Complementary column generation and bounding approaches for set partitioning formulations

We present a complementary column generation feature that produces tight upper bounds, thereby enhancing heuristic and exact column generation approaches for (minimization) set partitioning formulations that possess dense column structures. We also introduce a duality-based lower bound that prompts a useful termination criterion, which can be utilized to mitigate the tailing-off effect induced by column generation approaches. Computations are presented for the one-dimensional bin packing problem and a joint vehicle assembly-routing problem.