Airline Schedule Planning Accomplishments and Opportunities C Barnhart

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" (1970 s): 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 Maintenance Routing • How to route to satisfy maintenance Crew Scheduling • Which crews to assign to each aircraft

Core Problems 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 Fleet Asignment Aircraft Maintenance Routing Crew Scheduling Challenges: Complexity and Problem Size Data Availability and Accuracy Unconstrained market demand average fares

Core Problems Schedule Design Fleet Asignment Aircraft Maintenance Routing Crew Scheduling 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

Core Problems 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 Assignment Fleet Asignment Aircraft Maintenance Routing Estimation of spill cost with flight leg Crew Scheduling X leg 1 150 Y leg 2 150 İf flight leg based: spill cost of X-Z ($300) divided into 2 legs Z

Core Problems Schedule Design Fleet Assignment Fleet Asignment Aircraft Maintenance Routing Crew Scheduling Estimation of spill cost with flight leg 100 seats available 50 passengers of X-Z from leg 1 are spilled 75 passengers of X-Z from leg 2 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