Solving a robust airline crew pairing problem with column generation

In this study, we solve a robust version of the airline crew pairing problem. Our concept of robustness was partially shaped during our discussions with small local airlines in Turkey which may have to add a set of extra flights into their schedule at short notice during operation. Thus, robustness in this case is related to the ability of accommodating these extra flights at the time of operation by disrupting the original plans as minimally as possible. We focus on the crew pairing aspect of robustness and prescribe that the planned crew pairings incorporate a number of predefined recovery solutions for each potential extra flight. These solutions are implemented only if necessary for recovery purposes and involve either inserting an extra flight into an existing pairing or partially swapping the flights in two existing pairings in order to cover an extra flight. The resulting mathematical programming model follows the conventional set covering formulation of the airline crew pairing problem typically solved by column generation with an additional complication. The model includes constraints that depend on the columns due to the robustness consideration and grows not only column-wise but also row-wise as new columns are generated. To solve this dicult model, we propose a row and column generation approach. This approach requires a set of modifications to the multi-label shortest path problem for pricing out new columns (pairings) and various mechanisms to handle the simultaneous increase in the number of rows and columns in the restricted master problem during column generation. We conduct computational experiments on a set of real instances compiled from a local airline in Turkey

Pricing in column generation for a robust airline crew pairing problem

The crew pairing problem is to find the least costly set of pairings so that each flight given in the flight schedule is covered. In this study, the robust crew pairing problem is considered. That is, the selected pairings cover the regular flights and also provide solutions to cover some extra flights which may be introduced into the flight schedule during the operation at a later point in time. The crew pairing problem is usually solved by column generation in which the pricing subproblem becomes a multi-label shortest path problem. For the robust crew pairing problem the multi-label shortest path problem requires some modifications to solve two column generation approaches proposed by Çoban [10]. These modifications of the pricing problem with associated labels and the domination rules are presented. The complexity of the multi-label shortest path problem grows exponentially as the number of flights (nodes) in the flight schedule increases. This curse of dimensionality is solved by using approximate and exact pruning rules. Also, a buffer column pool is formed as an intermediate step in order to find a negative reduced cost pairing without solving the multi-label shortest path problem at every iteration of the column generation algorithm. In the multi-label shortest path problem, the approximate rules based on the score-calculation are used for early pruning of the paths on the processed nodes. The optimal solution may be missed because of the coarse structure of the approximate rules. When a pairing that improves the objective function cannot be found by applying the approximate rules, we switch to the exact pruning. Another method is using a hybrid approach that applies both approximate and exact rules in the same iteration to find the optimal solution. The performance of our solution approach is demonstrated through a computational study by using actual data from a local airline

Un modelo integrado para el enrutamiento de aeronaves y la programación de la tripulación: Relajación lagrangiana y algoritmo metaheurístico

[EN] Airline optimization is a significant problem in recent researches and airline industryl as it can determine the level of service, profit and competition status of the airline. Aircraft and crew are expensive resources that need efficient utilization. This paper focuses simultaneously on two major issues including aircraft maintenance routing and crew scheduling. Several key issues such as aircraft replacement, fairly night flights assignment and long-life aircrafts are considered in this model. We used the flight hours as a new framework to control aircraft maintenance. At first, an integrated mathematical model for aircraft routing and crew scheduling problems is developed with the aim of cost minimization. Then, Lagrangian relaxation and Particle Swarm Optimization algorithm (PSO) are used as the solution techniques. To evaluate the efficiency of solution approaches, model is solved with different numerical examples in small, medium and large sizes and compared with GAMS output. The results show that Lagrangian relaxation method provides better solutions comparing to PSO and also has a very small gap to optimum solution.[ES] La optimización de aerolíneas es un problema importante en investigaciones recientes e industria de aerolíneas, ya que puede determinar el nivel de servicio, el beneficio y el estado de competencia de la aerolínea. Las aeronaves y la tripulación son recursos costosos que necesitan una utilización eficiente. Este artículo se centra simultáneamente en dos cuestiones principales, incluyendo el enrutamiento de mantenimiento de aeronaves y la programación de la tripulación. En este modelo se consideran varios temas clave, como el reemplazo de aeronaves, la asignación de vuelos nocturnos y los aviones envejecidos. Usamos las horas de vuelo como un nuevo marco para controlar el mantenimiento de las aeronaves. Al principio, se desarrolla un modelo matemático integrado para el enrutamiento de aeronaves y los problemas de programación de la tripulación con el objetivo de la minimización de costos. A continuación, se utilizan como técnicas de solución la relajación lagran-giana y el algoritmo “Particle Swarm Optimization” (PSO). Para evaluar la eficiencia de los en-foques de la solución, el modelo se resuelve con diferentes ejemplos numéricos en tamaños pequeños, medianos y grandes y se compara con la salida GAMS. Los resultados muestran que el método de relajación lagrangiana proporciona mejores soluciones en comparación con PSO y también tiene una pequeña diferencia para una solución óptimaMirjafari, M.; Rashidi Komijan, A.; Shoja, A. (2020). An integrated model for aircraft routing and crew scheduling: Lagrangian Relaxation and metaheuristic algorithm. 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Operational aircraft maintenance routing problem with remaining time consideration, European Journal of Operational Research, Volume 235, Pages 315-328. https://doi.org/10.1016/j.ejor.2013.10.066Bazargan, Massoud (2010). Airline Operations and scheduling second edition, Embry-Riddle Aeronautical University, USA, Ashgate publishing limite.Belien, Jeroen, Demeulemeester, Eric and Brecht (2010). Integrated staffing and scheduling for an aircraft line maintenance problem, HUB RESEARCH PAPER Economics & Management.Ben Ahmed, M., Zeghal Mansour, Farah and Haouari, Mohamed (2018). Robust integrated maintenance aircraft routing and crew pairing, Journal of Air Transport Management, Volume 73, Pages 15-31. https://doi.org/10.1016/j.jairtraman.2018.07.007Ben Ahmed, M., Zeghal Mansour, F., Haouari, M. (2017). 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A robust mathematical model and heuristic algorithms for integrated aircraft routing and scheduling, with consideration of fleet assignment problem, Journal of Air Transport Management, Volume 58, Pages 21-30. https://doi.org/10.1016/j.jairtraman.2016.08.008Jiang, H., Barnhart, C. (2009) Dynamic airline scheduling, Transport. Sci, 43(3), Pages 336-354. https://doi.org/10.1287/trsc.1090.0269Kasirzadeh, A., Saddoune, M., Soumis, F. (2015). Airline crew scheduling: models, algorhitms and data sets, Euro Journal on Transportation and Logistics, 6(2), Pages 111-137. https://doi.org/10.1007/s13676-015-0080-xLacasse-Guay, E., Desaulniers, G., Soumis, F. (2010). Aircraft routing under different business processes, J. Air Transport. Manag, 16(5), Pages 258-263. https://doi.org/10.1016/j.jairtraman.2010.02.001Muter, İbrahim, Birbil, Ş. İlker, Bülbül, Kerem, Şahin, Güvenç,Yenigün, Hüsnü, Taş,Duygu andTüzün, Dilek (2013). Solving a robust airline crew pairing problem with column generation, Computers & Operations Research, Volume 40, Issue 3, Pages 815-830. https://doi.org/10.1016/j.cor.2010.11.005Saddoune, Mohammed, Desaulniers, Guy, Elhallaoui, Issmail and François Soumis (2011). Integrated airline crew scheduling: A bi-dynamic constraint aggregation method using neighborhoods, European Journal of Operational Research, Volume 212, Pages 445-454. https://doi.org/10.1016/j.ejor.2011.02.009Safaei, Nima and K.S.Jardine, Andrew (2018). Aircraft routing with generalized maintenance constraints, Omega, Volume 80, Pages 111-122. https://doi.org/10.1016/j.omega.2017.08.013Shao Shengzhi (2012). Integrated Aircraft Fleeting, Routing, and Crew Pairing Models and Algorithms for the Airline Industry, Faculty of the Virginia Polytechnic Institute and State University In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Industrial and Systems Engineering.Shao, S., Sherali, H.D., Haouari, M. (2017). A novel model and decomposition approach for the integrated airline fleet assignment, aircraft routing, crew pairing problem, Transport. Sci, 51(1), Pages 233-249. https://doi.org/10.1287/trsc.2015.0623Sherali, H.D., Bish, E.K., Zhu, X. (2006). Airline fleet assignment concepts, models and algorithms, Eur. J. Oper. Res, 172(1), Pages 1-30. https://doi.org/10.1016/j.ejor.2005.01.056Warburg, V., Hansen, T.G., Larsen, A., Norman, H., Andersson, E. (2008). Dynamic airline scheduling: an analysis of potentials of refleeting and retiming, J. Air Transport. Manag. 14(4), Pages 163-167. https://doi.org/10.1016/j.jairtraman.2008.03.004Yan, C. and Kung, J. (2018). 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Reliable reserve-crew scheduling for airlines

We study the practical setting in which regular- and reserve-crew schedules are dynamically maintained up to the day of executing the schedule. At each day preceding the execution of the schedule, disruptions occur due to sudden unavailability of personnel, making the planned regular and reserve-crew schedules infeasible for its execution day. This paper studies the fundamental question how to repair the schedules’ infeasibility in the days preceding the execution, taking into account labor regulations. We propose a robust repair strategy that maintains flexibility in order to cope with additional future disruptions. The flexibility in reserve-crew usage is explicitly considered through evaluating the expected shortfall of the reserve-crew schedule based on a Markov chain formulation. The core of our approach relies on iteratively solving a set-covering formulation, which we call the Robust Crew Recovery Problem, which encapsulates this flexibility notion for reserve crew usage. A tailored branch-and-price algorithm is developed for solving the Robust Crew Recovery Problem to optimality. The corresponding pricing problem is efficiently solved by a newly developed pulse algorithm. Based on actual data from a medium-sized hub-and-spoke airline, we show that embracing our approach leads to fewer flight cancellations and fewer last-minute alterations, compared to repairing disrupted schedules without considering our robust measure.</p

Reliable Reserve-Crew Scheduling for Airlines

We study the practical setting in which regular- and reserve-crew schedules are dynamically maintained up to the day of executing the schedule. At each day preceding the execution of the schedule, disruptions occur due to sudden unavailability of personnel, making the planned regular and reserve-crew schedules infeasible for its execution day. This paper studies the fundamental question how to repair the schedules' infeasibility in the days preceding the execution, taking into account labor regulations. We propose a robust repair strategy that maintains flexibility in order to cope with additional future disruptions. The flexibility in reserve-crew usage is explicitly considered through evaluating the expected shortfall of the reserve-crew schedule based on a Markov chain formulation. The core of our approach relies on iteratively solving a set-covering formulation, which we call the Robust Crew Recovery Problem, which encapsulates this flexibility notion for reserve crew usage. A tailored branch-and-price algorithm is developed for solving the Robust Crew Recovery Problem to optimality. The corresponding pricing problem is efficiently solved by a newly developed pulse algorithm. Based on actual data from a medium-sized hub-and-spoke airline, we show that embracing our approach leads to fewer flight cancellations and fewer last-minute alterations, compared to repairing disrupted schedules without considering our robust measure