We present algorithms for the following three-dimensional (3D) guillotine cutting problems: Unbounded Knapsack, Cutting Stock and Strip Packing. We consider the case where the items have fixed orientation and the case where orthogonal rotations around all axes are allowed. For the Unbounded 3D Knapsack problem, we extend the recurrence formula proposed by Beasley for the Rectangular Knapsack Pr...

algorithm was applied to the two-dimensional non-guillotine rectangular packing problems. In this study, two different weight mechanisms in the PSO algorithm are used: fixed inertia weight and nonlinear varying inertia weight. The nonlinear varying inertia weights help to improve the speed of convergence and the search ability. In order to compare the performances of these weight mechanisms, a ...

This paper addresses the two-dimensional bin packing problem with guillotine constraints. The requires a set of rectangular items to be cut from larger rectangles, known as bins, while only making use edge-to-edge (guillotine) cuts. goal is minimize total area needed all required items. also variants which permit 90∘ rotation and/or heterogeneous bins. A novel heuristic introduced based on ruin...

Abstract We advance the state of art in Mixed-Integer Linear Programming formulations for Guillotine 2D Cutting Problems by (i) adapting a previously-known reduction to our preprocessing phase (plate-size normalization) and (ii) enhancing previous formulation (PP-G2KP from Furini et alli) cutting down its size symmetries. Our focus is Knapsack Problem with orthogonal unrestricted cuts, constrai...

This paper addresses a constrained two-dimensional (2D), non-guillotine restricted, packing problem, where a xed set of small rectangles has to be paced into a larger stock rectangle so as to maximize the value of the rectangles packed. The algorithm we propose hybridizes a novel placement procedure with a genetic algorithm based on random keys. We propose also a new tness function to drive the...

The problem addressed in this paper is the decision problem of determining if a set of multi-dimensional rectangular boxes can be orthogonally packed into a rectangular bin while satisfying the requirement that the packing should be guillotine cuttable. That is, there should exist a series of face parallel straight cuts that can recursively cut the bin into pieces so that each piece contains a ...

I N T R O D U C T I O N In a number of industries, such as paper and film, there is an important class of problems OVER THE past 20 years, a substantial amount that falls in between the well known one and of work has been done on one and two-dimentwo-dimensional problems. These are referred sional cutting stock problems. A number of to here as two-stage cutting stock problems early authors [1, ...