Large proper gaps in bin packing and dual bin packing problems

Abstract

We consider the one-dimensional skiving stock problem, also known as the dual bin packing problem, with the aim of maximizing the best known dual and proper dual gaps. We apply the methods of computational search of large gaps initially developed for the one-dimensional cutting stock problem, which is related to the bin packing problem. The best known dual gap is raised from 1.0476 to 1.1795. The proper dual gap is improved to 1.1319. We also apply a number of new heuristics developed for the skiving stock problem back to the cutting stock problem, raising the largest known proper gap from 1.0625 to 1.1.