Browsing by Subject "Conic quadratic mixed integer programming"
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Item Open Access Airline rescheduling with aircraft unavailability period(Bilkent University, 2019-06) Yetimoğlu, Yücel NazAirlines design their initial schedules under the assumption that all resources will be available on time and ights will operate as planned. However, some disruptions occur due to mechanical failures and unexpected delays of maintenance, making the aircraft unavailable for a certain period of time. These deviations from the initial plan result in high operational costs in addition to the serious inconveniences experienced by passengers. In the literature, it is a common practice to develop sequential approaches at which aircraft and passenger recovery problems are consecutively handled. In this study, we address them simultaneously and propose an integrated math-heuristic framework with an aim to maximize the profit of the airline. In the first phase, we develop a nonlinear mixed integer optimization model for aircraft recovery and utilize conic programming approach to mitigate computational difficulty. We incorporate cancellation and re-routing decisions for ights utilizing cruise time controllability which results in nonlinear fuel burn and CO2 emission cost functions. In the second phase, we develop a passenger recovery algorithm that makes individual itinerary based recovery decisions under the seat capacity restrictions and provide realistic cancellation cost formulations. Lastly, we propose an integrated search algorithm to maintain the integration between two phases through fixing assignment variables in the first phase. We compare the performance of the proposed algorithm to the base policy where all disrupted ights are directly cancelled. We observe improvements in terms of profit and the number of overnight passengers.Item Open Access Flight network-based approach for integrated airline recovery with cruise speed control(Institute for Operations Research and the Management Sciences (I N F O R M S), 2017) Arıkan, U.; Gürel, S.; Aktürk, M. S.Airline schedules are generally tight and fragile to disruptions. Disruptions can have severe effects on existing aircraft routings, crew pairings, and passenger itineraries that lead to high delay and recovery costs. A recovery approach should integrate the recovery decisions for all entities (aircraft, crew, passengers) in the system as recovery decisions about an entity directly affect the others' schedules. Because of the size of airline flight networks and the requirement for quick recovery decisions, the integrated airline recovery problem is highly complex. In the past decade, an increasing effort has been made to integrate passenger and crew related recovery decisions with aircraft recovery decisions both in practice and in the literature. In this paper, we develop a new flight network based representation for the integrated airline recovery problem. Our approach is based on the flowof each aircraft, crewmember, and passenger through the flight network of the airline. The proposed network structure allows common recovery decisions such as departure delays, aircraft/crew rerouting, passenger reaccommodation, ticket cancellations, and flight cancellations. Furthermore, we can implement aircraft cruise speed (flight time) decisions on the flight network. For the integrated airline recovery problem defined over this network, we propose a conic quadratic mixed integer programming formulation that can be solved in reasonable CPU times for practical size instances. Moreover, we place a special emphasis on passenger recovery. In addition to aggregation and approximation methods, our model allows explicit modeling of passengers and evaluating a more realistic measure of passenger delay costs. Finally, we propose methods based on the proposed network representation to control the problem size and to deal with large airline networks. © 2017 INFORMS.Item Open Access Integrated aircraft and passenger recovery with cruise time controllability(Springer, 2016) Arıkan, U.; Gürel, S.; Aktürk, M. S.Disruptions in airline operations can result in infeasibilities in aircraft and passenger schedules. Airlines typically recover aircraft schedules and disruptions in passenger itineraries sequentially. However, passengers are severely affected by disruptions and recovery decisions. In this paper, we present a mathematical formulation for the integrated aircraft and passenger recovery problem that considers aircraft and passenger related costs simultaneously. Using the superimposition of aircraft and passenger itinerary networks, passengers are explicitly modeled in order to use realistic passenger related costs. In addition to the common routing recovery actions, we integrate several passenger recovery actions and cruise speed control in our solution approach. Cruise speed control is a very beneficial action for mitigating delays. On the other hand, it adds complexity to the problem due to the nonlinearity in fuel cost function. The problem is formulated as a mixed integer nonlinear programming (MINLP) model. We show that the problem can be reformulated as conic quadratic mixed integer programming (CQMIP) problem which can be solved with commercial optimization software such as IBM ILOG CPLEX. Our computational experiments have shown that we could handle several simultaneous disruptions optimally on a four-hub network of a major U.S. airline within less than a minute on the average. We conclude that proposed approach is able to find optimal tradeoff between operating and passenger-related costs in real time.