Airline Schedule Planning:
Accomplishments and
Opportunities
C. Barnhart and A. Cohn, 2004
Meltem Peker
04.11.2013
Introduction
 Optimization in Airline Industry
 After "The Airline Deregulation Act" (1970s):
 U.S. federal law intended to remove government control over fares,
routes and market entry off new airlines from commercial aviation
 To overcome;
 Revenue Management
 Schedule Planning
Introduction
 Schedule Planning
 Designing future airline schedules to maximize airline profitability
 Deals with;
 Which origin to destination with what frequency?
 Which hubs to be used?
 Departure time
 Aircraft type
 Importance: American Airlines claims that schedule planning
system generates over $500 million in incremental profits annually
Scheduling Problems
Scheduling Problems
 Obtaining solution is not easy:
 Nonlinearities in cost and constraints
 Interrelated decisions
 Thousands of constraints
 Billions of variables
Complexity and tractability
 Breaking up into subproblems
Core Problems
Schedule
Design
•Which markets with
what frequency
Fleet
Assignment
•What size of
aircraft
Aircraft
•How to route to satisfy
Maintenance maintenance
Routing
Crew
Scheduling
•Which crews to assign
to each aircraft
Core Problems
Schedule
Design
 Schedule Design
Fleet
Asignment
Aircraft
Maintenance
Routing
Crew
Scheduling
 Importance:
 Flight schedule is most important element
Flight legs
Departure time of each leg
 Defines market share
profitability
Core Problems
Schedule
Design
 Schedule Design
Fleet
Asignment
Aircraft
Maintenance
Routing
Crew
Scheduling
 Challenges:
 Complexity and Problem Size
 Data Availability and Accuracy
Unconstrained market demand and average fares
Core Problems
Schedule
Design
 Schedule Design
Fleet
Asignment
Aircraft
Maintenance
Routing
Crew
Scheduling
 Challenges:
 Unconstrained (maximum) market demand
"Chicken and egg effect"
Market
Demand
 Average fares
 Affected by revenue management and
it is affected by flight schedule
 Competitor pressure
Airline
Scheduling
Core Problems
Schedule
Design
 Schedule Design
Fleet
Asignment
Aircraft
Maintenance
Routing
Crew
Scheduling
Due to the challenges, limited optimization can be achieved
Thus; incremental optimization is used
Ex: Select flight legs to be added to the existing flight schedule
(Lohatepanont and Barnhart, 2001)
Core Problems
Schedule
Design
 Fleet Assignment
Fleet
Asignment
Aircraft
Maintenance
Routing
Crew
Scheduling
Assigning a particular fleet type to each flight leg to minimize
cost:
Operating cost: "cost" of aircraft type
Spill Cost: revenue lost (passengers turned away)
Core Problems
Schedule
Design
 Fleet Assignment
Fleet
Asignment
Aircraft
Maintenance
Routing
Crew
Scheduling
Importance:
 Significant cost savings
$100 million savings at
Delta Airlines (Wiper, 2004)
 Limited number of aircraft so assignment is not easy
Challenges:
 Assumption of same schedules for every day
 Assumption of flight leg demand is known
 Estimation of spill cost
Core Problems
Schedule
Design
Fleet
Asignment
Aircraft
Maintenance
Routing
 Fleet Assignment
 Estimation of spill cost with flight leg
Crew
Scheduling
X
leg1
150
Y
leg2
150
İf flight leg based:
spill cost of X-Z ($300)
divided into 2 legs
Z
Core Problems
Schedule
Design
Fleet
Asignment
Aircraft
Maintenance
Routing
Crew
Scheduling
 Fleet Assignment
 Estimation of spill cost with flight leg
100 seats available
50 passengers of X-Z from leg1 are spilled
75 passengers of X-Z from leg2 are spilled
underestimation
of true spill
Core Problems
Schedule
Design
 Fleet Assignment
Fleet
Asignment
Aircraft
Maintenance
Routing
Crew
Scheduling
 To overcome the inaccuracies
Itinerary (origin-destination) based fleet assignment models
 To solve the fleet assignment problem;
Multicommodity network flight problems
(i.e: aircraft type is commodity and objective is to flow is commodity
with minimum cost satisfying assignment constraints)
Core Problems
Schedule
Design
 Aircraft Maintenance Routing
Fleet
Asignment
Aircraft
Maintenance
Routing
Crew
Scheduling
Assignments of individual aircraft to the legs and decision of
routings or rotations that includes regular visits to
maintenance stations
 Maintenance between blocks of flying time without exceeding a
specified limit
Core Problems
Schedule
Design
 Aircraft Maintenance Routing
Fleet
Asignment
Aircraft
Maintenance
Routing
Crew
Scheduling
 Importance:
The network decomposed into subnetworks
Feasible solution can be found easily "if exists"
 Challenges:
Sequential solutions restricts the feasibility
Hub and spoke network vs. point to point network
Many aircraft of same type
at the same time at hubs
Core Problems
Schedule
Design
 Aircraft Maintenance Routing
Fleet
Asignment
Aircraft
Maintenance
Routing
Crew
Scheduling
 To satisfy feasibility;
Include pseudominate (maintenance) constraints to hub and spoke
network in the fleet assignment
 To solve aircraft maintenance routing problem;
Network Circulation Problem
Core Problems
Schedule
Design
 Crew Scheduling
Fleet
Asignment
Aircraft
Maintenance
Routing
Crew
Scheduling
Assigning of crews (cabin and cockpit crews) to the aircrafts
 Importance:
Second highest operating cost after fuel
Significant savings even in small increment
$50 million
savings annually
(Barnhart, 2003)
 Challenges:
Due to the sequential solution, range of possibilities is narrowed
True impact is not exactly known, rarely executed as planned
Core Problems
Schedule
Design
 Crew Scheduling
Fleet
Asignment
Aircraft
Maintenance
Routing
Crew
Scheduling
 To solve crew scheduling problem;
(1) a set of min-cost work schedules (pairings) is determined
(2) Assemble pairings to work schedules with bidlines or rosters
 Set partitioning problem used (pairing, bidline and
rostering)
Integrating Core Models
 Integration to decrease the drawbacks of sequential
solutions (i.e. infeasibility of aircraft maintenance routing)
 "partial integration"
 Merging two models that fully captures both models
 Enhancing a core model by adding some key elements of
another core model
 Integrating core models is "art and science"
Integrating Core Models
 Example 1: Integration Fleet Assignment and Aircraft
Maintenance Routing
 Feasibility of aircraft maintenance routing is guaranteed
 Example 4: Enhanced Fleet Assignment to include schedule
design decisions
 Increases aircraft productivity, decreases spill cost
(Rexing et al., 2000)
Modeling for Solvability
 Integrated models can yield fractional solutions in the LP
relaxation and large branch and bound tree
 Thus, modeling to achieve tighter LP relaxation is another
research area
expansion of definition
of the variable
Modeling for Solvability
 By expansion of the definition;
nonlinear costs and constraints can be modeled with
linear constraints and objective functions (crew scheduling)
 Expansion of variables is also "art and science"
balancing between capturing the complexity and maintaining
tractability
Solving
Scheduling Problems
Solving Scheduling Problems
 Even better modeling (i.e. set partitioning for crew
scheduling) obtaining "good" solutions is still challenging
 To manage problem size,
 Problem-size reduction methods
 Branch and price algorithms
Problem Size Reduction Methods
1) Variable Elimination
Some constraints may be redundant
(e.g. assignment of aircraft to ground and flight arc)
Rexing et al. (2000) decreased model size by 40%
2) Dominance
Effectiveness of solution depends on the ability of dominance
(e.g. shortest path algorithm eliminate all subpaths from consideration)
Cohn and Barnhart (2003) eliminated routing variables by integrating
the problems
Problem Size Reduction Methods
3) Variable Disaggregation
Tractability is enhanced if aggregated variables can be
disaggregated into variables
(e.g. decision variables for subnetworks of flight legs)
Barnhart et al. (2002) eliminated 90% of the variables
Branch and Price Algorithms
 Similar to branch and bound, but with B&B no guarantee for
existing of a "good" solution
 Difference is at B&P, LP's are solved with column generation
Column generation:
Branch and Price Algorithms
 Solution time of B&P is dependent on
 Number of iterations
 Amount of time for each iteration
 As well as obtaining solutions, obtaining in reasonable time to
maintain tractability is important
 Adding many columns than the only most negative column
generally decreases number of iteration
 To reduce number of branching, different heuristics are used
Marsten (1994) improved solutions in less CPU and memory with
"variable fixing"
Future Research and Challenges
1) Core Problems
Better optimization techniques lead to improved resource utilization
2) Integrated Scheduling
Similarly, better integration affects overall profitability
Balancing between tractability and reality is challenging
3) Robust Planning and Plan Implementation
"Snowballing effect"
"Are optimal plans optimal in practice?"
e.g. crew swapping or swapping between flights opportunities
Future Research and Challenges
4) Operations Recovery
Given a plan and disruptions, how to recover optimally?
e.g. using delays instead of cancelation of flights
5) Operations Paradigm
Similar to "The Airline Deregulation Act", airline industry faces upheavals