Multidimensional dual-feasible functions and fast lower bounds for the vector packing problem

In this paper, we address the 2-dimensional vector packing problem where an optimal layout for a set of items with two independent dimensions has to be found within the boundaries of a rectangle. Many practical applications in areas such as the telecommunications, transportation and production planning lead to this combinatorial problem. Here, we focus on the computation of fast lower bounds using original approaches based on the concept of dual-feasible functions.