This paper presents a new variant of the A class algorithms for solving the known one dimensional cutting stock problem in a card board factory where the objective is to minimise the useless remaining of a continuous cardboard surface The algorithm limits the number of nodes in the tree search by using a bound criterion based on the prob lem restrictions The process of computing the solution is...

One of the main issues in the glass industry is the minimization of the trim loss generated when cutting large parts (stocks) into small items. In our application stocks are produced in the plant. Many distinct stock sizes are feasible, and technical constraints limit the variety of cutting patterns to those producing a single type of item per stock. Consequently, the focus is not on seeking an...

Many numerical computations reported in the literature show an only small diierence between the optimal value of the one-dimensional cutting stock problem (1CSP) and that of its corresponding linear programming relaxation. Moreover, theoretical investigations have proven that this difference is smaller than 2 for a wide range of subproblems of the general 1CSP. In this paper we give a branch&bo...

We consider the feasibility problem OPP in higher-dimensional orthogonal packing: given a set of d-dimensional (d ≥ 2) rectangular items, decide whether all of them can be orthogonally packed in the given rectangular container without rotation. The 1D ‘bar’ LP relaxation of OPP reduces the latter to a 1D cutting-stock problem where the packing of each stock bar represents a possible 1D stitch t...

The purpose of this paper is to show that the gap is possibly smaller than 2. Some helpful results are summarized. Zusammenfassung: Es werden Ergebnisse vorgestellt und diskutiert, die bei der Untersuchung der maximalen Differenz zwischen den Optimalwerten des ganzzahligen und stetigen eindimensionalen Zuschnittproblems erhalten wurden.

Cutting and packing problems appear in many industrial settings where larger pieces are cut into smaller ones in order to produce items or products that are required by other industries or customers, e.g., paper, steel and fiber industries. A solution for the cutting problem consists in determining a group of patterns and their frequencies, that is, the number of times that a pattern is cut to ...

This paper presents the application of the one new approach using Genetic Algorithm in solving OneDimensional Cutting Stock Problems in order to minimize two objectives, usually conflicting, i.e., the number of processed objects and setup while simultaneously treating them as a single goal. The model problem, the objective function, the method denominated SingleGA10 and the steps used to solve ...

We consider two-dimensional cutting stock problems where single rectangular stocks have to be cut into some smaller rectangular so that the number of stocks needed to satisfy the demands is minimum. In this paper we focus our study to the problem where the stocks have to be cut with guillotine cutting type and fixed orientation of finals. We formulate the problem as an integer programming, wher...