Crew costs are the second largest direct operating cost of airlines next to fuel costs. Therefore much research has been devoted to the planning and scheduling of crews over the last thirty years. The planning and scheduling of crews is a highly complex combinatorial problem that consists two independent phases. The first phase is the Crew Pairing Problem (CPP), which concerns finding a set of tasks with minimum cost while satisfying the service requirements. The second phase is the Crew Rostering Problem (CRP), which concerns finding work assignment for crewmembers in a given period.
In this thesis we focus on a Crew Rostering Problem, where a main pilot and a copilot perform a task. The model is a variance minimization problem with 0-1 variables and constraints associated with ensuring collective agreements, rules and guaranteeing the production of flights service. We choose a sequential constructive method (heuristic) to solve this difficult combinatorial problem since: (1), minimizing quadratic function of discrete variables makes linear methods difficult to use, a monthly schedule for one hundred pilots can generate tens of thousands variables and millions of constraints; (2), it is a NP-hard problem, which means the CPU time of solution searching will grow exponentially as the instance dimension (the number of pilots and the number of tasks) increases. According to the characteristics of the model we propose, we do not find the global optimal solution; we find a satisfactory solution (or near optimal solution).
The basic idea in our heuristic method is to decompose the assigning process into many subphases day by day. Then in dealing with minimizing the objective function, two heristic principals are employed. Meanwhile, in coping with the constraints, a weighted matching model and its algorithm will be used. In the numerical simulation, the comprehensive method is tested for its effectiveness. We show that our method can produce a solution whose objective value is below a satisfactory bound.
