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A Scenario Aggregation–Based Approach for Determining a Robust Airline Fleet Composition for Dynamic Capacity Allocation

A Scenario Aggregation–Based Approach for Determining a Robust Airline Fleet Composition for Dynamic Capacity Allocation. Ovidiu Listes , Rommert Dekker. Agenda. Introduction Literature Review Fleet Composition Problem Model Deterministic Model Stochastic Model

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A Scenario Aggregation–Based Approach for Determining a Robust Airline Fleet Composition for Dynamic Capacity Allocation

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  1. A Scenario Aggregation–Based Approach forDetermining a Robust Airline Fleet CompositionforDynamicCapacityAllocation OvidiuListes, RommertDekker

  2. Agenda • Introduction • LiteratureReview • FleetComposition Problem • Model • Deterministic Model • Stochastic Model • ScenarioAggregationAlgorithm • ScenarioGeneration • CaseStudy • Conclusion

  3. 1.Introduction • Randomdemandfluctuationsleadto -lowaverageloadfactors -a significantnumberof not accepted passengers • Dynamic allocation of airline fleetcapacity: Using most recent estimates of customersdemandsfor accordingly updating the assignmentsof aircrafts to the flight schedule

  4. FleetAssignment • FleetComposition • Thispaperfocuses on creating an approachto the airline fleet composition problem thataccounts explicitly for stochastic demand fluctuations

  5. 2. LITERATURE REVIEW • Berge&Hopperstad(1993) • Hane et al.(1995) • Talluri(1996) • Gu et al.(1994)

  6. 3. TheFleet-Composition Problem • Complex, upper-managementdecides on it. • Paperadresses problem from OR perspective. Model it in relationtothebasicfleetassignment. • Demand is assumedtofollowindependent normal distribution, variability specified as the K-factor(sd/mean).

  7. Eachaircraft has -Fixedcost -Operationalcost -Capacityforeachfairclass -Rangecapability -Familyindicator • Assumptions: -Identicalflying&turnaround time -No recapture -Minimum number of aircraftsrequired is takenintoaccount

  8. 4.Model Fleetcomposition problem can be considered as a multicommodity flow problem based on the construction of a space-time network

  9. 4.1. Deterministic model NP-hard formorethanthreeaircrafttypes

  10. 4.2. Stochastic model S representativescenariosand solutionforindividualdemand scenarios is sameforeveryscenariohence, foreveryscenario s.

  11. Because of huge number of integer second-stage variables a branch-and-boundtype of procedure is not practical. Forsmallexamples: • LP relaxation of SP denotedby LSP includesmanyinteger-valueddecisionvariables. • LP relaxation gap turns out tobe less than 0.5% in these cases.

  12. 4.3.1 TheScenarioAggregation–BasedApproach • Scenario aggregation is a decomposition-type ofmethod. • MainIdea: Iterativelysolvingindividualscenarioproblems, perturbed in a certain sense, and to aggregate, ateach iteration, these individual solutions into an overallimplementablesolution

  13. 4.3.2. TheScenarioAggregationAlgorithm • Admissiblesolution: Feasibleforeachscenario s. • z variablesindexedoverscenario s thenadditionalconstraint: : solutionfrompreviousiteration Thisconstraint is relaxed in theLagrangian sense usingmultipliersws .

  14. TheScenarioAggregationAlgorithm

  15. is an implementablesolution not necessarilyadmissible w is interpreted as informationprices StoppingCriteria: Varianceerrorwrt z variables is used Stop when: • Lowρvaluesencourageprogress in primalsequence • ε is set to 3% of minimum total number of planes CriteriaSelection:

  16. Roundingprocedure fractionalfirststagesolutionwith Foranygivenfractionalsolution u [u] denotesintegerpart of u and {u} denotesfractionalpart of u A constant c is selectedbetween 0 and 0.5 RoundingProcedure:

  17. 4.4 ScenarioGeneration Demandassumedtofollow a normal distribution: DescriptiveSampling: A purposiveselectionof the sample values—aiming to achieve a closefit with the represented distribution—and the randompermutationsof thesevalues

  18. 4.5 FleetPerformanceEvaluation • New simulateddemandsfromdemanddistribution is used, size 3 to 4 timesgreaterthannumber of scenariosused. • GenericFleetFlexibility • FleetInterchangibility

  19. 5. CaseStudy • Smallcasevalidatesmethod, • Largecaseshowsextend • Nine aircrafttypes • 40% business, 60% economyseats • Smallcase: LargeCase: -342 flightlegs -18 airports -15 planes -50 scenarios -MeanDemand : 14-65 foreconomyclass 26-48 forbusinessclass -1978 flightlegs -50 airports -68 planes -25 scenarios -MeanDemand : 18-57 foreconomyclass 21-43 forbusinessclass

  20. GenericFlexibility-SmallCase

  21. FleetInterchangibility-SmallCase

  22. GenericFlexibility-LargeCase

  23. FleetInterchangibility-LargeCase

  24. 6.Conclusion • Increase in loadfactorupto 2.6% • Decrease in spillupto 3.3%. • Profitincreaseupto 14.5%. Finally, Thescenario-aggregationbasedapproachhandleseffects of fluctuatingpassengerdemand on fleet-planningprocessandgeneratesflexiblefleetconfigurationsthatsupportdynamicassignments.

  25. Thanksforlistening

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