The Single Polybag Loading Problem

In the logistics industry, not only cartons but also polybags are used to pack goods for delivery. We study a single polybag loading problem, which is faced by many e-retailers and courier companies. In the problem, a set of rotatable boxes and a two-dimensional rectangular polybag are given. Because the polybag is flexible, the three-dimensional space inside the polybag can be variable when the boxes are loaded. The problem is to choose a subset of the boxes and pack them orthogonally into the polybag so as to maximize the space utilization. We introduce a mixed integer programming formulation and propose a tree search heuristic for the problem. Methods are evaluated by computational experiments on randomly generated data.