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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Vydané v:	Transportation research. Part B: methodological Ročník 114; s. 39 - 67
Hlavní autori:	Şafak, Özge, Çavuş, Özlem, Selim Aktürk, M.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Oxford Elsevier Ltd 01.08.2018 Elsevier Science Ltd
Predmet:	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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Abstract	•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.
AbstractList	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. •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.
Author	Çavuş, Özlem Selim Aktürk, M. Şafak, Özge
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Snippet	•We propose a novel mixed-integer three-stage stochastic nonlinear programming model.•We suggest a scenario group-wise decomposition algorithm to provide lower... We propose a three-stage stochastic programming model which determines flight timing, fleeting and routing decisions while considering the randomness of demand...
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SubjectTerms	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
Title	Multi-stage airline scheduling problem with stochastic passenger demand and non-cruise times
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