Enhanced formulation for the Guillotine 2D Cutting Knapsack Problem

Iterated Local Search Algorithm for the Constrained Two-Dimensional Non-Guillotine Cutting Problem

An Iterated Local Search method for the constrained two-dimensional non-guillotine cutting problem is presented. This problem consists in cutting pieces from a large stock rectangle to maximize the total value of pieces cut. In this problem, we take into account restrictions on the number of pieces of each size required to be cut. It can be classified as 2D-SLOPP (two dimensional single large o...

Algorithms for 3D guillotine cutting problems: Unbounded knapsack, cutting stock and strip packing

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...

A New Graph-Theoretical Model for the Guillotine-Cutting Problem

We consider the problem of determining whether a given set of rectangular items can be cut from a larger rectangle using so-called guillotine cuts only. We introduce a new class of arc-colored directed graphs called guillotine graphs and show that each guillotine graph can be associated with a specific class of pattern solutions that we term a guillotine-cutting class. The properties of guillot...

An Exact Method for the 2D Guillotine Strip Packing Problem

We consider the two-dimensional strip packing problem with guillotine cuts. The problem consists in packing a set of rectangular items on one strip of width W and infinite height. The items packed without overlapping must be extracted by a series of cuts that go from one edge to the opposite edge guillotine constraint . To solve this problem, we use a dichotomic algorithm that uses a lower boun...

Parallelisation of the Two-dimensional Guillotine Strip Packing/Cutting Problem