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), 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 • Making Airline Schedules More Robust • Introduction • Problem Description • Objective • Model • Results • Summary • The KLM Airline Network • Future Work
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 164 destinations 131 aircrafts 23 mln. passengers 600.000 tons freight KLM Airline Network
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 • 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 • 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
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
Day of Week Technical Service (check-up, overhaul) Aircrafts (per type) Reserves (technical, operational) Rotation Schedule Rotation (Amsterdam - Bucharest - Amsterdam) Unassigned (Idle)
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
CDG OTP 0 0 0 Flight components Mon 17Feb03 Tue 18Feb03
CDG OTP 0 0 0 Flight components Mon 17Feb03 Tue 18Feb03
CDG OTP 0 0 0 GVA LHR CDG 00 0 0 0 Flight components Mon 17Feb03 Tue 18Feb03
CDG LHR CDG 0 0 0 0 GVA OTP 00 0 0 Flight components Mon 17Feb03 Tue 18Feb03
Consequence Aircraft rotation schedules are not invariant... ...but they change continuously due to the various corrective measures.
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) • 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 • Considered features: • Distribution of gaps • Total gap space per period of the day/week • Number of potential swaps • Number of aircraft at Schiphol Airport
Features Aircraft on the Ground vs. time of day (minutes)
Features Aircraft on the Ground vs. time of day (minutes) two consecutive days
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
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 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 Approximate linear relation between mean of peak 4 and departure punctuality Departure punct. peak 4 mean
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) Residuals against fitted values for Departure Punctuality using BB3 only Residues Fitted: peak 4 mean + peak 1 std + skewness + kurtosis
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 • 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) • 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 * 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 • 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!