1. A Modeling Framework for Flight Schedule Planning
Xagil Solutions
Southwest Airlines
March 2013

2. Presentation Outline Background Literature Review Problem Statement
Modeling Framework
Preliminary Results
Software Prototype
Summary and Discussion

3. Background
The goal of the airline schedule optimizer is to determine the optimal departure time for each flight considering the following objectives:
- Maximizing the airline’s market share
- Maximizing utilization of operational resources (aircraft, crew, gates, etc.)
- Satisfying all operational constraints

4. Schedule
Demand
Interdependency between the schedule and the market share results in a non-linear mixed integer problem (NP-hard)

5. Enplanement (Passenger Demand)
Attracting 20 more passengers results in an annual revenue increase of $1M.
20 pax x $150 (one way fare) x 365 = $1.1 M

6. Aircraft Utilization
Every minute saved in the aircraft turn time could result in additional annual revenue of about $40M.
if flights are optimally arranged :
3000 Flights/day → 1500 turns/day → 1500 Minutes →
~ 7 more flights in the schedule …
7 flights x 100 pax X $150 (one way fare) X 365 = $38 M

7. A relatively low load factor is reported for Southwest Airlines in 2012*

8. Historically, SWA has been operating at marginally lower load factors compared to competitors

9. Average Revenue Block Hours per Day
Aircraft utilization is systematically declining, especially after 2008
Average Revenue Block Hours per Day

10. Airline Schedule Planning
Demand Forecasting
Schedule Planning
Flight Frequency
Airline Schedule Planning
Flight Scheduling
Revenue Management
Fleet Assignment
Aircraft Routing
Crew Assignment

11. Literature Review
Two classes of models:
Fleet assignment only (given flight schedules)
Integrated flight scheduling and fleeting
A widely adopted solution approach is based on obtaining incremental improvements to a given schedule.
Approach I: Include a list of optional flight legs and choose the most profitable ones.
Examples: Hane et al. (1995) - Lohatepanont and Barnhart (2004) - Sherali et al. (2011)
Approach II: Define a time window for each flight which is divided into equal intervals, and select the optimal departure time for each flight.
Examples: Desaulniers et al. (1997), Rexing et al. (2000), Yan and Tseng (2002)

12. Two main limitations
Inability to capture interdependency between the designed schedule and the associated airline's market share while considering competition with other airlines.
Lacking adequate representation of the passengers' itinerary choice behavior which could affect the estimate of the amount of demand spill and recapture among the different itineraries.

13. Problem Statement Given:
The desired flight frequency for every city-pair
Required:
Optimal departure time for each flight while capturing the trade-off between
(a) market share maximization and
(b) efficient aircraft rotations.

14. 9:00 AM
Selecting a departure time that maximizes connecting traffic
Selecting a departure time that maximizes originating (local) traffic
5:00 PM
Maximizing local (non-stop) and connecting traffic

15. 7:00 AM
11:00 PM
Maintaining feasible aircraft rotations

16. Minimizing aircraft ground time

17. Minimum and maximum ground time constrains
Minimum allowed aircraft turn time
Maximum allowed aircraft turn time
Minimum and maximum ground time constrains

18. Departure times are all multiples of 5 (12:00, 12:05, 12:10, etc)
Departure time constrains

19. Departure Time window for flight 1
LAX
LAS
Departure Time window for flight 1 1
Constraining a flight’s departure time to a certain time widow
(or fixing the departure time for certain flights)
Departure Time window for flight 2 2
Departure Time window for flight 3 3
Departure Time window for flight 4 4
Departure Time window for flight 5 5
Departure time window constraints

20. Locking a flight, market, or station
LAX
LAS
EWR
EWR 1 2 3 4 5
Locking a flight, market, or station

21. Modeling Framework
The modeling framework consists of two main components:
- Randomized search algorithm (GA)
- Competition analysis model
A daily flight schedule is modeled as a chromosome. Each gene represents a departure time interval.

22. Modeling Framework Initial Population
Airline Competition Analysis Simulator
Other Fitness Criteria
New Population
Flight Passenger Demand
Parameters of Fitness Function
Fitness
Crossover and Mutation
Convergence
Report Optimal Schedule
Yes No
Modeling Framework

23. Competition Analysis Model
Input Data
Schedule Data
OD Demand Data
Host Airline Schedule
Other Airlines Schedule
Itinerary Builder Rules
Itinerary Builder
Set of Itineraries for Every City-pair
Itinerary Choice Models
Itinerary Valuation
Demand Assignment to Itineraries
Competition Analysis
Model
Demand on Flights for Host Airline

24. Fixed for all iterations
Varies by iteration
Fixed for all iterations
Schedule of Airline A
Schedule of Airline B
Schedule of Airline C
Schedule of the Host Airline …
Itineraries of the Host Airline …
Itineraries of Airline A
Itineraries of Airline B
Itineraries of Airline C
Itinerary Choice Model …
Demand Share of the Host Airline
Demand Share Airline A
Demand Share Airline B
Demand Share Airline C

25. Preliminary Results No. of flights for all airlines: 65,271
Total daily passenger demand: 1,128,090
No. of city pairs: 32,352
No. of flights for the host airline: 3,014
No. of city pairs for the host airline: 718
No. of destinations: 61

26. Impact of maximum allowed aircraft turn time
Minimum allowed aircraft turn time
Maximum allowed aircraft turn time
3 to 6 hours

27. Fitness = number of passengers + α * fully rotated flights
α =1000

28. Fitness = number of passengers + α * fully rotated flights α =1000
Cold start
Fitness = number of passengers + α * fully rotated flights
α =1000

29. Average Aircraft Turn Time

30. Aircraft Turn Time

31. No. of Flights with Infeasible Turns

32. Impact of fitness coefficient
Fitness = number of passengers + α * fully rotated flights

33. Maximum allowed aircraft turn time = 6 Hrs

35. Maximum allowed aircraft turn time = 6 Hrs

37. User Interface Prototype

38. Market-based View

39. Market-based View (Table Format)

40. Market-based View (Aircraft Routing)

41. Network-based View

42. Network-based (with Flight Information)

43. Tabular Format with Filtering Capabilities

44. Itinerary Builder View

45. Summary
A modeling framework for flight schedule planning is presented.
The framework consists of two main components: (a) randomized search algorithm (GA) and (b) competition analysis model
The framework captures the trade-off between creating attractive itineraries (market share) and maximizing the aircraft utilization.
The model is also an adequate tool for benchmarking other solutions
A user friendly interface is presented.

46. Questions?