Solving Airline’s Pilot – Copilot Rostering Problem by Successive Bipartite Weighted Matching

In large airlines, the planning and scheduling of aircrafts and crews is a very important operation. It starts from the analysis of the customers’ demands, passes the stages including timetable construction, fleet planning, and crew pairing, finally ends up with crew rostering. During the past decades, researches had been focused on two complex problems: crew pairing problem and crew rostering problem. Since the crew pairing problem is more related to the cost of airlines, it received much more attentions than the crew rostering problem. The aim of this paper is to identify, formulate and solve a crew rostering problem common in large airlines. In this paper, we model the crew rostering problem as a multi-objective 0-1 integer programming with some non-deterministic parameters. While satisfying the constraints stemming from the nature of the problem and the airlines’ rules and regulations, the objectives are to let all pilots in same fleet at same hub have approximately equal cumulative flying time, let all copilots in same fleet at same hub have approximately equal cumulative flying time as well. Due to its large scale and NP-hardness, we build a sequential constructive heuristic algorithm to find satisfactory solution. The basic idea is to sequentially decompose the dispatching process into a series of subphases. In each subphase, we partition the partial rostering problem into three subproblems. Each of the three subproblems can be formulated as a bipartite weighted matching problem. We design a network flow method to solve this bipartite weighted matching problem. In the numerical simulation, the overall algorithm is tested for its effectiveness and efficiency.