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...

In this work we consider the 3-staged 2-dimensional cutting stock problem, which appears in many real-world applications such as glass and wood cutting and various scheduling tasks. We suggest a variable neighborhood search (VNS) employing “ruin-and-recreate”based very large neighborhood searches (VLNS). We further present a polynomial-sized integer linear programming model (ILP) for solving th...

A cutting stock problem is one of the main and classical problems in operations research that is modeled as Lp < /div> problem. Because of its NP-hard nature, finding an optimal solution in reasonable time is extremely difficult and at least non-economical. In this paper, two meta-heuristic algorithms, namely simulated annealing (SA) and tabu search (TS), are proposed and deve...

The nesting problem is an irregular two-dimensional cutting problem where the shapes of the pieces to cut and the master surfaces are irregular in shape and different in size. In particular, we consider nesting problems where the master surface could contain defects. Some of them can be accepted (i.e., incorporated) in certain types of pieces, while other defected areas must be avoided. The pro...

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...

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 consider a Two-Dimensional Cutting Stock Problem (2DCSP) where stock of different sizes is available, and a set of rectangular items has to be obtained through two-stage guillotine cuts. We propose and computationally compare three Mixed-Integer Programming models for the 2DCSP developing formulations from the literature. The first two models have a polynomial and pseudo-polynomial number of...

In this paper the cutting stock problem for the corrugated board boxes industry is presented. The problem is solved by means of a two step strategy. First, patterns pre-generation model is formulated which are then used as input in a mathematical MILP model that optimizes the cutting process minimizing the paper trim-loss costs. Several parameters have been added to the system such that the pla...

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...