Minimization of the wood wastes for an industry of furnishing: a two dimensional cutting stock problem

• Autorzy: Bouaine A. , Lebbar M. , Ha M. A.

Identyfikatory

DOI

10.24425/119524

• Języki publikacji: EN

Abstrakty

EN

This paper presents the modeling and the resolution of a two dimensional cutting stock problem for a wooden industry. It is about a real problem of minimization of the wood wastes for an industry of furnishing. The raw material to be cut is a set of beams of various sizes. The purpose of the cut is to supply a list of orders characterized by a set of articles of various sizes. The problem is converted into an integer linear program where the decision variables are the numbers of beams to cut according to a set of feasible “patterns”. The designed solution is a heuristic in two stages: – Generation of the feasible patterns by various classic heuristics of the Bin-packing Problem. – Resolution of the integer linear program with the generated patterns as input variables. Moreover, based on this approach, the “Application Cutting Optimization” is developed to allow the immediate resolution of the problem and widening the stock management horizon. To end, a real case is studied to confirm the effectiveness of this approach.

Słowa kluczowe

EN

two-dimensional cutting stock problem; industry of furnishing; heuristic in two stages; bin packing problem; generating patterns

• Wydawca: Production Engineering Committee of the Polish Academy of Sciences ; Polish Association for Production Management
• Czasopismo: Management and Production Engineering Review
• Rocznik: 2018
• Tom: Vol. 9, No. 2
• Strony: 42--51
• Opis fizyczny: Bibliogr. 20 poz., rys., tab., zdj.

Twórcy

autor

Bouaine A.

• Department of Mathematics and Computer Science, Faculty of Sciences Ben M’Sik, Hassan II University, Morocco
• Department of Mathematics and Computer Science, Faculty of Sciences Ben M’Sik, Hassan II University, Morocco

autor

Lebbar M.

• Department of Industrial Engineering, École Nationale supérieure de Mines de Rabat, Morocco

autor

Ha M. A.

• Department of Industrial Engineering, École Nationale supérieure de Mines de Rabat, Morocco

Bibliografia

• [1] Gilmore P., Gomory R., A linear programming approach to the cutting stock problem, Operations Research, 9, 849–859, 1961.
• [2] Gilmore P., Gomory R., A linear programming approach to the cutting-stock problem II, Operations Research, 11, 863–888, 1963.
• [3] Gilmore P., Gomory R., ‘Multistage cutting stock problems of two and more dimensions, Operations Research, 14, 94–120, 1965.
• [4] Gilmore P., Gomory R., Theory and computation of knapsack functions, Operations Research, 14, 1045– 1074, 1966.
• [5] Lodi A., Martello S., Monaci M., Two-dimensional packing problems: a survey, Eur. J. Oper. Res., 141, 241–252, 2002.
• [6] Cheng C.H., Feiring B.R., Cheng T.C.E., The cutting stock problem – a survey, Int. J. Prod. Econ., 36, 291–305, 1994.
• [7] Wäscher G., Haubner H., Schumann H., An improved typology of cutting and packing problems, Eur. J. Oper. Res., 183, 1109–1130, 2007.
• [8] Morabito R., Arenales M., Optimizing the cutting of stock plates in a furniture company, International Journal of Production Research, 38(12), 2725–2742, 2000.
• [9] Cherri A.C., Arenales M.N., Yanasse H.H., The onedimensional cutting stock problem with usable leftover – a heuristic approach, Eur. J. Oper. Res., 3, 897–908, 2008.
• [10] Erjavec J., Gradiar M., Trkman P., Renovation of the cutting stock process, International Journal of Production Research, 47(14), 3979–3996, 2009.
• [11] Erjavec J., Gradisar M., Trkman P., Assessment of stock size to minimize cutting stock production costs, Int. J. Prod. Econ., 135, 170–176, 2012.
• [12] Vacharapoom B., Sdhabhon B., Three-step solutions for cutting stock problem of construction steel bars, J. Civil. Eng., 5, 1239–1247, 2014.
• [13] Gracia C., Andre’s C., Gracia L., A hybrid approach based on genetic algorithms to solve the problem of cutting structural beams in a metalwork company, J. Heuristics, 19, 253–273, 2013.
• [14] Li K., Liu H., Wu Y., Xu X., A two-dimensional binpacking problem with conflict penalties, International Journal of Production Research, 52(24), 7223– 7238, 2014.
• [15] Toscano A., Rangel S., Yanasse H.H., A heuristic approach to minimize the number of saw cycles in small-scale furniture factories, Ann. Oper. Res., 2015, doi: 10.1007/s10479-015-1955-9.
• [16] Dems A., Rousseau L. M., Frayret J.M., Effects of different cut-to-length harvesting structures on the economic value of a wood procurement plan problem, Ann. Oper. Res., 232, 65, 2015.
• [17] Kujawińska A., Diering M., Rogalewicz M., Żywicki K., Hetman Ł., Soft modelling-based methodology of raw material waste estimation, [in:] Burduk A., Mazurkiewicz D. [Eds.], Intelligent Systems in Production Engineering and Maintenance, ISPEM 2017, Advances in Intelligent Systems and Computing, Springer, Cham., 637, 407–417, 2018.
• [18] El Hayek J., Le probléme de bin-packing en deux dimensions, le cas non-orienté: résolution approchée et bornes inférieures, Université de Technologie Compiégne, 2006.
• [19] Clautiaux F., Bornes inférieures et méthodes exactes pour le probléme de bin-packing en deux dimensions avec orientation fixe, Université de Technologie Compiégne, 2005.
• [20] Lebbar M., Résolution de problémes combinatoire dans l’industrie: apport de la programmation mathématique et de la décomposition, Thése de doctorat, École Centrale Paris, 2000.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).