@phdthesis{Dovica2014, author = {Dovica, Ivan}, title = {Robust tail assignment}, year = {2014}, abstract = {The first part of this thesis is devoted to the general problem of stochastic shortest path problem. It is about searching for the shortest path in a graph in which arc lengths are uncertain and specified by continuous random variables. This problem is at the core of various applications, especially in robust transportation planning where paths correspond to aircraft, train, or bus rotations, crew duties or rosters, etc. We propose a novel solution method based on a discretisation of random variables which is applicable to any class of continuous random variables. We also give bounds on the approximation error of the discretised path lengths compared to the continuous path lengths. In addition, we provide theoretical results for the computational complexity of this method. In the second part we apply this method to a real world airline transportation problem: the so-called tail assignment problem. The goal of the tail assignment problem is to construct aircraft rotations, routes consisting of flight segments, for a set of individual aircraft in order to cover a set of flight segments (legs) while considering operational constraints of each individual aircraft as well as short- to long-term individual maintenance requirements. We state a stochastic programming formulation of this problem and we show how to solve it efficiently by using our method within a column generation framework. We show the gain of our stochastic approach in comparison to standard KPI in terms of less propagated delay and thus less operational costs without growth of computational complexity. A key point of our complex approach to robust optimisation problem is the fit of the underlying stochastic model with reality. We propose a delay propagation model that is realistic, not overfitted, and can therefore be used for forecasting purposes. We benchmark our results using extensive simulation. We show a significant decrease of arrival delays and thus monetary savings on average as well as in the majority of our disruption scenarios. We confirm these benefits in even more life-like benchmarks as simulation where recovery actions are taken and in scenarios which use historical delays directly instead of the stochastic model.}, language = {en} } @article{Maher2015, author = {Maher, Stephen J.}, title = {A novel passenger recovery approach for the integrated airline recovery problem}, volume = {57}, journal = {Computers \& Operations Research}, doi = {10.1016/j.cor.2014.11.005}, pages = {123 -- 137}, year = {2015}, abstract = {Schedule disruptions require airlines to intervene through the process of recovery; this involves modifications to the planned schedule, aircraft routings, crew pairings and passenger itineraries. Passenger recovery is generally considered as the final stage in this process, and hence passengers experience unnecessarily large impacts resulting from flight delays and cancellations. Most recovery approaches considering passengers involve a separately defined module within the problem formulation. However, this approach may be overly complex for recovery in many aviation and general transportation applications. This paper presents a unique description of the cancellation variables that models passenger recovery by prescribing the alternative travel arrangements for passengers in the event of flight cancellations. The results will demonstrate that this simple, but effective, passenger recovery approach significantly reduces the operational costs of the airline and increases passenger flow through the network. The integrated airline recovery problem with passenger reallocation is solved using column-and-row generation to achieve high quality solutions in short runtimes. An analysis of the column-and-row generation solution approach is performed, identifying a number of enhancement techniques to further improve the solution runtimes.}, language = {en} } @misc{BorndoerferDovicaNowaketal.2010, author = {Bornd{\"o}rfer, Ralf and Dovica, Ivan and Nowak, Ivo and Schickinger, Thomas}, title = {Robust Tail Assignment}, organization = {Zuse-Institut Berlin}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11707}, number = {10-08}, year = {2010}, abstract = {We propose an efficient column generation method to minimize the probability of delay propagations along aircraft rotations. In this way, delay resistant schedules can be constructed. Computational results for large-scale real-world problems demonstrate substantial punctuality improvements. The method can be generalized to crew and integrated scheduling problems.}, language = {en} } @article{FroylandMaherWu2014, author = {Froyland, Gary and Maher, Stephen J. and Wu, Cheng-Lung}, title = {The recoverable robust tail assignment problem}, volume = {48}, journal = {Transportation Science}, number = {3}, doi = {10.1287/trsc.2013.0463}, pages = {351 -- 372}, year = {2014}, abstract = {Schedule disruptions are commonplace in the airline industry with many flight-delaying events occurring each day. Recently there has been a focus on introducing robustness into airline planning stages to reduce the effect of these disruptions. We propose a recoverable robustness technique as an alternative to robust optimisation to reduce the effect of disruptions and the cost of recovery. We formulate the recoverable robust tail assignment problem (RRTAP) as a stochastic program, solved using column generation in the master and subproblems of the Benders' decomposition. We implement a two-phase algorithm for the Benders' decomposition and identify pareto-optimal cuts. The RRTAP includes costs due to flight delays, cancellation, and passenger rerouting, and the recovery stage includes cancellation, delay, and swapping options. To highlight the benefits of simultaneously solving planning and recovery problems in the RRTAP we compare our tail assignment solution against current approaches from the literature. Using airline data we demonstrate that by developing a better tail assignment plan via the RRTAP framework, one can reduce recovery costs in the event of a disruption.}, language = {en} } @article{MaherDesaulniersSoumis2014, author = {Maher, Stephen J. and Desaulniers, Guy and Soumis, Francois}, title = {Recoverable robust single day aircraft maintenance routing problem}, volume = {51}, journal = {Computers \& Operations Research}, doi = {10.1016/j.cor.2014.03.007}, pages = {130 -- 145}, year = {2014}, abstract = {Aircraft maintenance planning is of critical importance to the safe and efficient operations of an airline. It is common to solve the aircraft routing and maintenance planning problems many months in advance, with the solution spanning multiple days. An unfortunate consequence of this approach is the possible infeasibility of the maintenance plan due to frequent perturbations occurring in operations. There is an emerging concept that focuses on the generation of aircraft routes for a single day to ensure maintenance coverage that night, alleviating the effects of schedule perturbations from preceding days. In this paper, we present a novel approach to ensure that a sufficient number of aircraft routes are provided each day so maintenance critical aircraft receive maintenance that night. By penalising the under supply of routes terminating at maintenance stations from each overnight airport, we construct a single day routing to provide the best possible maintenance plan. This single day aircraft maintenance routing problem (SDAMRP) is further protected from disruptions by applying the recoverable robustness framework. To efficiently solve the recoverable robust SDAMRP acceleration techniques, such as identifying Pareto-optimal cuts and a trust region approach, have been applied. The SDAMRP is evaluated against a set of flight schedules and the results demonstrate a significantly improved aircraft maintenance plan. Further, the results demonstrate the magnitude of recoverability improvement that is achieved by employing recoverable robustness to the SDAMRP.}, language = {en} } @article{Maher2015, author = {Maher, Stephen J.}, title = {Solving the integrated airline recovery problem using column-and-row generation}, volume = {50}, journal = {Transportation Science}, number = {1}, doi = {10.1287/trsc.2014.0552}, pages = {216 -- 239}, year = {2015}, abstract = {Airline recovery presents very large and difficult problems requiring high quality solutions within very short time limits. To improve computational performance, the complete airline recovery problem is generally formulated as a series of sequential stages. While the sequential approach greatly simplifies the complete recovery problem, there is no guarantee of global optimality or solution quality. To address this, there has been increasing interest in the development of efficient solution techniques to solve an integrated recovery problem. In this paper, an integrated airline recovery problem is proposed by integrating the schedule, crew and aircraft recovery stages. To achieve short runtimes and high quality solutions, this problem is solved using column-and-row generation. Column-and-row generation achieves an improvement in solution runtimes by reducing the problem size and thereby achieving a faster execution of each LP solve. Further, the results demonstrate that a good upper bound achieved early in the solution process, indicating an improved solution quality with the early termination of the algorithm. This paper also details the integration of the row generation procedure with branch-and-price, which is used to achieve integral optimal solutions. The benefits of applying column-and-row generation to solve the integrated recovery problem are demonstrated with a comparison to a standard column generation technique.}, language = {en} } @misc{MaherDesaulniersSoumis2015, author = {Maher, Stephen J. and Desaulniers, Guy and Soumis, Francois}, title = {The tail assignment problem with look-ahead maintenance constraints}, issn = {1438-0064}, doi = {10.1016/j.ejor.2017.06.041}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-56717}, year = {2015}, abstract = {The tail assignment problem is a critical part of the airline planning process that assigns specific aircraft to sequences of flights, called lines-of-flight, to be operated the next day. The aim of this paper is to develop an operationally flexible tail assignment that satisfies short-range---within the next three days---aircraft maintenance requirements and performs the aircraft/flight gate assignment for each input line-of-flight. While maintenance plans commonly span multiple days, the related tail assignment problems can be overly complex and provide little recourse in the event of schedule perturbations. The presented approach addresses operational uncertainty by extending the one-day routes aircraft maintenance routing approach to satisfy maintenance requirements explicitly for the current day and implicitly for the subsequent two days. A mathematical model is presented that integrates the gate assignment and maintenance planning problems. To increase the satisfaction of maintenance requirements, an iterative algorithm is developed that modifies the fixed lines-of-flight provided as input to the tail assignment problem. The tail assignment problem and iterative algorithm are demonstrated to effectively satisfy maintenance requirements within appropriate run times using input data collected from three different airlines.}, language = {en} }