Higher-Dimensional Packing with Order Constraints

TL;DR

This paper introduces an exact branch-and-bound algorithm for higher-dimensional packing problems with order constraints, applicable in logistics and computer architecture, using graph theory and order-theoretic characterizations.

Contribution

It develops a novel exact algorithm for complex packing problems with order constraints, extending prior work with new theoretical insights and computational validation.

Findings

Algorithm successfully solves higher-dimensional packing problems with order constraints.

New order-theoretic characterization improves solution efficiency.

Computational results demonstrate practical applicability.

Abstract

We present a first exact study on higher-dimensional packing problems with order constraints. Problems of this type occur naturally in applications such as logistics or computer architecture and can be interpreted as higher-dimensional generalizations of scheduling problems. Using graph-theoretic structures to describe feasible solutions, we develop a novel exact branch-and-bound algorithm. This extends previous work by Fekete and Schepers; a key tool is a new order-theoretic characterization of feasible extensions of a partial order to a given complementarity graph that is tailor-made for use in a branch-and-bound environment. The usefulness of our approach is validated by computational results.