965 research outputs found
A decision support system for crew planning in passenger transportation using a flexible branch-and-price algorithm
This paper discusses a decision support system for airline and railway crew planning. The system is a state-of-the-art branch-and-price solver that is used for crew scheduling and crew rostering. We briefly discuss the mathematical background of the solver, of which most part is covered in the Operations Research literature. Crew scheduling is crew planning for one or a few days that results in crew duties or pairings, and crew rostering is crew planning for at least one week for individual crew members. Technical issues about the system and its implementation are covered in more detail, as well as several applications. In particular, we focus on
Trois variantes du problĂšme de rotations pour une approche semi-intĂ©grĂ©e de la planification dâhoraires de personnel aĂ©rien
RĂSUMĂ: Les horaires dâĂ©quipages aĂ©riens sont gĂ©nĂ©ralement crĂ©Ă©s Ă lâaide dâune procĂ©dure sĂ©quentielle
impliquant la rĂ©solution de deux problĂšmes : le problĂšme de rotations dâĂ©quipage (CPP) et le problĂšme dâhoraires personnalisĂ©s (CRP). Le CPP crĂ©e un ensemble de rotations couvrant tous les vols dâune pĂ©riode donnĂ©e Ă coĂ»t minimum. Une rotation est une sĂ©quence de vols,
repositionnements, connexions et repos sâĂ©talant sur un ou plusieurs jours, et qui doit ĂȘtre assignĂ©e Ă un Ă©quipage composĂ© de plusieurs membres (pilote, copilote, agent de bord, etc.). Une rotation doit Ă©galement dĂ©buter et se terminer Ă la mĂȘme base (aĂ©roport oĂč sont affectĂ©s
des membres dâĂ©quipage), et satisfaire plusieurs contraintes imposĂ©es par les autoritĂ©s, ainsi que par les conventions collectives en place. Le CRP utilise les rotations crĂ©Ă©es par le CPP afin de construire un horaire personnalisĂ© pour chaque membre dâĂ©quipage. Les horaires
personnalisĂ©s doivent couvrir toutes les rotations et doivent Ă©galement satisfaire un ensemble de contraintes. Le principal dĂ©savantage de cette procĂ©dure sĂ©quentielle est que lâensemble de rotations gĂ©nĂ©rĂ©es par le CPP est gĂ©nĂ©ralement inadĂ©quat pour le CRP. Par exemple, certains vols doivent ĂȘtre opĂ©rĂ©s par un Ă©quipage possĂ©dant des qualifications spĂ©cifiques (e.g. des qualifications
de langues). Il est possible que dans la solution du CPP, ces vols soient dispersĂ©s dans un grand nombre de rotations, de sorte quâil soit impossible de crĂ©er un horaire respectant toutes les contraintes de qualification. IdĂ©alement, il serait prĂ©fĂ©rable de rĂ©soudre un seul problĂšme dâoptimisation intĂ©grant la crĂ©ation de rotations et la composition dâhoraires personnalisĂ©s. Bien que de telles approches aient Ă©tĂ© proposĂ©es dans la littĂ©rature, les temps de calcul nĂ©cessaires Ă lâobtention de solutions de qualitĂ© sont prohibitifs pour des instances de grande taille. Les approches semi-intĂ©grĂ©es permettent de surmonter certaines limites de lâapproche sĂ©quentielle, en Ă©vitant les consĂ©quences nĂ©gatives des approches intĂ©grĂ©es. Ces mĂ©thodes sont des variantes de lâapproche sĂ©quentielle dans lesquelles la formulation mathĂ©matique du CPP
est enrichie. LâidĂ©e est dâinclure dans le CPP certains Ă©lĂ©ments qui sont traditionnellement traitĂ©s au niveau du CRP, afin de crĂ©er des rotations qui sont mieux adaptĂ©es au CRP. Dans cette thĂšse, nous Ă©tudions trois variantes du CPP qui conviennent aux approches semiintĂ©grĂ©es.
Chacune de ces variantes est dĂ©finie comme un problĂšme de partitionnement dâensemble avec contraintes supplĂ©mentaires dans lequel les variables de dĂ©cision principales sont associĂ©es Ă des rotations rĂ©alisables. Ces problĂšmes sont rĂ©solus par un algorithme de gĂ©nĂ©ration de colonnes qui utilise un problĂšme maĂźtre restreint pour sĂ©lectionner les rotations et des sous-problĂšmes pour gĂ©nĂ©rer des rotations Ă ajouter au problĂšme maĂźtre restreint. Dans le premier sujet de cette thĂšse, nous nous intĂ©ressons au CPP avec contraintes de base (CPPBC). Les contraintes de base pĂ©nalisent le temps de travail excĂ©dentaire Ă chaque base, afin de distribuer Ă©quitablement la charge de travail entre les diffĂ©rentes bases. Bien que la plupart des logiciels commerciaux incorporent des contraintes de base dans le CPP, aucune
Ă©tude scientifique ne sâest penchĂ©e sur leur impact sur le processus de rĂ©solution du CPP. Nous montrons quâen prĂ©sence de contraintes de base assez restrictives, les algorithmes de branchement heuristiques traditionnellement utilisĂ©s peinent Ă obtenir une solution entiĂšre de qualitĂ©. Ces algorithmes prennent un plus grand nombre de dĂ©cisions de branchement risquĂ©es, ce qui nuit Ă la qualitĂ© des solutions obtenues. Afin de remĂ©dier Ă ce problĂšme, nous dĂ©veloppons un algorithme de branchement heuristique, appelĂ© branchement rĂ©trospectif,
qui Ă©limine certaines mauvaises dĂ©cisions de branchement lorsque lâĂ©cart relatif entre la meilleure solution fractionnaire et la solution fractionnaire au noeud courant est trop grand, et ce, sans avoir Ă effectuer de retour en arriĂšre. Lâalgorithme de branchement rĂ©trospectif est testĂ© sur sept instances hebdomadaires. Nous montrons que le branchement rĂ©trospectif permet
dâobtenir des solutions de meilleure qualitĂ© quâavec les autres mĂ©thodes de branchement couramment utilisĂ©es, en des temps de calcul raisonnables. Lâalgorithme de branchement rĂ©trospectif est prĂ©sentement implĂ©mentĂ© dans un logiciel commercial de planification aĂ©rienne, et a Ă©tĂ© utilisĂ© afin dâobtenir des solutions de qualitĂ© pour des problĂšmes contenant plusieurs dizaines de milliers de vols par mois. Dans le deuxiĂšme article de cette thĂšse, nous proposons une variante du CPP, appelĂ©e CPP
avec caractĂ©ristiques complexes (CPPCF), qui prend en compte les prĂ©fĂ©rences de vols et de vacances des membres dâĂ©quipage, dans le but dâaugmenter la satisfaction de ceux-ci envers leurs horaires. Pour ce faire, nous identifions six caractĂ©ristiques des rotations en lien avec les prĂ©fĂ©rences des membres dâĂ©quipage et qui pourraient ĂȘtre bĂ©nĂ©fiques au CRP. Un bonus est accordĂ© aux rotations contenant une ou plusieurs de ces caractĂ©ristiques, de maniĂšre Ă favoriser leur prĂ©sence dans la solution retournĂ©e. La mĂ©thode de rĂ©solution du CPP est adaptĂ©e au CPPCF : nous modifions les rĂšgles de dominance de lâalgorithme dâĂ©tiquetage utilisĂ© pour rĂ©soudre les sous-problĂšmes. Cela permet de rĂ©soudre les sous-problĂšmes du CPPCF en des temps raisonnables. LâefficacitĂ© de cette mĂ©thode est dĂ©montrĂ©e sur sept instances mensuelles. Nous montrons que les solutions obtenues Ă lâaide du CPPCF permettent la crĂ©ation
dâhoraires personnalisĂ©s dans lesquels un plus grand nombre de prĂ©fĂ©rences sont accordĂ©es, augmentant ainsi la satisfaction des membres dâĂ©quipage. Le troisiĂšme sujet de cette thĂšse porte sur les contraintes de langues. Il sâagit de contraintes sur les qualifications linguistiques pour lâĂ©quipage de certains vols. Cette recherche est fectuĂ©e dans un contexte de crĂ©ation dâhoraires pour les agents de bord. Le respect des
contraintes de langues est primordial pour les compagnies aĂ©riennes qui dĂ©sirent offrir un service sĂ©curitaire et de qualitĂ©. Or, les mĂ©thodes actuelles sont inadĂ©quates pour traiter les problĂšmes contenant un grand nombre de contraintes de langues et peu de membres dâĂ©quipage
parlant ces langues. En effet, le CPP ne prend pas en considération les contraintes de langues, de sorte que les vols qui possÚdent des contraintes de langues similaires se retrouvent distribuées dans un grand nombre de rotations. Nous formulons le CPP avec contraintes de
langues (CPPLC), une variante du CPP qui favorise le regroupement de plusieurs vols ayant les mĂȘmes contraintes de langues Ă lâintĂ©rieur dâune rotation. La difficultĂ© principale que pose cette variante est lâexplosion combinatoire du nombre de sous-problĂšmes. Nous mettons de lâavant une stratĂ©gie de sĂ©lection de sous-problĂšmes dans laquelle un petit ensemble de
sous-problĂšmes prometteurs est rĂ©solu Ă chaque itĂ©ration de gĂ©nĂ©ration de colonnes. Nous dĂ©veloppons Ă©galement une stratĂ©gie dâaccĂ©lĂ©ration permettant de diminuer significativement les temps de calcul au dĂ©but du processus de rĂ©solution. Nous montrons que lâutilisation
du CPPLC permet de rĂ©duire considĂ©rablement le nombre de contraintes de langues violĂ©es dans les horaires personnalisĂ©s. Bien que seules les contraintes de langues soient traitĂ©es, la mĂ©thode proposĂ©e pourrait Ă©galement sâappliquer Ă une grande variĂ©tĂ© de contraintes de
qualification, autant pour les agents de bord que pour les pilotes et copilotes.----------ABSTRACT: Aircrew scheduling is usually performed according to a two-step sequential procedure: crew pairing and crew rostering. While the crew pairing problem (CPP) finds a set of pairings that covers the legs of a given period at minimum cost, the crew rostering problem (CRP) uses
those pairings in order to create a personalized schedule for each crew member. A pairing is a sequence of legs, deadheads, connections and rests spanning over one or multiple days, and that can be assigned to a crew member. A pairing must also begin and end at the same crew base (airport where crew members are stationed), and comply with many rules imposed by airline authorities as well as collective agreements. The crew schedules must cover all
pairings, and are also subject to many regulations.
The main drawback of this sequential approach is that the set of pairings produced by the CPP is often ill-suited for the CRP. For instance, the CPP solution might assign too much work to a given base, resulting in an imbalance in the work distribution among the bases. Ideally, both steps would be integrated into a single optimization problem. Even though many such approaches have been proposed in the literature, computing times required to
solve those integrated problems are prohibitive, even for small-sized instances. Semi-integrated approaches are designed to overcome some limitations of the sequential approaches, without unduly increasing computing times. The main idea is to solve a variant of the CPP that includes some elements that traditionally belong in the CRP. This enables the CPP to create pairings that are better-suited for the CRP. In this thesis, we study three such CPP variants. Each variant is formulated as a setpartitionning problem with additional constraints, in which the main decision variables are associated with feasible pairings. These problems are solved by a column generation algorithm that uses a restricted master problem to select the pairings and multiple subproblems to generate the pairings to add to the restricted master problem. In the first subject of this thesis, we study the CPP with base constraints (CPPBC). Base constraints penalize excess work performed at each crew base in order to evenly distribute the workload among them. Although most commercial softwares include base constraints in
the CPP, no academic research has studied their impact on the existing solution methods. Preliminary tests show that when base constraints are very restrictive, the heuristic branching algorithms traditionally used struggle to find a good-quality integer solution: they take a larger number of risky branching decisions, which negatively impact the quality of the solutions. We develop a new heuristic branching scheme, called retrospective branching, that identifies risky branching decisions in the branch-and-bound tree, and removes poor branching decisions when the gap between the current and the best fractional solution becomes too large, without backtracking. The proposed method is tested on seven weekly instances. We show that the retrospective branching algorithm produces solutions of better quality than with the other commonly used branching methods, in reasonable computing times. The retrospective branching is currently implemented in a commercial crew scheduling software, and has been used to obtain good-quality solutions to monthly instances containing tens of thousands of legs. In the second subject of this thesis, we propose a variant of the CPP, called the CPP with
complex features (CPPCF) which takes into account legs and vacations preferences of crew members, with the aim of increasing the number of preferences awarded in the CRP, and thus, crew member satisfaction towards their schedule. We identify six pairing features related to
those preferences, which could be beneficial to the CRP. Pairings containing one or more of those features are granted a bonus in order to promote their presence in the solutions. The solution method for the CPP is adapted to the CPPCF. We modify the dominance rules of the labeling algorithm used to solve the subproblems, based on the values of new state resources. The proposed method is tested on seven monthly instances. We show that using
the CPPCF allows for a significantly higher number of awarded preferences in the CRP. The third subject of this thesis deals with language constraints â constraints on the language qualifications of the crew operating some legs. Satisfying these constraints is essential for airlines, which would otherwise have to pay high penalties, or even cancel some legs. Current methods are inadequate to deal with problems containing a large number of language constraints and few crew members with language qualifications. This is because the CPP does not account for language constraints, resulting in a spreading of the legs with language constraints among many pairings. We study this problem in the context of cabin crew scheduling. We formulate a CPP variant, called CPP with language constraints (CPPLC), which favors the grouping of legs with similar language constraints within the same pairing. The main challenge in solving the CPPLC is the combinatorial explosion in the number of subproblems. We put forward a subproblem selection strategy in which only a fraction of these subproblems are solved at each column generation iteration. We show that taking into account the language constraints in the CPP allows for a significant reduction of the number of language constraint violations in the CRP solutions. Although this study was conducted only for language constraints, the proposed method can be applied to many types of qualification constraints for cabin crews as well as pilots and copilots
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Integrating the fleet assignment model with uncertain demand
This thesis was submitted for the degree of Master of Philosophy and awarded by Brunel University.One of the main challenges facing the airline industry is planning under uncertainty, especially in the context of schedule disruptions. The robust models and solution algorithms that have been proposed and developed to handle the uncertain parameters will be discussed. Fleet assignment models (FAM) are used by many airlines to assign aircraft to fights in a schedule to maximize profit. In the context of FAM, the goal of robustness is to produce solutions that perform well relative to uncertainties in demand and operation. In this thesis, we introduce new FAMs (i.e. DFAM1 and DFAM2) that tackles the common problem associated with aircraft utilization. Subsequently, stochastic programming (SP) is presented as a method of choice for the research. Through the use of a two-stage SP with recourse technique, the DFAMs are extended to SP-FAMs (SP-FAM1 and SP-FAM2). The main distinction of the SP-FAM compared with other FAMs is that, given a stochastic passenger demand, it gives a strategic fleet assignment solution that hedges against all possible tactical solutions. In addition, we have a tactical solution for every scenario. In generating the demand scenarios, we use a network-simulation model embedded with a time-series engine that gives a snapshot of one week that is representative of any other week of the scheduling season. We later outline the approach of solving the SP-FAMs where the schedule is compacted through several preprocessing steps before inputting it into SAS-AMPL converter. The SAS-AMPL converter prepares all the data into readable AMPL format. Finally, we execute the optimizer using a FortMP solver (integrated in AMPL) that invokes branch-and-bound algorithm. We give a proof of concept using real data from a Middle East airline. Our investigations establish clear benefits of the recourse FAM compared to alternative models. Finally, we propose areas of future research to improve SP-FAM robustness through solution algorithms, revenue management (RM) effects, calibration of network-simulation models and system integration
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