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The KLM Airline Network. S Jain Mathematics School of Engineering & Applied Science Aston University, Birmingham B4 7ET,UK. The KLM Airline Network. Bian F . & Suleman M.O. (University of Oxford),

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The klm airline network l.jpg
The KLM Airline Network

S Jain

Mathematics

School of Engineering & Applied Science

Aston University, Birmingham B4 7ET,UK


The klm airline network2 l.jpg
The KLM Airline Network

Bian F. & Suleman M.O.(University of Oxford),

Burke E.K., Kendall G. & Landa Silva J.D.(The University of Nottingham), Koole G.M. (Free University of Amsterdam), Reeves C. (Coventry University), Rusdi I. (Technical University of Delft),

Marc Paelinck,

Jeroen Mulder (KLM)

Nallangithal, S (Aston University)


Contents l.jpg
CONTENTS

  • Making Airline Schedules More Robust

    • Introduction

    • Problem Description

    • Objective

    • Model

    • Results

  • Summary

  • The KLM Airline Network

  • Future Work


Airline schedules l.jpg
Airline Schedules

  • Effective schedule can lead to savings and higher customer satisfaction

  • Quality of a schedule: ROBUSTNESS

    (how well it can cope with delay(s) to a particular aircraft(s))

  • Enough slack in the schedule?

    If no slack in the schedule, delay to one aircraft could have knock on effect → other aircraft, missed connections → incurred costs

    Building slack → aircraft idle → costs

  • Effective balance: robustness v aircraft idle time


Klm airline network l.jpg

KLM

164 destinations

131 aircrafts

23 mln. passengers

600.000 tons freight

KLM Airline Network


Schedule development l.jpg

Network department develops a schedule 4 times per year

Schedule transfer

1 month

before season starts

Operations Control department runs the daily operation

Schedule development

Maximize profit

  • # flights

  • # connections at Schiphol Airport

  • Maximize performance

    • punctuality

    • completion factor


Peformance indicators l.jpg
Peformance Indicators

  • Departure and Arrival punctuality

  • Completion factor (all flights that were not cancelled).

  • “No Connection Passenger” factor (percentage of transfer passengers who missed their connections due to operational problems.)

  • Irregularity-rate (the number of bags that were not delivered on time.)


Building blocks l.jpg
Building Blocks

  • BB1: Flight

  • BB2: Arriving aircraft

  • BB3: Layover aircraft

  • BB4: Departing aircraft

  • BB5: BB5.1 Transferring passengersBB5.2 Transferring baggage

  • BB6: BB6.1 Arriving passengers BB6.2 Arriving baggage

  • BB7: BB7.1 Departing passengers BB7.2 Departing baggage


Bb sequences and relationships l.jpg

All Doors Closed

1st door open

1

Flight

5.2

Transferring baggage

2

Arriving aircraft

5.2

Transferring baggage

4

Departing aircraft

1

Flight

3

Layover

6.1

Arriving passengers

6.2

Arriving

baggage

7.1

Departing passengers

7.2

Departing

baggage

5.1

Transferring passengers

5.1

Transferring passengers

1st door open

All Doors Closed

BB Sequences and Relationships


Rotation schedule l.jpg

Day of Week

Technical Service

(check-up, overhaul)

Aircrafts

(per type)

Reserves

(technical, operational)

Rotation Schedule

Rotation

(Amsterdam - Bucharest - Amsterdam)

Unassigned (Idle)


Flight components l.jpg
Flight components

Mon 18Feb08

Tue 19Feb08

CDG

OTP

0

0

0

Departure Service AMS

Flight AMS-CDG

Turnaround Service CDG

Flight CDG-AMS

Turnaround Service AMS

Flight AMS-OTP

Arrival Service OTP

Night Stop OTP

Departure Service OTP

Turnaround Service AMS

Flight OTP-AMS


Flight components12 l.jpg

CDG

OTP

0

0

0

Flight components

Mon 17Feb03

Tue 18Feb03


Flight components13 l.jpg

CDG

OTP

0

0

0

Flight components

Mon 17Feb03

Tue 18Feb03


Flight components14 l.jpg

CDG

OTP

0

0

0

GVA

LHR

CDG

00

0

0

0

Flight components

Mon 17Feb03

Tue 18Feb03


Flight components15 l.jpg

CDG

LHR

CDG

0

0

0

0

GVA

OTP

00

0

0

Flight components

Mon 17Feb03

Tue 18Feb03


Consequence l.jpg
Consequence

Aircraft rotation schedules are not invariant...

...but they change continuously due to the various corrective measures.


Objective l.jpg
Objective

  • Without corrective measures, the performance of the network would be much lower.

  • So when forecasting the performance, these measures will have to be taken into account.

  • KLM is currently developing a simulation model, but simulation is time-consuming.

  • KLM is looking for a method to forecast the network performance, that is rapid and easy to use.

    • During schedule development

    • When changes are made to an existing schedule

  • Of a number of alternative schedules, schedule X will provide the best performance


Model klm europe l.jpg
Model (KLM: Europe)

  • Identify features in each schedule

    For instance: - statistical measures

    - time gaps

    - number of potential swaps

  • Collect feature data and performance data for various schedules

  • Determine a method to model the data:

    Associate the inputs (features) with the outputs (performance)

  • Fit the model


Features l.jpg
Features

  • Considered features:

    • Distribution of gaps

    • Total gap space per period of the day/week

    • Number of potential swaps

    • Number of aircraft at Schiphol Airport


Features20 l.jpg
Features

Aircraft on the Ground vs. time of day (minutes)


Features21 l.jpg
Features

Aircraft on the Ground vs. time of day (minutes)

two consecutive days


Features22 l.jpg

Flight

Flight

Gap

BB1

BB2+3+4

BB1

Departure

service

Arrival

service

Flight

Flight

Gap

BB1

BB2

BB4

BB3

BB1

Features

Building block 3 versus 2+3+4


Features23 l.jpg
Features

  • Chosen features

    • Consider the distribution of the number of aircraft on the ground during the day (at AMS airport)

    • Focus on the four transfer peaks

    • Gather the first four moments for each peak

      • Mean

      • Standard deviation

      • Skewness

      • Kurtosis


Model l.jpg
Model

Multiple Linear Regression

  • Eleven schedules were available summer/winter 2006-08, apart from the last 13 weeks of 2008.

  • 4 peaks daily, for each peak the first 4 moments of ACOG, leading to 16 features as inputs.

  • Performance Indicators (PIs) used: Departure and Arrival punctualities.


Departure punctuality l.jpg
Departure Punctuality

Approximate linear relation between mean of peak 4 and departure punctuality

Departure punct.

peak 4 mean


Fitted models l.jpg

PI – Departure Punctuality

Using BB3 only

Using BB2+3+4

Predictor sets

p4m, p1sd, p1sk, p1k

p2m, p4m, p2sd, p4sd, p3sk

R-squared

95.6%

91.6%

P value(F-test)

.00032

.01028

PI – Arrival Punctuality

Predictor sets

p4m, p1sk, p3sk, p3k

p1m, p4m

R-squared

95.2%

84.1%

P value(F-test)

.00042

.00064

Fitted Models

PI – Departure Punctuality

PI – Arrival Punctuality


Residual plots 1 l.jpg
Residual Plots (1)

Residuals against fitted values for Departure Punctuality using BB3 only

Residues

Fitted: peak 4 mean + peak 1 std + skewness + kurtosis


Summary l.jpg
Summary

  • Conclusions

    • No need to consider the historical data on the processes involved

    • No need to consider the measures taken by the Operations Control Front Office

    • This model is rapid and easy to use

  • Further work?

    • Peak locations

    • Day-to-day variations

    • Day of week effect?

    • Nonlinear models?

    • Intercontinental fleet


Constructing the klm airline network l.jpg
Constructing the KLM Airline Network

  • KLM (and partners) timetable published on 30 Nov 2008

  • Number of nodes: N = 630 (airports)

  • Number of edges: E = 1400 (no of direct connections)

  • Connectivity of the network

    • G(N,E): ROUTEMAP

    • W(N,E): includes traffic flow between connections

  • Node degree:

    • Out degree of node i ~ in degree of node i = k i

  • Node strength:

    • Out strength of node i ~ in strength of node i = s i


Point to point pp v hub and spoke hs l.jpg
Point to Point (PP) v Hub and Spoke (HS)

  • Use Gini coefficient:-

  • The degree Gini coefficient, G(k), for network of size N, measures the magnitude of the difference in node degree between all pairs of nodes.

where < k > = 2 E / N, is the average node degree.

G(k) is such that Low value PP

High value HS (Wuellner et al, 2009)


Network properties l.jpg
Network Properties

* From Wuellner et al (2009); SW is PP, US & AA (HS)

Figures in brackets correspond to an Erdos-Renyi (ER) random graph with the same N and E

All carriers have < L > < ln N and < C > > < CER > and hence can be considered “small world”.


Future work l.jpg
Future work

  • Resilience to

    • Random edge deletion (weather)?

    • Random node deletion (closure of airport)?

  • PP (used by Ryanair and Easyjet) v HS for merged Air France – KLM network?

    THANK YOU!


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