An improved best-first branch and bound algorithm for the pallet-loading problem using a staircase structure

This study concerns the pallet-loading problem (PLP), which requires maximizing the number of identical boxes loaded on a large rectangular pallet. The proposed algorithm generates layouts of a specific structure, known as the staircase structure that is very efficient due to its geometrical properties for removing unnecessary patterns and obtaining upper and lower bounds corresponding to the patterns. Efficient methods to remove the dominated and duplicated patterns in the staircase structure are proposed. We then apply these methods to the best-first branch and bound algorithm. Computational results demonstrated the superiority of the proposed algorithm compared with other existing exact algorithms.