A new heuristic branching scheme for the crew pairing problem with base constraints

Airline crew scheduling is typically performed in two steps : crew pairing followed by crew assignment. The crew pairing problem (CPP) finds a set of pairings (sequences of flights separated by connections or rests starting and ending at the same crew base) that covers a set of flights at minimum cost. The crew assignment problem consists of assigning the crew members to these pairings to create their individual schedules. The main downside of this sequential approach is that the pairings generated in the first step are not all suitable for the crew assignment step, yielding poor-quality solutions. This paper studies an extension of the CPP that includes additional constraints limiting the total worked time at each crew base. This problem, called the CPP with base constraints (CPPBC), is designed to improve the coupling of the two scheduling steps. To solve the CPPBC, we develop four branch-and-price heuristics: three of them rely on known heuristic branching schemes, the other introduces a new branching method, called retrospective branching. This branching scheme is designed to detect and revise poor branching decisions made earlier in the search tree, without backtracking. We tested and compared these four heuristics on real-world datasets. Our results show that the algorithm with retrospective branching yields, most of the times, better-quality solutions than the other tested methods.