Extending an Integer Formulation for the Guillotine 2D Bin Packing Problem

We employ a state-of-the-art Mixed-Integer Linear Programming (MILP) formulation of the literature, and our enhanced version of it, to solve a classical instance dataset for the Guillotine 2D variants of both the Knapsack Problem (G2KP) and the Bin Packing Problem (G2BPP). The results with the G2KP allow us to establish our reimplementation as fair to the original implementation (not available). As far as we know, before this work the considered instances have never been optimally solved for the considered variant of the G2BPP, i.e., the unlimited stages variant, only for the simpler two-staged variant. We also believe this work is the first to gather empirical results of a pure MILP formulation for the G2BPP, even considering the possibility of adaptation was previously known. As we focus on pure and adaptable formulations, we do not employ pricing frameworks or problem-specific heuristics in this short paper. We examine the differences in the running times caused by the change of problems, formulations, number of threads, and, for a subset of the runs, the solver random seed. Some of our findings follow: except for a few G2BPP instances, our enhanced formulation has better timings; 8 of the 30 considered instances have better solutions for unlimited stages G2BPP than for the two-staged G2BPP; the speed-up with 12 threads is smaller than expected and, for the G2BPP, the solver random seed may have a larger effect than the number of threads. (C) 2021 The Authors. Published by Elsevier B.V.