An effective placement method for the single container loading problem

• The studied 3D container loading problem is formed as a mixed integer linear programming.
• Due to the NP-hardness, we propose a simple but effective loading placement heuristic.
• The experiments demonstrate that proposed heuristic outperforms reference methods.
• The proposed heuristic is capable of solving large-scale instances efficiently.

This study investigates a three-dimensional single container loading problem, which aims to pack a given set of unequal-size rectangular boxes into a single container such that the length of the occupied space in the container is minimized. Motivated by the practical logistics instances in literature, the problem under study is formulated as a zero-one mixed integer linear programming model. Due to the NP-hardness of the studied problem, a simple but effective loading placement heuristic is proposed for solving large-size instances. The experimental results demonstrate that the developed heuristic is capable of solving the instances with more than two hundred boxes and more efficient than the state-of-the-art mixed integer linear program and existing heuristic methods.