Náklady na posádky v aerolinkách jsou po nákladech na palivo druhé největší. Cílem aerolinky je zajistit bezpečný provoz s minimálním počtem posádek a tím optimalizovat náklady. Práce popisuje metodiku odhadu počtu posádek na roční období. Používá přiřazení, ve kterém je každému dnu člena posádky přiřazena činnost, kterou vykonává. V práci je popsán nelineární model, který využívá přiřazení a následně agreguje dny pro získání celkového počtu posádek. Model je řešen v programu Premium Solver Platform a Lingu 7.

Cette thèse développe des algorithmes pour les problèmes de plus court chemin sous cont-rain-tes de ressources, et les applique à l'optimisation des rotations des avions et des équipages d'une compagnie aérienne dans le cadre d'approches par génération de colonnes.Les problèmes de plus court chemin sous contraintes de ressources sont généralement résolus grâce à une énumération intelligente de tous les chemins non dominés. Les approches récentes utilisent des bornes sur les ressources des chemins pour éliminer des solutions partielles. L'efficacité de la méthode est conditionnée par la qualité des bornes utilisées. Notre principale contribution au domaine est l'introduction d'une procédure générique pour calculer des bornes qui s'applique à la plupart des problèmes de chemins sous contraintes, et en particulier les problèmes stochastiques. A cette fin, nous introduisons une généralisation du problème de plus court chemin sous contraintes dans laquelle les ressources des chemins appartiennent à un monoïde ordonné comme un treillis. La ressource d'un chemin est la somme des ressources de ses arcs, le terme somme désignant l'opérateur du monoïde. Le problème consiste à trouver parmi les chemins qui satisfont une contrainte donnée celui dont la ressource minimise une fonction de coût croissante de la ressource des chemins. Nous généralisons les algorithmes d'énumération à ce nouveau problème. La théorie des treillis nous permet de construire une procédure polynomiale pour trouver des bornes de qualité. L'efficacité pratique de la méthode est évaluée au travers d'une étude numérique détaillée sur des problèmes de chemins déterministes et stochastiques. Les procédures de calcul des bornes peuvent être interprétées comme des généralisations aux monoïdes ordonnés comme des treillis d'algorithmes de la littérature définis pour résoudre un problème de chemin pour lequel les ressources des chemins prennent leur valeur dans un semi-anneau.Nos algorithmes de chemins ont été appliqués avec succès au problème de crew pairing. Étant donné un ensemble de vols opérés par une compagnie aérienne, les problèmes d'aircraft routing et de crew pairing construisent respectivement les séquences de vols opérées par les avions et par les équipages de manière à couvrir tous les vols à moindre coût. Comme certaines séquences de vols ne peuvent être réalisées par un équipage que s'il reste dans le même avion, les deux problèmes sont liés. La pratique actuelle dans l'industrie aéronautique est de résoudre tout d'abord le problème d'aircraft routing, puis le problème de crew pairing, ce qui aboutit à une solution non-optimale. Des méthodes de résolution pour le problème intégré ont été développées ces dix dernières années. Nous proposons une méthode de résolution pour le problème intégré reposant sur deux nouveaux ingrédients : un programme linéaire en nombre entier compact pour le problème d'aircraft routing, ainsi que de nouveaux pour le problème esclave de l'approche usuelle par génération de colonnes du problème de crew pairing. Ces algorithmes pour le problème esclave sont une application de nos algorithmes pour le problème de plus court chemin sous contraintes. Nous généralisons ensuite cette approche de manière à prendre en compte des contraintes de probabilités sur la propagation du retard. Ces algorithmes permettent de résoudre quasiment à l'optimum les instances industrielles d'Air France / This thesis develops algorithms for resource constrained shortest path problems, and uses them to solve the pricing subproblems of column generation approaches to some airline operations problems.Resource constrained shortest path problems are usually solved using a smart enumeration of the non-dominated paths. Recent improvements of these enumeration algorithms rely on the use of bounds on path resources to discard partial solutions. The quality of the bounds determines the performance of the algorithm. Our main contribution to the topic is to introduce a standard procedure to generate bounds on paths resources in a general setting which covers most resource constrained shortest path problems, among which stochastic versions. In that purpose, we introduce a generalization of the resource constrained shortest path problem where the resources are taken in a lattice ordered monoid. The resource of a path is the monoid sum of the resources of its arcs. The problem consists in finding a path whose resource minimizes a non-decreasing cost function of the path resource among the paths that satisfy a given constraint. Enumeration algorithms are generalized to this framework. We use lattice theory to provide polynomial procedures to find good quality bounds. The efficiency of the approach is proved through an extensive numerical study on deterministic and stochastic path problems. Interestingly, the bounding procedures can be seen as generalizations to lattice ordered monoids of some algebraic path problem algorithms which initially work with resources in a semiring.Given a set of flight legs operated by an airline, the aircraft routing and the crew pairing problem build respectively the sequences of flight legs operated by airplanes and crews at minimum cost. As some sequences of flight legs can be operated by crews only if they stay in the same aircraft, the two problems are linked. The current practice in the industry is to solve first the aircraft routing, and then the crew pairing problem, leading to a non-optimal solution. During the last decade, solution schemes for the integrated problem have been developed. We propose a solution scheme for the integrated problem based on two new ingredients: a compact integer program approach to the aircraft routing problem, and a new algorithm for the pricing subproblem of the usual column generation approach to the crew pairing problem, which is based on our resource constrained shortest path framework. We then generalize the algorithm to take into account delay propagation through probabilistic constraints. The algorithms enable to solve to near optimality Air France industrial instances

Crew pairing and vehicle routing are combinatorial optimization problems that have been studied for many years by researchers worldwide. The aim of this research work is to investigate effective methods for solving large scale crew pairing problems and vehicle routing problems. In the airline industry, to address the complex nature of crew pairing problems, we propose a duty tree method followed by a primal-dual subproblem simplex method. The duty tree approach captures the constraints that apply to crew pairings and generate candidate pairings taking advantage of various proposed strategies. A huge number of legal pairings are stored in the duty tree and can be enumerated. A set partitioning formulation is then constructed, and the problem is solved using a primal-dual subproblem simplex method tailored to the duty tree approach. Computational experiments are conducted to show the effectiveness of the methods. We also present our efforts addressing the capacitated vehicle routing problem (CVRP) that is the basic version of many other variants of the problem. We do not attempt to solve the CVRP instances that have been solved to optimality. Instead, we focus on investigating good solutions for large CVRP instances, with particular emphasis on those benchmark problems from the public online library that have not yet been solved to optimality by other researchers and determine whether we can find new best-known solutions. In this research, we propose a route network that can store a huge number of routes with all routes being legal, a set partitioning formulation that can handle many columns, and the primal-dual subproblem simplex method to find a solution. The computational results show that our proposed methods can achieve better solutions than the existing best-known solutions for some difficult instances. Upon convergence of the primal-dual subproblem simplex method on the giant-tour based networks, we use the near optimal primal and dual solution as well as solve the elementary shortest path problem with resource constraints to achieve the linear programming relaxation global optimal solution.

The air transportation market has been growing steadily for the past three decades since the airline deregulation in 1978. With competition also becoming more intense, airline companies have been trying to enhance their market shares and profit margins by composing favorable flight schedules and by efficiently allocating their resources of aircraft and crews so as to reduce operational costs. In practice, this is achieved based on demand forecasts and resource availabilities through a structured airline scheduling process that is comprised of four decision stages: schedule planning, fleet assignment, aircraft routing, and crew scheduling. The outputs of this process are flight schedules along with associated assignments of aircraft and crews that maximize the total expected profit. Traditionally, airlines deal with these four operational scheduling stages in a sequential manner. However, there exist obvious interdependencies among these stages so that restrictive solutions from preceding stages are likely to limit the scope of decisions for succeeding stages, thus leading to suboptimal results and even infeasibilities. To overcome this drawback, we first study the aircraft routing problem, and develop some novel modeling foundations based on which we construct and analyze an integrated model that incorporates fleet assignment, aircraft routing, and crew pairing within a single framework. Given a set of flights to be covered by a specific fleet type, the aircraft routing problem (ARP) determines a flight sequence for each individual aircraft in this fleet, while incorporating specific considerations of minimum turn-time and maintenance checks, as well as restrictions on the total accumulated flying time, the total number of takeoffs, and the total number of days between two consecutive maintenance operations. This stage is significant to airline companies as it directly assigns routes and maintenance breaks for each aircraft in service. Most approaches for solving this problem adopt set partitioning formulations that include exponentially many variables, thus requiring the design of specialized column generation or branch-and-price algorithms. In this dissertation, however, we present a novel compact polynomially sized representation for the ARP, which is then linearized and lifted using the Reformulation-Linearization Technique (RLT). The resulting formulation remains polynomial in size, and we show that it can be solved very efficiently by commercial software without complicated algorithmic implementations. Our numerical experiments using real data obtained from United Airlines demonstrate significant savings in computational effort; for example, for a daily network involving 344 flights, our approach required only about 10 CPU seconds for deriving an optimal solution. We next extend Model ARP to incorporate its preceding and succeeding decision stages, i.e., fleet assignment and crew pairing, within an integrated framework. We formulate a suitable representation for the integrated fleeting, routing, and crew pairing problem (FRC), which accommodates a set of fleet types in a compact manner similar to that used for constructing the aforementioned aircraft routing model, and we generate eligible crew pairings on-the-fly within a set partitioning framework. Furthermore, to better represent industrial practice, we incorporate itinerary-based passenger demands for different fare-classes. The large size of the resulting model obviates a direct solution using off-the-shelf software; hence, we design a solution approach based on Benders decomposition and column generation using several acceleration techniques along with a branch-and-price heuristic for effectively deriving a solution to this model. In order to demonstrate the efficacy of the proposed model and solution approach and to provide insights for the airline industry, we generated several test instances using historical data obtained from United Airlines. Computational results reveal that the massively-sized integrated model can be effectively solved in reasonable times ranging from several minutes to about ten hours, depending on the size and structure of the instance. Moreover, our benchmark results demonstrate an average of 2.73% improvement in total profit (which translates to about 43 million dollars per year) over a partially integrated approach that combines the fleeting and routing decisions, but solves the crew pairing problem sequentially. This improvement is observed to accrue due to the fact that the fully integrated model effectively explores alternative fleet assignment decisions that better utilize available resources and yield significantly lower crew costs. / Ph. D.