Heuristic Methods for Minimizing Cut Bars and Using Leftovers from the One-dimensional Cutting Process (original) (raw)

A Tree-Based Heuristic for the One-Dimensional Cutting Stock Problem Optimization Using Leftovers

Materials

Cutting problems consist of cutting a set of objects available in stock in order to produce the desired items in specified quantities and sizes. The cutting process can generate leftovers (which can be reused in the case of new demand) or losses (which are discarded). This paper presents a tree-based heuristic method for minimizing the number of cut bars in the one-dimensional cutting process, satisfying the item demand in an unlimited bar quantity of just one type. The results of simulations are compared with the RGRL1 algorithm and with the limiting values for this considered type of problem. The results show that the proposed heuristic reduces processing time and the number of bars needed in the cutting process, while it provides a larger leftover (by grouping losses) for the one-dimensional cutting stock problem. The heuristic contributes to reduction in raw materials or manufacturing costs in industrial processes.

The one-dimensional cutting stock problem with usable leftover – A heuristic approach

European Journal of Operational Research, 2009

In this work we consider a one-dimensional cutting stock problem in which the non-used material in the cutting patterns may be used in the future, if large enough. This feature introduces difficulties in comparing solutions of the cutting problem, for example, up to what extent a minimum leftover solution is the most interesting one when the leftover may be used. Some desirable characteristics of good solutions are defined and classical heuristic methods are modified, so that cutting patterns with undesirable leftover (not large enough to be used, nor too small to be acceptable waste) are redesigned. The performance of the modified heuristics is observed by solving instances from the literature, practical instances and randomly generated instances.

A New Heuristic Algorithm for the One-Dimensional Cutting Stock Problem

Applied and Computational Mathematics, 2010

This paper describes an attempt to solve the one-dimensional cutting stock problem heuristically by using dynamic programming used to solve subset-sum problem which is considered as a sub-problem. Thisway an optimal solution is found for the sub-problem, which yields solution for the original problem. Thus an economical gain is achieved by decreasing the rate of trim loss. Moreover the cutting-cost can be reduced by minimizing the number of different cutting-patterns by this algorithm. Toward this goal, a new mathematical model is proposed and a novel algorithm is developed. The proposed algorithm is coded with Delphi and then through computational experiments on real-life constrainted optimization problems, the results are compared with the others in the literature. The computational experiments show the efficiency of the algorithm.

An iterative sequential heuristic procedure to a real-life 1.5-dimensional cutting stock problem

European Journal of Operational Research, 2006

This paper addresses a real-life 1.5D cutting stock problem, which arises in a make-to-order plastic company. The problem is to choose a subset from the set of stock rectangles to be used for cutting into a number of smaller rectangular pieces so as to minimize total production cost and meet orders. The total production cost includes not only material wastage, as in traditional cutting stock problems, but also production time. A variety of factors are taken into account, like cutter knife changes, machine restrictions, due dates and other work in progress limitations. These restrictions make the combinatorial structure of the problem more complex. As a result, existing algorithms and mathematical models are no longer appropriate. Thus we developed a new 1.5D cutting stock model with multiple objectives and multi-constraints and solve this problem in an incomplete enumerative way. The computational results show that the solution procedure is easy to implement and works very well. Ó 2005 Published by Elsevier B.V.

The one-dimensional cutting stock problem with usable leftovers – A survey

European Journal of Operational Research, 2014

The usable leftover one-dimensional cutting stock problem-a priority-in-use heuristic

International Transactions in Operational Research, 2013

We consider a one-dimensional cutting stock problem in which the material not used in the cutting patterns, if large enough, is kept for use in the future. Moreover, it is assumed that leftovers should not remain in stock for a long time, hence, such leftovers have priority-in-use compared to standard objects (objects bought by the industry) in stock. A heuristic procedure is proposed for this problem, and its performance is analyzed by solving randomly generated dynamic instances where successive problems are solved in a time horizon. For each period, new demands arise and a new problem is solved on the basis of the information about the stock of the previous periods (remaining standard objects in the stock) and usable leftovers generated during those previous periods. The computational experiments show that the solutions presented by the proposed heuristic are better than the solutions obtained by other heuristics from the literature.

One Dimensional Cutting Stock Problem with Redevelopment of the Surplus Material

engopt.org

This work deals with the One Dimensional Cutting Stock Problem, in which a demand of a set of small pieces named items, gotten from large pieces named objects, has to be produced. It is desirable that the cutting layouts have a small waste or the remaining piece must be big enough to be reused in the future. This is an important problem, since even small improvements in the cutting layouts result in large savings of raw material and energy when the amount of produced material is huge. The Cutting Stock Problem is NPhard, so a heuristic combining the Modified First Fit Decreasing (FFD) method, an Integer Programming (IP) model and a Data Mining (DM) module is proposed to solve it. The FFD heuristic is used to produce an upper bound. With this upper bound the IP model becomes able to be solved more quickly. Then, the DM module is proposed to extract common parts from the best current solutions obtained from several iterations of the IP model. Finally the extracted common parts are used to guide the search for better solutions in less computational time. Computational results have shown that the proposed method is able to generate good quality and competitive solutions when compared to the ones presented in the related literature.

Resolution of the unidimensional cutting stock problem with usable leftover

2007

In this work we consider a one-dimentional cutting stock problem in which the non-used material in the cutting patterns may be used in the future, if large enough. This feature introduces difficulties in comparing solutions of the cutting problem, for example, up to what extent a minimum leftover solution is the most interesting one when the leftover may be used? Some desirable characteristics of good solutions are defined and classical heuristic methods are modified, so that cutting patterns with undesirable leftover (not large enough to be used, nor too small to be acceptable waste) are redesigned. The performance of the modified heuristics are observed by solving instances from the literature and practical instances.

A software for the one-dimensional cutting stock problem

In this paper, one-dimensional cutting stock problem is taken into consideration and a new heuristic algorithm is proposed to solve the problem. In this proposed algorithm, a new dynamic programming algorithm is applied for packing each of the bins. The algorithm is coded with Delphi and then by computational experiments with the real-life constraint optimization problems , and the obtained results are compared with the other one-dimensional cutting stock commercial packages. The computational experiments show the efficiency of the algorithm.

The Ordered Cutting Stock Problem

Decision Sciences, 2004

The one-dimensional cutting stock problem (CSP) is a classic combinatorial optimization problem in which a number of parts of various lengths must be cut from an inventory of standard-size material. The classic CSP ensures that the total demand for a given part size is met but ignores the fact that parts produced by a given cutting pattern may be destined for different jobs. As a result, applying the classic CSP in a dynamic production environment may result in many jobs being open (or partially complete) at any point in time-requiring significant material handling or sorting operations. This paper identifies and discusses a new type of one-dimensional CSP, called the ordered CSP, which explicitly restricts to one the number of jobs in a production process that can be open, or in process, at any given point in time. Given the growing emphasis on mass customization in the manufacturing industry, this restriction can help lead to a reduction in both in-process inventory levels and material handling activities. A formal mathematical formulation is provided for the new CSP model, and its applicability is discussed with respect to a production problem in the custom door and window manufacturing industry. A genetic algorithm (GA) solution approach is then presented, which incorporates a customized heuristic for reducing scrap levels. Several different production scenarios are considered, and computational results are provided that illustrate the ability of the GA-based approach to significantly decrease the amount of scrap generated in the production process.

Heuristic Methods for Minimizing Cut Bars and Using Leftovers from the One-dimensional Cutting Process (original) (raw)

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