Logic-based Benders decomposition for planning and scheduling: a computational analysis

Logic-based Benders decomposition (LBBD) has improved the state of the art for solving a variety of planning and scheduling problems, in part by combining the complementary strengths of constraint programming (CP) and mixed integer programming (MIP). We undertake a computational analysis of specific factors that contribute to the success of LBBD, to provide guidance for future implementations. We study a problem class that assign tasks to multiple resources and poses a cumulative scheduling problem on each resource. We find that LBBD is at least 1000 times faster than state-ofthe-art MIP on larger instances, despite recent advances in the latter. Further, we conclude that LBBD is most effective when the planning and scheduling aspects of the problem are roughly balanced in difficulty. The most effective device for improving LBBD is the inclusion of a subproblem relaxation in the master problem. The strengthening of Benders cuts also plays an important role when the master and subproblem complexity are properly balanced. These findings suggest future research directions. This paper is partially based on results presented by the same authors at CPAIOR 2013.