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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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slide1

A Scenario Aggregation–Based Approach forDetermining a Robust Airline Fleet CompositionforDynamicCapacityAllocation

OvidiuListes, RommertDekker

agenda
Agenda
  • Introduction
  • LiteratureReview
  • FleetComposition Problem
  • Model
    • Deterministic Model
    • Stochastic Model
    • ScenarioAggregationAlgorithm
    • ScenarioGeneration
  • CaseStudy
  • Conclusion
1 introduction
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

slide4

FleetAssignment

  • FleetComposition
  • Thispaperfocuses on creating an approachto the airline fleet composition problem thataccounts explicitly for stochastic demand fluctuations
2 literature review
2. LITERATURE REVIEW
  • Berge&Hopperstad(1993)
  • Hane et al.(1995)
  • Talluri(1996)
  • Gu et al.(1994)
3 the fleet composition problem
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).
slide7

Eachaircraft has

-Fixedcost

-Operationalcost

-Capacityforeachfairclass

-Rangecapability

-Familyindicator

  • Assumptions:

-Identicalflying&turnaround time

-No recapture

-Minimum number of aircraftsrequired is takenintoaccount

4 model
4.Model

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

4 1 deterministic model
4.1. Deterministic model

NP-hard formorethanthreeaircrafttypes

4 2 stochastic model
4.2. Stochastic model

S representativescenariosand

solutionforindividualdemand

scenarios

is sameforeveryscenariohence,

foreveryscenario s.

slide11

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.
4 3 1 the scenario aggregation based approach
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
4 3 2 the scenario aggregation algorithm
4.3.2. TheScenarioAggregationAlgorithm
  • Admissiblesolution: Feasibleforeachscenario s.
  • z variablesindexedoverscenario s thenadditionalconstraint:

: solutionfrompreviousiteration

Thisconstraint is relaxed in theLagrangian sense usingmultipliersws .

slide15

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:

rounding procedure
Roundingprocedure

fractionalfirststagesolutionwith

Foranygivenfractionalsolution u [u] denotesintegerpart of u and {u} denotesfractionalpart of u

A constant c is selectedbetween 0 and 0.5

RoundingProcedure:

4 4 scenario generation
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

4 5 fleet performance evaluation
4.5 FleetPerformanceEvaluation
  • New simulateddemandsfromdemanddistribution is used, size 3 to 4 timesgreaterthannumber of scenariosused.
  • GenericFleetFlexibility
  • FleetInterchangibility
5 case study
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

6 conclusion
6.Conclusion
  • Increase in loadfactorupto 2.6%
  • Decrease in spillupto 3.3%.
  • Profitincreaseupto 14.5%.

Finally,

Thescenario-aggregationbasedapproachhandleseffects of fluctuatingpassengerdemand on fleet-planningprocessandgeneratesflexiblefleetconfigurationsthatsupportdynamicassignments.