An Exact Method for the 2D Guillotine Strip Packing Problem

Abstract

We consider the two-dimensional strip packing problem with guillotine cuts. The problem consists in packing a set of rectangular items on one strip of width W and infinite height. The items packed without overlapping must be extracted by a series of cuts that go from one edge to the opposite edge (guillotine constraint). To solve this problem, we use a dichotomic algorithm that uses a lower bound, an upper bound, and a feasibility test algorithm. The lower bound is based on solving a linear program by introducing new valid inequalities. A new heuristic is used to compute the upper bound. Computational results show that the dichotomic algorithm, using the new bounds, gives good results compared to existing methods.