The two-dimensional cutting stock problem within the roller blind production process

In this paper we consider a two-dimensional cutting stock problem encountered at a large manufacturer of window covering products. The problem occurs in the production process of made-to-measure roller blinds. We develop a solution method that takes into account the characteristics of the specific problem. In particular, we deal with the fact that fabrics may contain small defects that should end up with the waste. Comparison to previous practice shows significant waste reductions.cutting;trim loss;two-dimensional cutting stock problem

Cuckoo Search Approach for Cutting Stock Problem

Cutting Stock Problem has been used in many industries like paper, glass, wood and etc. Cutting Stock Problem has helped industries to reduce trim loss and at the same time meets the customer’s requirement. The purpose of this paper is to develop a new approach which is Cuckoo Search Algorithm in Cutting Stock Problem. Cutting Stock Problem with Linear Programming based method has been improved down the years to the point that it reaches limitation that it cannot achieve a reasonable time in searching for solution. Therefore, many researchers have to turn to metaheuristic algorithms as a solution to the problem which also makes these algorithms become famous. Cuckoo Search Algorithm is selected because it is a new algorithm and outperforms many algorithms. Hence, this paper intends to experiment the performance of Cuckoo Search in Cutting Stock Problem

Mini Max Wallpaper

Mini Max company formulated a problem for the automatic calculation of the number of wallpaper rolls necessary for decorating a room with wallpaper. The final goal is the development of a web-based calculator open for use to both Mini Max staff and the general public. We propose an approach for reducing the studied problem to the one-dimensional cutting-stock problem. We show this in details for the case of plain wallpapers as well as for the case of patterned wallpapers with straight match. The one-dimensional cutting-stock problem can be formulated as a linear integer programming problem. We develop an approach for calculating the needed number of wallpapers for relatively small problems, create an algorithm in a suitable graphical interface and make different tests. The tests show the efficiency of the proposed approach compared with the existent (available) wallpapers’ calculators

A column generation approach to a carpentry cutting stock problem: a case study for planks cutting in Zimbabwe

The carpentry sector like any other industry is faced with a cutting stock problem to minimize incurred waste. The main purpose of this project was to develop a mathematical model which will solve the cutting stock problem using column generation approach for Ashtons Company in Chinhoyi. The interview method was used to collect data relating to the cutting stock problem. The column generation approach of iterative computational routines was used because it develops successively better solutions until an optimal solution is obtained. The results revealed that the method is an appropriate method in solving business problems, that is, how many boards should be cut to meet demand with minimum incurred waste. A user friendly graphical user interface was developed using Visual Basic programming which could be used by the carpentry manager.Keywords: cutting stock problem, feasible solution, optimal solution, integer programmingAfrican Journal of Educational Studies in Mathematics and Sciences Vol. 9, 201

Application of Cutting Stock Problem in Minimizing the Waste of Al-Quran Cover

Cutting stock problem is the problem of cutting standard-sized pieces of stock material, such as vinyl rolls (synthetic leather) into pieces of specified sizes while minimizing material wasted. The study of cutting stock problem is expected to provide an alternative solution to publishing industrial. This study examines the cutting stock problem based on illustrative example of Quran Publisher using the integer programming. The problem is transformed into optimization model so that it can be solved using solver menu in Microsoft Excel. The results provide decision that meets the consumer demand and has a minimum waste of raw material that used for Al-Quran cover

Bun splitting: a practical cutting stock problem

We describe a new hierarchical 2D-guillotine Cutting Stock Problem. In contrast to the classic cutting stock problem, waste is not an issue. The problem relates to the removal of a defective part and assembly of the remaining parts into homogeneous size blocks. The context is the packing stages of cake manufacturing. The company's primary objective is to minimise total processing time at the subsequent, packing stage. This objective reduces to one of minimising the number of parts produced when cutting the tray load of buns. We offer a closed form optimization approach to this class of problems for certain cases, without recourse to mathematical programming or heuristics. The methodology is demonstrated through a case study in which the number of parts is reduced by almost a fifth, and the manufacturer's subsidiary requirement to reduce isolated single bun parts and hence customer complaints is also satisfied

A hybrid approach based on genetic algorithms to solve the problem of cutting structural beams in a metalwork company

This work presents a hybrid approach based on the use of genetic algorithms to solve efficiently the problem of cutting structural beams arising in a local metalwork company. The problem belongs to the class of one-dimensional multiple stock sizes cutting stock problem, namely 1-dimensional multiple stock sizes cutting stock problem. The proposed approach handles overproduction and underproduction of beams and embodies the reusability of remnants in the optimization process. Along with genetic algorithms, the approach incorporates other novel refinement algorithms that are based on different search and clustering strategies.Moreover, a new encoding with a variable number of genes is developed for cutting patterns in order to make possible the application of genetic operators. The approach is experimentally tested on a set of instances similar to those of the local metalwork company. In particular, comparative results show that the proposed approach substantially improves the performance of previous heuristics.Gracia Calandin, CP.; Andrés Romano, C.; Gracia Calandin, LI. (2013). A hybrid approach based on genetic algorithms to solve the problem of cutting structural beams in a metalwork company. Journal of Heuristics. 19(2):253-273. doi:10.1007/s10732-011-9187-xS253273192Aktin, T., Özdemir, R.G.: An integrated approach to the one dimensional cutting stock problem in coronary stent manufacturing. Eur. J. Oper. Res. 196, 737–743 (2009)Alves, C., Valério de Carvalho, J.M.: A stabilized branch-and-price-and-cut algorithm for the multiple length cutting stock problem. Comput. Oper. Res. 35, 1315–1328 (2008)Anand, S., McCord, C., Sharma, R., et al.: An integrated machine vision based system for solving the nonconvex cutting stock problem using genetic algorithms. J. Manuf. 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A simple OPT + 1 algorithm for cutting stock under the modified integer round-up property assumption

We present a simple algorithm for the cutting stock problem with a constant number d of object sizes that produces solutions of value at most OPT +1 in time d^{O(d)} log^7 n, where OPT is the value of an optimum solution. This algorithm works under the assumption that the modified integer round-up property of Scheithauer and Terno for the cutting stock problem holds

Minimal proper non-IRUP instances of the one-dimensional Cutting Stock Problem

We consider the well-known one dimensional cutting stock problem (1CSP). Based on the pattern structure of the classical ILP formulation of Gilmore and Gomory, we can decompose the infinite set of 1CSP instances, with a fixed demand n, into a finite number of equivalence classes. We show up a strong relation to weighted simple games. Studying the integer round-up property we computationally show that all 1CSP instances with $n\le 9$ are proper IRUP, while we give examples of a proper non-IRUP instances with $n=10$. A gap larger than 1 occurs for $n=11$. The worst known gap is raised from 1.003 to 1.0625. The used algorithmic approaches are based on exhaustive enumeration and integer linear programming. Additionally we give some theoretical bounds showing that all 1CSP instances with some specific parameters have the proper IRUP.Comment: 14 pages, 2 figures, 2 table