The generalized bin packing problem

In the Generalized Bin Packing Problem (GBPP), given two sets of compulsory and non-compulsory items characterized by volume and profit and a set of bins with given volume and cost, we want to select the subset of profitable non-compulsory items to be loaded together with the compulsory ones into the appropriate bins in order to minimize the total net cost. Lower and upper bounds to the GBPP are given. The results of extensive computational experiments show that the proposed procedures are efficient and the bounds are tight.

► This problem arises in packing, transportation, and logistics. ► It considers both bin costs and item profits at the same time. ► It generalizes several bin packing and knapsack problems. ► Efficient lower and upper bounds are introduced. ► The proposed procedures solve a large set of instances.