Analysis of upper bounds for the Pallet Loading Problem

This paper is concerned with upper bounds for the well-known Pallet Loading Problem (PLP), which is the problem of packing identical boxes into a rectangular pallet so as to maximize the number of boxes ®tted. After giving a comprehensive review of the known upper bounds in the literature, we conduct a detailed analysis to determine which bounds dominate which others. The result is a ranking of the bounds in a partial order. It turns out that two of the bounds dominate all others: a bound due to Nelissen and a bound obtained from the linear programming relaxation of a set packing formulation. Experiments show that the latter is almost always optimal and can be computed quickly.