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...

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 ...

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 ...

This paper presents an approach for solving a new real problem in Cutting and Packing. At its core is an innovative mixed integer programme model that places irregular pieces and defines guillotine cuts. The two-dimensional irregular shape bin packing problem with guillotine constraints arises in the glass cutting industry, for example, the cutting of glass for conservatories. Almost all cuttin...

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...

In this study, a dynamic programming approach to deal with the unconstrained twodimensional non-guillotine cutting problem is presented. The method extends the recently introduced recursive partitioning approach for the manufacturer’s pallet loading problem. The approach involves two phases and uses bounds based on unconstrained two-staged and non-staged guillotine cutting. Since a counterexamp...

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...

PVC frame cutting process by guillotine is a common method that attracted attention of car parts and PVC decorating furniture producers. In this paper, the effects of main parameters such as cutting speed, lubricants and cutting frame holder pressure force on PVC frame section surface smoothness is investigated by experimental methods on a specified PVC frame sample and then by FEM simulation u...

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...