A best-fit branch-and-bound heuristic for the unconstrained two-dimensional non-guillotine cutting problem

This paper studies the unconstrained two-dimensional non-guillotine cutting problem, in which the objective is to select and pack a set of rectangles into a sheet with fixed sizes and maximize the profit of the selected rectangles. The orientation of the rectangle is fixed and the available number of each rectangle is not limited. We present a staircase based best-fit branch-and-bound method to solve this problem. To speed up the process, a greedy heuristic is used to generate a complete solution from a partial one and an iterative application of the branch-and-bound method is introduced. The results on the well-known instances show that the proposed approach gives optimality certificates for 50 out of 95 instances and improves the results for 29 instances.