The minimum size instance of a Pallet Loading Problem equivalence class

The Pallet Loading Problem (PLP) maximizes the number of identical rectangular boxes placed within a rectangular pallet. Boxes may be rotated 90° so long as they are packed with edges parallel to the pallet's edges, i.e., in an orthogonal packing. This paper defines the Minimum Size Instance (MSI) of an equivalence class of PLP, and shows that every class has one and only one MSI. We develop bounds on the dimensions of box and pallet for the MSI of any class. Applying our new bounds on MSI dimensions, we present an algorithm for MSI generation.