Modeling and Solving A Crew Assignment Problem in Air Transportation

Ecole Polytechnique de Tunisie, CORG-ROI, BP 743, 2078, La Marsa, Tunisia
European Journal of Operational Research (Impact Factor: 2.36). 11/2006; 175(1):187-209. DOI: 10.1016/j.ejor.2004.11.028
Source: DBLP


A typical problem arising in airline crew management consists in optimally assigning the required crew members to each flight segment of a given time period, while complying with a variety of work regulations and collective agreements. This problem called the Crew Assignment Problem (CAP) is currently decomposed into two independent sub-problems which are modeled and solved sequentially: (a) the well-known Crew Pairing Problem followed by (b) the Working Schedules Construction Problem. In the first sub-problem, a set of legal minimum-cost pairings is constructed, covering all the planned flight segments. In the second sub-problem, pairings, rest periods, training periods, annual leaves, etc. are combined to form working schedules which are then assigned to crew members.In this paper, we present a new approach to the Crew Assignment Problem arising in the context of airline companies operating short and medium haul flights. Contrary to most previously published work on the subject, our approach is not based on the concept of crew-pairings, though it is capable of handling many of the constraints present in crew-pairing-based models. Moreover, contrary to crew-pairing-based approaches, one of its distinctive features is that it formulates and solves the two sub-problems (a) and (b) simultaneously for the technical crew members (pilots and officers) with specific constraints. We show how this problem can be formulated as a large scale integer linear program with a general structure combining different types of constraints and not exclusively partitioning or covering constraints as usually suggested in previous papers. We introduce then, a formulation enhancement phase where we replace a large number of binary exclusion constraints by stronger and less numerous ones: the clique constraints. Using data provided by the Tunisian airline company TunisAir, we demonstrate that thanks to this new formulation, the Crew Assignment Problem can be solved by currently available integer linear programming technology. Finally, we propose an efficient heuristic method based on a rounding strategy embedded in a partial tree search procedure.The implementation of these methods (both exact and heuristic ones) provides good solutions in reasonable computation times using CPLEX 6.0.2: guaranteed exact solutions are obtained for 60% of the test instances and solutions within 5% of the lower bound for the others.

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    • "Zeghal and Minoux (2006), Souai and Teghem (2009), and Gomes and Gualda (2010) proposed integrated strategies in which the rosters of the crew members are formed from grouping the duty periods (instead of the pairings) with other activities, such as day offs, training periods, medical exams and others, thereby skipping the intermediate phase to obtain a pairing solution and leading to a more realistic solution. Zeghal and Minoux (2006) formulated the CAP as a large scale integer linear program, replacing the set partitioning (and covering) models. Since a feasible integer solution was not obtained in some test problems, the authors also proposed a heuristic approach based on a rounding strategy embedded in a partial tree-search procedure. "
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    ABSTRACT: A typical problem related to airline crew management consists of optimally assigning the required crew members to planned flights for a given period of time, while complying with a variety of labor regulations, safety rules and policies of the airline. This problem, called crew assignment problem (CAP), is of the NPHard class. So, it is usually divided into two independent subproblems, crew pairing problem (CPP) and crew rostering problem (CRP), modeled and solved sequentially. This division does not provide a global treatment to the CAP in terms of total cost and quality of the final solution. The state of the art involves the integrated solution of CAP, with both subproblems (CPP and CRP) solved simultaneously. It still requires high computational effort. Its combinatorial nature makes it difficult (or even impossible) to be solved by exact methods. The methodology proposed in this research provides an integrated solution of the CAP with heuristic procedures. The methodology was tested to solve instances related to small and medium-sized Brazilian airlines. The results were also compared with those obtained through an exact model adapted from the literature.
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    • "There are two different strategies used to solve crew scheduling problems. First, one solves the problem in just one phase (Crew pairing and crew rostering together) like in references [1] and [2]. However, the requirement of high calculation capabilities and an overlarge search space, reduces the probability of generating a feasible solution using an optimization algorithm. "
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    • "Com isso, a quantidade de variáveis do PPT é reduzida, já que o número de jornadas viáveis enumeradas é sempre da mesma ordem de grandeza que o número de voos, o que possibilita a sua enumeração completa em instâncias reais. Zeghal e Minoux (2006) destacaram que o modelo proposto considera apenas as regras e regulamentações aplicáveis ao contexto operacional da empresa TunisAir, porém novas restrições podem ser acrescentadas, o que evidentemente aumentaria a complexidade de solução integrada do PPT por métodos exatos. O modelo foi resolvido através do CPLEX 6.0.2, considerando 20 problemas reais da TunisAir (com no máximo 210 voos e 289 jornadas). "
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