The two-dimensional Single Large Object Placement Problem (SLOPP) problem consists of determining a cutting pattern of a set of n small rectangular piece types (little object) on a rectangular stock plate (large object) of length L and width W, as to maximize the sum of the profits of the pieces to be cut. Each piece type i, i = 1, . . ., m, is characterized by a length li, a width wi, a profit...

Efficient cutting design is essential to reduce the costs of production in the open die forging industry. This article discusses a slab cutting design problem that occurs when parallel piped items are cut from raw material steel slabs with varying widths and lengths to meet a volume requirement. The problem is modeled as a two-dimensional cutting stock problem or bin packing problem with size-c...

The present work proposes new heuristics and algorithms for the 3D Cutting and Packing class of problems. Specifically the cutting stock problem and a real-world application from the retail steel distribution industry are addressed. The problem being addressed for the retail steel distribution industry is the retail steel cutting problem, which is how to cut steel in order to satisfy the custom...

Abstract About 15 years ago, a paper proposed the first integer linear programming formulation for constrained two‐dimensional guillotine cutting problem (with unlimited stages). Since then, eight other formulations followed, seven of them in last four years. This spike interest gave no opportunity comprehensive comparison between formulations. We review each and compare their empirical results...

We describe an exact model for the two-dimensional Cutting Stock Problem with two stages and the guillotine constraint. It is a linear programming arc-flow model, formulated as a minimum flow problem, which is an extension of a model proposed by Valério de Carvalho for the one dimensional case. In this paper, we explore how this model behaves when it is solved with a commercial software, explic...

A strong hyperbox-respecting coloring of an n-dimensional hyperbox partition is a coloring of the corners of its hyperboxes with 2n colors such that any hyperbox has all the colors appearing on its corners. A guillotine-partition is obtained by starting with a single axis-parallel hyperbox and recursively cutting a hyperbox of the partition into two hyperboxes by a hyperplane orthogonal to one ...

Original scientific papers This paper mainly addresses a two-dimensional defective stocks guillotine cutting stock problem where stock of different sizes is available. Herein a new heuristic algorithm which is based on tree is proposed to discuss this problem. In particular, such an algorithm consists of two parts: the first part is an initial solution of the cutting stock problem where there a...

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