Multi-stage airline scheduling problem with stochastic passenger demand and non-cruise times

•We propose a novel mixed-integer three-stage stochastic nonlinear programming model.•We suggest a scenario group-wise decomposition algorithm to provide lower and upper bounds.•We present a cutting plane algorithm to solve scenario group subproblems by utilizing second order cone duality.•Incorpora...

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Veröffentlicht in:Transportation research. Part B: methodological Jg. 114; S. 39 - 67
Hauptverfasser: Şafak, Özge, Çavuş, Özlem, Selim Aktürk, M.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Oxford Elsevier Ltd 01.08.2018
Elsevier Science Ltd
Schlagworte:
Aircraft
Aircraft routing
Airline operations
Airline scheduling
Algorithms
Commercial aircraft
Conic integer programming
Costs
Cruise speed control
Decision trees
Emissions
Fleet assignment
Flight
Mathematical models
Mixed integer
Multi-stage stochastic programming
Optimization
Passengers
Randomness
Routing
Stochastic models
Stochastic programming
Travel demand
Upper bounds
Aircraft routing
Multi-stage stochastic programming
Fleet assignment
Conic integer programming
Cruise speed control
Airline scheduling
ISSN:0191-2615, 1879-2367
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Zusammenfassung:•We propose a novel mixed-integer three-stage stochastic nonlinear programming model.•We suggest a scenario group-wise decomposition algorithm to provide lower and upper bounds.•We present a cutting plane algorithm to solve scenario group subproblems by utilizing second order cone duality.•Incorporating operational level decisions leads to important cost savings over classical two-stage stochastic approaches. We propose a three-stage stochastic programming model which determines flight timing, fleeting and routing decisions while considering the randomness of demand and non-cruise times. Our model differs from the existing two-stage stochastic models by considering not only flight timing and potential passenger demand, but also expected operational expenses, such as fuel burn and carbon emission costs. We include aircraft cruise speed decisions to compensate for non-cruise time variability so as to satisfy the time requirements of the passenger connections. We handle nonlinear functions of fuel and emission costs associated with cruise speed adjustments by utilizing mixed integer second order cone programming. Because the three-stage stochastic model leads to a large decision tree and can be very time-consuming to solve optimally, we suggest a scenario group-wise decomposition algorithm to obtain lower and upper bounds for the optimal value of the proposed model. The lower and upper bounds are obtained by solving a number of group subproblems, which are similar to proposed multi-stage stochastic model defined over a reduced number of scenarios. We suggest a cutting plane algorithm, along with improvements, to efficiently solve each group subproblem. In the numerical experiments, we provide a significant cost savings over two-stage stochastic programming and deterministic approaches.
Bibliographie:ObjectType-Article-1
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ISSN:0191-2615
1879-2367
DOI:10.1016/j.trb.2018.05.012