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

Bin Packing and Related Problems: General Arc-flow Formulation with Graph Compression

We present an exact method, based on an arc-flow formulation with side constraints, for solving bin packing and cutting stock problems --- including multi-constraint variants --- by simply representing all the patterns in a very compact graph. Our method includes a graph compression algorithm that usually reduces the size of the underlying graph substantially without weakening the model. As opposed to our method, which provides strong models, conventional models are usually highly symmetric and provide very weak lower bounds. Our formulation is equivalent to Gilmore and Gomory's, thus providing a very strong linear relaxation. However, instead of using column-generation in an iterative process, the method constructs a graph, where paths from the source to the target node represent every valid packing pattern. The same method, without any problem-specific parameterization, was used to solve a large variety of instances from several different cutting and packing problems. In this paper, we deal with vector packing, graph coloring, bin packing, cutting stock, cardinality constrained bin packing, cutting stock with cutting knife limitation, cutting stock with binary patterns, bin packing with conflicts, and cutting stock with binary patterns and forbidden pairs. We report computational results obtained with many benchmark test data sets, all of them showing a large advantage of this formulation with respect to the traditional ones

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. Syst. 18, 396–415 (1999)Belov, G., Scheithauer, G.: A cutting plane algorithm for the one-dimensional cutting stock problem with multiple stock lengths. Eur. J. Oper. Res. 141, 274–294 (2002)Christofides, N., Hadjiconstantinou, E.: An exact algorithm for orthogonal 2-D cutting problems using guillotine cuts. Eur. J. Oper. Res. 83, 21–38 (1995)Elizondo, R., Parada, V., Pradenas, L., Artigues, C.: An evolutionary and constructive approach to a crew scheduling problem in underground passenger transport. J. Heuristics 16, 575–591 (2010)Fan, L., Mumford, C.L.: A metaheuristic approach to the urban transit routing problem. J. Heuristics 16, 353–372 (2010)Gau, T., Wäscher, G.: CUTGEN1: a problem generator for the standard one-dimensional cutting stock problem. Eur. J. Oper. Res. 84, 572–579 (1995)Gilmore, P.C., Gomory, R.E.: A linear programming approach to the cutting stock problem. Oper. Res. 9, 849–859 (1961)Gilmore, P.C., Gomory, R.E.: A linear programming approach to the cutting stock problem. Part II. Oper. Res. 11, 863–888 (1963)Ghiani, G., Laganà, G., Laporte, G., Mari, F.: Ant colony optimization for the arc routing problem with intermediate facilities under capacity and length restrictions. J. Heuristics 16, 211–233 (2010)Gonçalves, J.F., Resende, G.C.: Biased random-key genetic algorithms for combinatorial optimization. J. Heuristics (2011). doi: 10.1007/s10732-010-9143-1Gradisar, M., Kljajic, M., Resinovic, G., et al.: A sequential heuristic procedure for one-dimensional cutting. Eur. J. Oper. Res. 114, 557–568 (1999)Haessler, R.W.: One-dimensional cutting stock problems and solution procedures. Math. Comput. Model. 16, 1–8 (1992)Haessler, R.W., Sweeney, P.E.: Cutting stock problems and solution procedures. Eur. J. Oper. Res. 54(2), 141–150 (1991)Haessler, R.W.: Solving the two-stage cutting stock problem. Omega 7, 145–151 (1979)Hinterding, R., Khan, L.: Genetic algorithms for cutting stock problems: with and without contiguity. In: Yao, X. (ed.) Progress in Evolutionary Computation. LNAI, vol. 956, pp. 166–186. Springer, Berlin (1995)Holthaus, O.: Decomposition approaches for solving the integer one-dimensional cutting stock problem with different types of standard lengths. Eur. J. Oper. Res. 141, 295–312 (2002)Kantorovich, L.V.: Mathematical methods of organizing and planning production. Manag. Sci. 6, 366–422 (1939) (Translation to English 1960)Liang, K., Yao, X., Newton, C., et al.: A new evolutionary approach to cutting stock problems with and without contiguity. Comput. Oper. Res. 29, 1641–1659 (2002)Poldi, K., Arenales, M.: Heuristics for the one-dimensional cutting stock problem with limited multiple stock lengths. Comput. Oper. Res. 36, 2074–2081 (2009)Suliman, S.M.A.: Pattern generating procedure for the cutting stock problem. Int. J. Prod. Econ. 74, 293–301 (2001)Talbi, E.-G.: A taxonomy of hybrid metaheuristics. J. Heuristics 8, 541–564 (2002)Vahrenkamp, R.: Random search in the one-dimensional cutting stock problem. Eur. J. Oper. Res. 95, 191–200 (1996)Vanderbeck, F.: Exact algorithm for minimizing the number of set ups in the one dimensional cutting stock problems. Oper. Res. 48, 915–926 (2000)Wagner, B.J.: A genetic algorithm solution for one-dimensional bundled stock cutting. Eur. J. Oper. Res. 117, 368–381 (1999)Wäscher, G., Haußner, H., Schumann, H.: An improved typology of cutting and packing problems. Eur. J. Oper. Res. 183, 1109–1130 (2007

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

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

ONE-DIMENSIONAL CUTTING STOCK PROBLEM THAT MINIMIZES THE NUMBER OF DIFFERENT PATTERNS

Cutting stock problem (CSP) is a problem of cutting an object into several smaller objects to fulfill the existing demand with a minimum unused object remaining. Besides minimizing the remaining of the object, sometimes there is another additional problem in CSP, namely minimizing the number of different cutting patterns. This happens because there is a setup cost for each pattern. This study shows a way to obtain a minimum number of different patterns in the cutting stock problem (CSP). An example problem is modeled in linear programming and then solved by a column generation algorithm using the Lingo 18.0 software

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

Review of The Literature Associated Wth 2 D Stock Cutting

ABSTRAK The cutting stock problem arises from many physical applications in industry. This paper looks specifically at the literature associated with tit.° dimensional stock cutting. There have been solutions suggested to One dimensional problems, and suggested solutions for the two dimensional problem. In both cases 11w algorithms suggested are dependent on the number of items to be fitted to the \u27stock\u27, and in certain cases pre selected placement strategies. A review of the available literature will provide the background for an exploration of the current and past attempts to solve this problem. it ss ill also provide a suggested focus for future work, and suitable computer algorithms and graphical layouts to aid the cutting processes. Key Words : Cutting stock, Bin Packin