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1. Introduction
The airline industry is characterized by tight competitive market, high operational cost, variable passenger demand, heavy traffic, and strong regulations. In this situation, airline companies have to efficiently manage their resources that include flights, aircraft, and crews (Sherali et al., 2013a). In order to manage these resources, airline schedule planning problems are solved by the airline companies, while considering the vast number of regulations related to aircraft and crews that result in complex and nontractable problems. Consequently, airline scheduling is decomposed into four stages: the flight scheduling problem (FSP), the fleet assignment problem (FAP), the aircraft maintenance routing problem (AMRP), and finally the crew scheduling problem (CSP). Traditionally, these problems are solved sequentially, where the solution in each stage is used as an input for the subsequent stage, as shown in Figure 1.
Figure 1 describes the sequential operations that take place before the departure of an aircraft. At the beginning, the flight schedule is constructed considering marketing issues such as passenger demand and ticket price (Yan et al., 2007; Lee et al., 2007). Thereafter, each flight is covered by the specific aircraft type, and feasible maintenance routes are constructed for each fleet. These two steps are performed by fleet assignment (Rexing et al., 2000; Barnhart et al., 2002; Barnhart et al., 2009) and aircraft maintenance routing (AMR) (Gopalan and Talluri, 1998; Sriram and Haghani, 2003; Sarac et al., 2006; Başdere and Bilge, 2014). In the last stage, cabin crew and cockpit are assigned to each flight in order to form an anonymous pairing, while satisfying the regulations and contractual issues (Vance et al., 1997; Ehrgott and Ryan, 2002; Zeghal and Minoux, 2006; Muter et al., 2013). The generated pairings are grouped in order to form personal rosters, considering vacations and crew requests. Although there are interrelations between each stage, they are usually solved sequentially due to their complexity. The sequential approach leads to suboptimality solution, which means the solution is optimal in one stage and not in others. In order to avoid this problem, scholars now pay much attention to solving more integrated airline scheduling models so as to ameliorate the solution quality and the anticipated profit of the airline companies (Mercier et...