More-Dimensional Packing with Order Constraints

Sándor P. Fekete, Ekkehard Köhler, and Jürgen Teich

scheduling, more-dimensional packing, precedence constraints, exact algorithms, interval graphs, partial orders.

We present a first systematic study on more-dimensional packing problems with order constraints. Problems of this type occur naturally in applications such as logistics or computer architecture. They can be interpreted as more-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.

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