Hybrid column generation approaches for urban transit crew management problems

This article considers the overall crew management problem arising from the daily operation of an urban transit bus company that serves the metropolitan area of the city of Belo Horizonte, Brazil. Due to its intrinsic complexity, the problem is divided in two distinct subproblems: crew scheduling and crew rostering. We have investigated each of these problems using mathematical programming (MP) and constraint logic programming (CLP) approaches. In addition, we developed hybrid column generation algorithms for solving these problems, combining MP and CLP. The hybrid algorithms always performed better, when obtaining optimal solutions, than the two previous isolated approaches. In particular, they proved to be much faster for the scheduling problem. All the proposed algorithms have been implemented and tested over real-world data obtained from the aforementioned company. The coefficient matrix of the linear program associated with some instances of the scheduling problem contains tens of millions of columns; this number is even larger for the rostering problem. The analysis of our experiments indicates that it was possible to find high-quality, and many times optimal, solutions that were suitable for the company's needs. These solutions were obtained within reasonable computational times on a desktop PC.