Efficient Heuristics for the Variable Size Bin Packing Problem with Fixed Costs

We consider the Variable Size Bin Packing Problem with Fixed Costs, a generalization of the well-known bin packing problem where a set of items must be packed within a set of heterogeneous bins characterized by possibly different volumes and fixed costs. The objective of the problem is to select the bins to pack all items while minimizing the total cost incurred for the selected bins. We present new heuristic solution methods for the problem that integrate lower and upper bound techniques. Extensive numerical tests conducted on instances with up to 1000 items show the effectiveness of these methods in terms of computational effort and solution quality.