Airline Schedule Planning: Accomplishments and

Opportunities C. Barnhart and A. Cohn,

2004

Meltem Peker04.11.2013

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 ProblemsSchedule 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 elementFlight legsDeparture time of each leg

Defines market share profitability

Schedule Design

Fleet Asignment

Aircraft Maintenance

RoutingCrew

Scheduling

Core Problems Schedule Design

Challenges:

Complexity and Problem Size

Data Availability and AccuracyUnconstrained market demand and average fares

Schedule Design

Fleet Asignment

Aircraft Maintenance

RoutingCrew

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

RoutingCrew

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

RoutingCrew

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

RoutingCrew

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

RoutingCrew

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

RoutingCrew

SchedulingX ZYleg

1leg2

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

RoutingCrew

Scheduling 100 seats available

underestimation of true spill

50 passengers of X-Z from leg1 are spilled75 passengers of X-Z from leg2 are spilled

Core Problems Fleet Assignment

To overcome the inaccuraciesItinerary (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

RoutingCrew

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

RoutingCrew

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 feasibilityHub and spoke network vs. point to point network

Schedule Design

Fleet Asignment

Aircraft Maintenance

RoutingCrew

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

RoutingCrew

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

RoutingCrew

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

RoutingCrew

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 Methods1) 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 Methods3) 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 usedMarsten (1994) improved solutions in less CPU and memory with "variable fixing"

Future Research and Challenges1) Core Problems

Better optimization techniques lead to improved resource utilization

2) Integrated Scheduling Similarly, better integration affects overall profitabilityBalancing 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 Challenges4) 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