2004

How to deal with this ?

In the standard Logitand the QSItheory no accouting for correlation/coupling effects !

( ) ( )iiuiV +=)(

[ ]

j

jijiiiii exp*exp~)(2

Have a look at the Probitapproach:

Bi-linear term accounting for correlations


16/23

Presentation

Chart 16

May 30th, 2004

Extended Logit approach

Include bi-linear terms into the Logitapproach:

( ) ( )iiuiV +=)(

( ) [ ] ,...,,*))(exp(*))(exp(exp~ kjiiii

Define a suitable expression to account for coupling between alternatives


17/23

Presentation

Chart 17

May 30th, 2004

Agenda



A Practical Example

Summary and Outlook


18/23

Presentation

Chart 18

May 30th, 2004

Example

European regional marketn Short haul, high frequency market

nMainly nonstop services of different airlines

n Elapsed timeand connect typeno relevant choice parameter !

n Choice parameters are

n Arrival/departure timing

n Timing competition

n Airline competition/correlation

Nr. Dep. Time Blocktime Airline Stops

1 06:50 75 2 0

2 07:45 65 3 0

3 08:15 70 1 0

4 09:55 75 2 0

5 10:00 70 1 0

6 10:30 65 3 0

7 14:40 65 3 0

8 17:15 70 1 0

9 18:40 65 3 0

10 20:20 65 3 0


19/23

Presentation

Chart 19

May 30th, 2004

Influence of Correlation/Coupling

n Example: Correlation of departure times:

competitive coupling

leading to decrease in marketshare

n Example: Correlation of operating/marketing airline of schedule alternatives:

competitive coupling (I want to fly with airlines xyz !)

synergistic coupling due to better overall service

...2

,22

*2

,1

*1

++= xxzj

xi

xzij

B

Determine overall coupling parameter for two alternatives:

Weights Attributes


20/23

Presentation

Chart 20

May 30th, 2004

Results - I

Extended Logit

Good correlation

Peaks and valleys adequately represented

Standard Logit

Essential properties of market not represented adequately

0

10

20

30

40

50

60

70

80

1 2 3 4 5 6 7 8 9 10

Itinerary

Passenger(Forecast)

Legend:

n Observed bookings

n Standard Logit forecast

n Extended Logit forecast


21/23

Presentation

Chart 21

May 30th, 2004

Results II

Values of Coefficients:

n Timing Correlation: negative contribution parameter (TC = - 0.976 )

Significant competition present between trip alternatives

Itineraries close in departure time compete for the same passengers

n Airline Correlation: positive contribution parameter ( AC = + 0.102 )

Synergistic effect outweighs competition

High marketpresence gives competitive advantage


22/23

Presentation

Chart 22

May 30th, 2004

Agenda



A Practical Example

Summary and Outlook


23/23

Presentation

Chart 23

May 30th, 2004

Summary + Outlook

n More sophisticated model leads to higher accuracy of forecasts

Getting around pitfalls of previous models

A better understanding of highly competitive O&Ds

n Suitable for scenario studies

n Combine speed of Logit with accuracy of Probit

Fast evaluation

Also suitable as goal function for optimization

All requirements for a good model fulfilled

extended log it

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