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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
Breaking up into subproblems
Complexity and tractability
Core Problems
Schedule Design
• Which markets with what frequency
Fleet Assignment
• What size
of aircraft
Aircraft Maintenance
Routing
• How to route to satisfy maintenance
Crew Scheduling
• Which crews to assign to each aircraft
Core Problems
Schedule Design
Importance:
Flight schedule is most important element
Flight legs
Departure time of each leg
Defines market share profitability
Schedule Design
Fleet Asignment
Aircraft Maintenance
Routing
Crew Scheduling
Core Problems
Schedule Design
Challenges:
Complexity and Problem Size
Data Availability and Accuracy
Unconstrained market demand and average fares
Schedule Design
Fleet Asignment
Aircraft Maintenance
Routing
Crew Scheduling
Core Problems
Schedule Design
Challenges:
Unconstrained (maximum) market demand
"Chicken and egg effect"
Average fares
Affected by revenue management and
it is affected by flight schedule
Competitor pressure
Market Demand
Airline Scheduling
Schedule Design
Fleet Asignment
Aircraft Maintenance
Routing
Crew Scheduling
Core Problems
Schedule Design
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)
Schedule Design
Fleet Asignment
Aircraft Maintenance
Routing
Crew Scheduling
Core Problems
Fleet Assignment
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)
Schedule Design
Fleet Asignment
Aircraft Maintenance
Routing
Crew Scheduling
Core Problems
Fleet Assignment
Importance: Significant cost savings
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
Schedule Design
Fleet Asignment
Aircraft Maintenance
Routing
Crew Scheduling
$100 million savings at Delta Airlines (Wiper, 2004)
Core Problems
Fleet Assignment
Estimation of spill cost with flight leg
Schedule Design
Fleet Asignment
Aircraft Maintenance
Routing
Crew Scheduling
X ZYleg1
leg2
İf flight leg based:spill cost of X-Z ($300) divided into 2 legs
150
150
Core Problems
Fleet Assignment
Estimation of spill cost with flight leg
Schedule Design
Fleet Asignment
Aircraft Maintenance
Routing
Crew Scheduling 100 seats available
underestimation of true spill
50 passengers of X-Z from leg1 are spilled
75 passengers of X-Z from leg2 are spilled
Core Problems
Fleet Assignment
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)
Schedule Design
Fleet Asignment
Aircraft Maintenance
Routing
Crew Scheduling
Core Problems
Aircraft Maintenance Routing
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
Schedule Design
Fleet Asignment
Aircraft Maintenance
Routing
Crew Scheduling
Core Problems
Aircraft Maintenance Routing
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
Schedule Design
Fleet Asignment
Aircraft Maintenance
Routing
Crew Scheduling
Many aircraft of same type at the same time at hubs
Core Problems
Aircraft Maintenance Routing
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
Schedule Design
Fleet Asignment
Aircraft Maintenance
Routing
Crew Scheduling
Core Problems
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
Challenges: Due to the sequential solution, range of possibilities is
narrowed
True impact is not exactly known, rarely executed as planned
Schedule Design
Fleet Asignment
Aircraft Maintenance
Routing
Crew Scheduling
$50 million savings annually (Barnhart, 2003)
Core Problems
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)
Schedule Design
Fleet Asignment
Aircraft Maintenance
Routing
Crew Scheduling
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
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