The Ordered Cutting Stock Problem (original) (raw)
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International Journal of Applied Evolutionary Computation, 2011
This paper presents the application of the one new approach using Genetic Algorithm in solving One-Dimensional 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 the problem are also presented. The obtained results of the SingleGA10 are compared to the following methods: SHP, Kombi234, ANLCP300 and Symbio10, found in literature, verifying its capacity to find feasible and competitive solutions. The computational results show that the proposed method, which only uses a genetic algorithm to solve these two objectives inversely related, provides good results.
Cutting stock process optimisation in custom door and window manufacturing industry
International Journal of Decision Sciences, Risk and Management, 2009
In this paper we present a decision support system that has been developed to address the short-term scheduling and the medium-term planning decisions that need to be taken by companies operating in the custom door and window manufacturing industry. The modules of the proposed DSS are presented with an emphasis on the model module which implements variations of two well known cutting stock heuristic algorithms that have been modified to support the evaluation of alternative leftover handling policies. Real data obtained by a small Greek company were used for a 'what if' analysis using the proposed DSS. The results obtained, are of particular practical importance since they suggest that the gains achieved by new or improved cutting stock algorithms are in fact lower than the improvements achieved by utilising the leftover pieces.
Cutting optimization with variable-sized stock and inventory status data
International Journal of Production Research, 2002
Many production environments require economical cutting of onedimensional items according to bills of materials from objects of several standard lengths. However, even with optimised cutting substantial trim loss may occur. This trim loss should not be regarded as waste. It is returned to store and can be reused in future optimisations. Optimisation of packing linear items into standard lengths is presented for items which cannot be packed into available lengths from inventory status data. The core of the proposed optimisation tackles the variable-sized bin packing problem (VBPP). The article presents a hybrid genetic algorithm which packs items into both available objects from the inventory and variable-sized objects from the stock. The algorithm tries to minimise waste. Large trim-loss items are returned as remnants to the inventory for subsequent optimisations.
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 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.
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.
Applied Artificial Intelligence, 2019
This paper addressed an important variant of two-dimensional cutting stock problem. The objective was not only to minimize trim loss, as in traditional cutting stock problems, but rather to minimize the number of machine setups. This additional objective is crucial for the life of the machines and affects both the time and the cost of cutting operations. Since cutting stock problems are well known to be NP-hard, we proposed an approximate method to solve this problem in a reasonable time. This approach differs from the previous works by generating a front with many interesting solutions. By this way, the decision maker or production manager can choose the best one from the set based on other additional constraints. This approach combined a genetic algorithm with a linear programming model to estimate the optimal Pareto front of these two objectives. The effectiveness of this approach was evaluated through a set of instances collected from the literature. The experimental results for different-size problems show that this algorithm provides Pareto fronts very near to the optimal ones.
The combined cutting stock and lot-sizing problem in industrial processes
European Journal of Operational Research, 2006
Despite its great applicability in several industries, the combined cutting stock and lot-sizing problem has not been sufficiently studied because of its great complexity. This paper analyses the trade-off that arises when we solve the cutting stock problem by taking into account the production planning for various periods. An optimal solution for the combined problem probably contains non-optimal solutions for the cutting stock and lot-sizing problems considered separately. The goal here is to minimize the trim loss, the storage and setup costs. With a view to this, we formulate a mathematical model of the combined cutting stock and lot-sizing problem and propose a solution method based on an analogy with the network shortest path problem. Some computational results comparing the combined problem solutions with those obtained by the method generally used in industry-first solve the lot-sizing problem and then solve the cutting stock problem-are presented. These results demonstrate that by combining the problems it is possible to obtain benefits of up to 28% profit. Finally, for small instances we analyze the quality of the solutions obtained by the network shortest path approach compared to the optimal solutions obtained by the commercial package AMPL.
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.
A Hybrid Genetic Algorithm for Optimization of Two-dimensional Cutting-Stock Problem
International Journal of Applied Metaheuristic Computing, 2010
Cutting problems are encountered in several industries with different objectives and constraints. The ship building, textile and leather industry (Farley, 1988) are mainly concerned with the cutting of irregular shapes, whereas in the glass wood and paper industry, regular shapes are to be cut. In particular, rectangular shape which can be obtained through guillotine or non guillotine cut and oriented or non-oriented cut. A guillotine cut means that each cut must go from one side of a rectangle straight to the opposite. Then, each cut