Conference PaperPDF Available

Simultaneous Cutting of Master Reels and Stocked Rolls in Solving Trim Loss Minimization Problem at Paper Mill

Authors:
  • Hitec University Taxila

Figures

Content may be subject to copyright.
A preview of the PDF is not available
ResearchGate has not been able to resolve any citations for this publication.
Article
Full-text available
The cutting-stock problem is the problem of filling an order at minimum cost for specified numbers of lengths of material to be cut from given stock lengths of given cost. When expressed as an integer programming problem the large number of variables involved generally makes computation infeasible. This same difficulty persists when only an approximate solution is being sought by linear programming. In this paper, a technique is described for overcoming the difficulty in the linear programming formulation of the problem. The technique enables one to compute always with a matrix which has no more columns than it has rows.
Article
Full-text available
In this paper, the methods for stock cutting outlined in an earlier paper in this Journal [Opns Res 9, 849--859 1961] are extended and adapted to the specific full-scale paper trim problem. The paper describes a new and faster knapsack method, experiments, and formulation changes. The experiments include ones used to evaluate speed-up devices and to explore a connection with integer programming. Other experiments give waste as a function of stock length, examine the effect of multiple stock lengths on waste, and the effect of a cutting knife limitation. The formulation changes discussed are i limitation on the number of cutting knives available, n balancing of multiple machine usage when orders are being filled from more than one machine, and m introduction of a rational objective function when customers' orders are not for fixed amounts, but rather for a range of amounts. The methods developed are also applicable to a variety of cutting problems outside of the paper industry.
Article
Full-text available
The “trim loss problem” (TLP) is one of the most challenging problems in context of optimization research. It aims at determining the optimal cutting pattern of a number of items of various lengths from a stock of standard size material to meet the customers’ demands that the wastage due to trim loss is minimized. The resulting mathematical model is highly nonconvex in nature accompanied with several constraints with added restrictions of binary variables. This prevents the application of conventional optimization methods. In this paper we use synergetic differential evolution (SDE) for the solution of this type of problems. Four hypothetical but relevant cases of trim loss problem arising in paper industry are taken for the experiment. The experimental results compared with those of the other techniques show the competence of the SDE to solve the problem.
Article
A Two-level method is proposed to solve the one-dimensional cutting-stock problem during the production process in this paper. First, nested layer cycle is designed to enumerate all the feasible cutting patterns, then a integer linear programming model is established with quantity demands as the constraint. The best cutting scheme is obtained finally according to the branch and bound method. The effectiveness of the proposed method is proved through a real world example, the calculations demonstrate that scheme obviously improves the utilization rate of stock
Article
In this paper, we study the Cutting Stock Problem with Setup Cost (CSP-S) which is a more general case of the well-known Cutting Stock Problem (CSP). In the classical CSP, one wants to minimize the number of stock items used while satisfying the demand for smaller-sized items. However, the number of patterns/setups to be performed on the cutting machine is ignored. In most cases, one has to find the trade-off between the material usage and the number of setups in order to come up with better production plans. In CSP-S, we have different cost factors for the material and the number of setups, and the objective is to minimize total production cost including both material and setup costs. We develop a mixed integer linear program and analyze a special case of the problem. Motivated by this special case, we propose two local search algorithms and a column generation based heuristic algorithm. We demonstrate the effectiveness of the proposed algorithms on the instances from the literature.
Article
A problem of a line-cutting procedure is discussed for ship hull construction. This procedure includes five steps: stock arrangement, piece arrangement, marking, cutting and special processes, and delivering the work. The line-cutting procedure will be optimized when two objectives are considered: minimizing the total trim loss and keeping the working efficiency of the cutting procedure. The developed way for the discussed problem is to optimize the stock arrangement associated with a proposed rule-based piece arrangement where the former is optimized for minimizing the total trim loss and the latter for keeping the working efficiency. A tabu search is chosen for the optimization of stock arrangement. In addition, two proposed replacement moves, the aggregative and the breaking, are adopted to improve the effectiveness of the tabu search. Two real cases and some random instances are used for test and comparison. The results show that the stock arrangement was optimized satisfyingly by the tabu search and the rule-based piece arrangement is capable of keeping the working efficiency as usual. In addition, the effectiveness of the tabu search was apparently improved by two proposed replacement moves.
Article
In this study we analysed practical aspects of the application of a cutting stock model to a Brazilian company that manufactures furniture on a large scale with a high degree of standardization. The model is based on the classical approach of Gilmore and Gomory (1965, Operations Research, 14, 94-120), which combines a linear program and a column generation procedure. Besides the two-stage and three-stage guillotine cutting patterns, we also considered one-group guillotine patterns that improve the productivity of the cutting equipment. Examples derived from the furniture company are used to illustrate some of the trade-offs involved, in particular the trade-off between cutting simpler patterns and patterns that yield less waste material, but reduce the productivity of the cutting machine.
Article
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.
Article
The article examines the Sequential Heuristic Procedure (SHP) for optimising one-dimensional stock cutting when all stock lengths are different. In order to solve a bicriterial multidimensional knapsack problem with side constraints a lexicographic approach is applied. An item-oriented solution was found through a combination of approximations and heuristics that minimize the influence of ending conditions leading to almost optimal solutions. The computer program CUT was developed, based on the proposed algorithm. Two sample problems are presented and solved. A statistical analysis of parameters that affect material utilisation was also made.
Article
In this paper, various methods proposed for the solution of cutting stock problems are reviewed. The impact of expert systems and artificial intelligence on solving these problems is assessed. An intelligent system architecture is proposed. The structure uses knowledge-based scheduling concepts and provides a basis for exploring integration of expert systems and operations research techniques in generating cutting patterns with minimum scrap.