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...

Cutting stock problems are within knapsack optimization problems and are considered as a non-deterministic polynomial-time (NP)-hard problem. In this paper, two-dimensional cutting stock problems were presented in which items and stocks were rectangular and cuttings were guillotine. First, a new, practical, rapid, and heuristic method was proposed for such problems. Then, the ...

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...

In this paper we study the two-dimensional non-guillotine cutting problem, the problem of cutting rectangular pieces from a large stock rectangle so as to maximize the total value of the pieces cut. The problem has many industrial applications whenever small pieces have to be cut from or packed into a large stock sheet. We propose a tabu search algorithm. Several moves based on reducing and ins...

This study presents an application to optimise the use of an Lcut guillotine machine. The application has two distinct parts to it; first, a number of rectangular shapes are placed on as few metal sheets as possible by using Genetic Algorithms. Secondly, the sequence for cutting these pieces has to be generated. The guillotine’s numeric control then uses this sequence to make the cuts.

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...

We investigate a new application of DC (Difference of Convex functions) programming and DCA (DC Algorithm) in solving the constrained two-dimensional non-guillotine cutting problem. This problem consists of cutting a number of rectangular pieces from a large rectangular object. The cuts are done under some constraints and the objective is to maximize the total value of the pieces cut. We reform...

We investigate a new application of DC (Difference of Convex functions) programming and DCA (DC Algorithm) in solving the constrained two-dimensional non-guillotine cutting problem. This problem consists of cutting a number of rectangular pieces from a large rectangular object. The cuts are done under some constraints and the objective is to maximize the total value of the pieces cut. We reform...

This paper presents a greedy randomized adaptive search procedure (GRASP) for the constrained two-dimensional non-guillotine cutting problem, the problem of cutting the rectangular pieces from a large rectangle so as to maximize the value of the pieces cut. We investigate several strategies for the constructive and improvement phases and several choices for critical search parameters. We perfor...

The Backtracking Heuristic (BH) methodology consists in to construct of items by combination between heuristics that solve mathematical programming models, and backtrack search algorithm to figure out the best heuristics and their best ordering. BH was firstly introduced in the literature in order to solve three-dimensional Knapsack Loading Problems, showing promising results. In this present w...