Column generation for the variable cost and size bin packing problem with fragmentation

Bin Packing Problems with Item Fragmentation (BPPIF) are variants of classical Bin Packing in which items can be split at a price. We extend BPPIF models from the literature by allowing a set of heterogeneous bins, each potentially having a different cost and capacity. We introduce extended formulations and column generation algorithms to obtain good bounds with reasonable computing effort. We test our algorithms on instances from the literature. Our experiments prove our approach to be more effective than state-of-the-art general purpose solvers.