The paper examines a new problem in the irregular packing literature that has existed in industry for decades; two-dimensional irregular (convex) bin packing with guillotine constraints. Due to the cutting process of certain materials, cuts are restricted to extend from one edge of the stock-sheet to another, called guillotine cutting. This constraint is common place in glass cutting and is an ...

Starting from a two-dimensional rectangular Cutting-Stock pattern with gaps, this paper is focuses on the problem of determination if the pattern is with guillotine restrictions or not and proposes an algorithm for solving it. First we present two new graph representations of the cutting pattern, weighted graph of downward adjacency and weighted graph of rightward adjacency. Using these represe...

We propose a framework to model general guillotine restrictions in two-dimensional cutting problems formulated as Mixed Integer Linear Programs (MIP). The modeling framework requires a pseudo-polynomial number of variables and constraints, which can be effectively enumerated for medium-size instances. Our modeling of general guillotine cuts is the first one that, once it is implemented within a...

We consider a two-dimensional rectangular Cutting-Stock problem in case of a cutting pattern with gaps. First we present two new graph representations of the cutting pattern, weighted graph of downward adjacency and weighted graph of rightward adjacency. Using this kind of representation we propose a method to verify guillotine restrictions of the pattern which can be applied for cutting-stock ...

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...

We undertake an empirical study in which the performance of a good genetic algorithm is tested against some well-known bin packing heuristics on a range of two-dimensional bin packing problems. We restrict our study to problems involving guillotine patterns which are produced using a series of vertical and horizontal edge–to–edge cuts. Many applications of two-dimensional cutting and packing in...

In this study we deal with the two-dimensional non-guillotine cutting problem of how to cut a set of larger rectangular objects to a set of smaller rectangular items in exactly a demanded number of pieces. We are concerned with the special case of the problem in which the non-used material of the cutting patterns (objects leftovers) may be used in the future, for example if it is large enough t...

We consider the Cutting and Covering problem with guillotine restrictions. In one of our previous works, we have shown the connection between the connex components of a graph representation for the covering model and the guillotine cuts. Based on this, in this paper we propose an algorithm which can be used to verify guillotine restrictions in a two-dimensional covering model. Key–Words: bidime...