A General Framework for Bounds for Higher-Dimensional Orthogonal Packing Problems

Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. In the context of a branch-and-bound framework for solving these packing problems to optimality, it is of crucial importance to have good and easy bounds for an optimal solution. Previous efforts have produced a number of special classes of such bounds. Unfortunately, some of these bounds are somewhat complicated and hard to generalize. We present a new approach for obtaining classes of lower bounds for higher-dimensional packing problems; our bounds improve and simplify several well-known bounds from previous literature. In addition, our approach provides an easy framework for proving correctness of new bounds. This is the second in a series of four articles describing new approaches to higher-dimensional packing. Key words: Cutting and packing, Higher-dimensional packing, Geometric optimization, Discrete structures, Lower bounds

• Type: Journal
• Year: 2004
• Where: CORR
• Authors: Sándor P. Fekete, Jörg Schepers
• Keywords: CORR 2004, Easy Bounds, Education, Lower Bounds, Packing Problems