Minimization of the Wood Wastes for an Industry of Furnishing: a Two Dimensional Cutting Stock Problem

• Autorzy: Amine Bouaine , Maria Lebbar , Mohamed Ait Ha
• 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.(original abstract)

Słowa kluczowe

EN

Furniture market; Furniture production; Industrial design

PL

Rynek meblarski; Produkcja mebli; Wzornictwo przemysłowe

• Czasopismo: Management and Production Engineering Review
• Rocznik: 2018
• Tom: 9
• Numer: nr 2
• Strony: 42--51

Twórcy

autor

Amine Bouaine

• Ecole Nationale sup´erieure de Mines de Rabat, Morocco ; Hassan II University, Morocco

autor

Maria Lebbar

• Ecole Nationale sup´erieure de Mines de Rabat, Morocco

autor

Mohamed Ait Ha

• Ecole Nationale sup´erieure de Mines de Rabat, Morocco

Bibliografia

• Gilmore P., Gomory R., A linear programming approach to the cutting stock problem, Operations Research, 9, 849-859, 1961.
• Gilmore P., Gomory R., A linear programming approach to the cutting-stock problem II, Operations Research, 11, 863-888, 1963.
• Gilmore P., Gomory R., 'Multistage cutting stock problems of two and more dimensions, Operations Research, 14, 94-120, 1965.
• Gilmore P., Gomory R., Theory and computation of knapsack functions, Operations Research, 14, 1045- 1074, 1966.
• Lodi A., Martello S., Monaci M., Two-dimensional packing problems: a survey, Eur. J. Oper. Res., 141, 241-252, 2002.
• Cheng C.H., Feiring B.R., Cheng T.C.E., The cutting stock problem - a survey, Int. J. Prod. Econ., 36, 291-305, 1994.
• W¨ascher G., Haubner H., Schumann H., An improved typology of cutting and packing problems, Eur. J. Oper. Res., 183, 1109-1130, 2007.
• Morabito R., Arenales M., Optimizing the cutting of stock plates in a furniture company, International Journal of Production Research, 38(12), 2725-2742, 2000.
• 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.
• Erjavec J., Gradiar M., Trkman P., Renovation of the cutting stock process, International Journal of Production Research, 47(14), 3979-3996, 2009.
• Erjavec J., Gradisar M., Trkman P., Assessment of stock size to minimize cutting stock production costs, Int. J. Prod. Econ., 135, 170-176, 2012.
• Vacharapoom B., Sdhabhon B., Three-step solutions for cutting stock problem of construction steel bars, J. Civil. Eng., 5, 1239-1247, 2014.
• 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.
• 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.
• 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.
• 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.
• 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.
• El Hayek J., Le probl`eme de bin-packing en deux dimensions, le cas non-orient´e: r´esolution approch´ee et bornes inf´erieures, Universit´e de Technologie Compi´egne, 2006.
• Clautiaux F., Bornes inf´erieures et m´ethodes exactes pour le probl´eme de bin-packing en deux dimensions avec orientation fixe, Universit´e de Technologie Compi´egne, 2005.
• Lebbar M., R´esolution de probl´emes combinatoire dans l'industrie: apport de la programmation math´ematique et de la d´ecomposition, Th´ese de doctorat, ´Ecole Centrale Paris, 2000.

Identyfikatory

DOI

10.24425/119524