An Improved Column Generation Algorithm for Crew Scheduling Problems ⋆

Column Generation (CG) technique is popularly applied in solving the crew scheduling problem of large size, which is generally modeled as an Integer Linear Programming (ILP) problem. The traditional CG algorithms for bus and rail crew scheduling encounter difficulties on either the generation of all potential shifts or solving subproblems. A subproblem embedded in the CG is generally represented as a Resource-constrained Shortest Path Problem (RCSPP), which is NP-hard and constitutes a major reason for the CG’s slow convergence. This paper presents a novel CG strategy to improve the efficiency of the proposed crew scheduling approach. The main idea is that a reasonably large set of “good” potential shifts (called a shift-pool) is pre-compiled using problem-specific knowledge. During the CG process, the RCSPP is not constructed to generate potential shifts as new columns until no columns with Negative Reduced Cost (NRC) exist in the shift-pool. Experiments are carried out on a series of Chinese real-world problem instances, and the computational results show that the solving process is significantly accelerated.