This paper discusses some of the basic formulation issues and solution procedures for solving oneand twodimensional cutting stock problems. Linear programming, sequential heuristic and hybrid solution procedures are described. For two-dimensional cutting stock problems with rectangular shapes, we also propose an approach for solving large problems with limits on the number of times an ordered s...

The one-dimensional cutting stock problem (1D-CSP) and the twodimensional two-stage guillotine constrained cutting problem (2D-2CP) are considered in this paper. The Gilmore-Gomory model of these problems has a very strong continuous relaxation which provides a good bound in an LP-based solution approach. In recent years, there have been several efforts to attack the one-dimensional problem by ...

In this paper, we consider a multi-staged two-dimensional cutting stock problem (CSP) in a paper industry. Paper production relies on the sequential processes of various large machines (pulp preparation, paper formation, winding, and sheet cutting), which has various machine related constraints. In addition, there are the operational constraints from the real-world situation. The problem is mod...

In this paper we consider a simplified version of the stock cutting (two-dimensional bin packing) problem. We compare three meta-heuristic algorithms (genetic algorithm (GA), tabu search (TS) and simulated annealing (SA)) when applied to this problem. The results show that tabu search and simulated annealing produce good quality results. This is not the case with the genetic algorithm. The prob...

In this paper we consider the problem of placing eeciently a rectangle in a two-dimensional layout that may not have the bottom-left placement property. This problem arises when we apply any one of a number of iterative improvement algorithms to the cutting stock problem or its variants. Chazelle has given an O(n)-time placement algorithm when the layout has the bottom-left property; we extend ...

This paper investigates the one-dimensional cutting stock problem considering two conflicting objective functions: minimization of both the number of objects and the number of different cutting patterns used. A new heuristic method based on the concepts of genetic algorithms is proposed to solve the problem. This heuristic is empirically analyzed by solving randomly generated instances and also...

This work presents a genetic symbiotic algorithm to solve the one-dimensional cutting stock problem with multiple objectives. We considered two important objectives for an industry (1) cost of trim loss and (2) cost of setup. We use a symbiotic relationship, between the population of solutions and the population of cutting patterns, together with a niche strategy to obtain an approximation of t...

We confront a practical cutting stock problem from a production plant of plastic rolls. The problem is a variant of the well-known one dimensional cutting stock, with particular constraints and optimization criteria defined by the experts of the company. We start by giving a problem formulation in which optimization criteria have been considered in linear hierarchy according to expert preferenc...

Branch-and-price is a well established technique for solving large scale integer programming problems. This method combines the standard branch-and-bound framework of solving integer programming problems with Column Generation. In each node of the branch-and-bound tree, the bound is calculated by solving the LP relaxation. The LP relaxation is solved using Column Generation. In this report, we ...

In this article, a combined method for the solution of the General one-Dimensional Cutting Stock Problem (G1D-CSP) is proposed. The main characteristic of G1D-CSP is that all stock lengths can be different. The new approach combines two existing methods: Sequential Heuristic Procedure, and branch-and-bound. The algorithm based on the proposed method leads to almost optimal solutions, which are ...