A note on Robot-packable and Orthogonal variants of the three-dimensional bin packing problem

In the three-dimensional bin packing problem the task is to orthogonally pack a given set of rectangular items into a minimum number of three-dimensional rectangular bins. We give a characterization of the algorithm proposed by Martello, Pisinger and Vigo (2000) for the exact solution of the problem, showing that not all orthogonal packings can be generated by the proposed algorithm. The packings however have the property of being robot packings, which is of great relevance to the industry. A new (and correct) algorithm for solving the general orthogonal packing problem is presented based on constraint programming. Extensive computational experiments compare the algorithm for the three-dimensional bin packing when solving general orthogonal packings and when restricted to robot packings.