Solving the Two-Dimensional Bin-Packing Problem with Variable Bin Sizes by Greedy Randomized Adaptive Search Procedures and Variable Neighborhood Search

Introduction. In this work we consider a special variant of a two-dimensional bin packing problem where a finite number of bins of different dimensions are given, and a given set of two-dimensional rectangular items must be packed into (a subset of) these bins. This problem obviously has many practical applications, e.g. in the wood, glass and metal industry. For this particular problem variant we require the solutions to be guillotine-cuttable, which means that it must be possible to cut the items from a blank (bin) by only straight slices. The items are allowed to be rotated by 90 degrees. More formally, we are given a set of two-dimensional objects (items) I = {1, . . . , imax} with dimensions wi × hi, for all i ∈ I and a set of blanks or bins B = {1, . . . , bmax} with dimensions wi × hi, for all i ∈ B. For each blank b ∈ B we are further given costs cb ∈ N. We assume the instances to be feasible, i.e. a feasible packing exists for the given set of items and blanks. The optimization goal is to find a feasible packing with minimum costs of the used blanks. Figure 1 shows an example of such a packing.