Dynamic Programming and Column Generation Based Approaches for Two-Dimensional Guillotine Cutting Problems

We investigate two cutting problems and their variants in which orthogonal rotations are allowed. We present a dynamic programming based algorithm for the Two-dimensional Guillotine Cutting Problem with Value (GCV) that uses the recurrence formula proposed by Beasley and the discretization points defined by Herz. We show that if the items are not so small compared to the dimension of the bin, this algorithm requires polynomial time. Using this algorithm we solved all instances of GCV found at the OR–LIBRARY, including one for which no optimal solution was known. We also investigate the Two-dimensional Guillotine Cutting Problem with Demands (GCD). We present a column generation based algorithm for GCD that uses the algorithm above mentioned to generate the columns. We propose two strategies to tackle the residual instances. We report on some computational experiments with the various algorithms we propose in this paper. The results indicate that these algorithms seem to be suitable for solving real-world instances.