The Generalized Bin Packing Problem

We introduce the Generalized Bin Packing Problem, a new packing problem where, given a set of items characterized by volume and profit and a set of bins with given volumes and costs, one aims to select the subsets of profitable items and appropriate bins to optimize an objective function combining the cost of using the bins and the profit yielded by loading the selected items. The Generalized Bin Packing Problem thus generalizes many other packing problems, including Bin Packing and Variable Sized Bin Packing, as well as Knapsack, Multiple Homogeneous and Heterogeneous Knapsack. We present two formulations for the problem, as well as an efficient column-generation-based lower bound method, plus first fit, best fit, and column-generation-based upper bound procedures. The paper introduces new instance sets and analyzes the results of extensive computational experiments, which show that the proposed procedures are very efficient and the bounds are very tight.