1. Airline Schedule Planning: Accomplishments and Opportunities Airline Schedule Planning: Accomplishments and Opportunities C. Barnhart and A. Cohn, 2004 Meltem Peker 04.11.2013

2. 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

3. 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

4. Scheduling Problems

5.  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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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)

13. Core Problems  Fleet Assignment  Estimation of spill cost with flight leg Schedule Design Fleet Asignment Aircraft Maintenance Routing Crew Scheduling XZ Y leg1 leg2 İf flight leg based: spill cost of X-Z ($300) divided into 2 legs 150

14. 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

15. 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

16. 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

17. 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

18. Core Problems  Aircraft Maintenance Routing  To satisfy feasibility; I nclude 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

19. 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)

20. 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

21. 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"

22. 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)

23. 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

24. 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

25. Solving Scheduling Problems

26. 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

27. 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

28. 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

29. 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:

30. 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"

31. 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

32. 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

34.  Example 2: Integration Aircraft Maintenance Routing and Crew Pairing  Increase the possible crew scheduling opportunities, and decrease crew cost