Solving large scale crew scheduling problems

The crew pairing problem is posed as a set partitioning zero-one integer program. Variables are generated as legal pairings meeting all work rules. Dual values obtained from solving successive large linear program relaxations are used to prune the search tree. In this paper we present a graph based branching heuristic applied to a restricted set partitioning problem representing a collection of 'best' pairings. The algorithm exploits the natural integer properties of the crew pairing problem. Computational results are presented to show realized crew cost savings.