A mixed-integer linear programming model for the cutting stock problem in the steel industry

A mixed-integer linear programming (MILP) model is proposed for solving a one dimension cutting stock problem (1D-CSP) in the steel industry. A case study of a metallurgical company is presented and the objective is to minimize waste in the cutting process of steel bars, considering inventory constr...

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Autores:
Morillo-Torres, Daniel
Torres Baena, Mauricio
Escobar, John Wilmer
Romero-Conrado, Alfonso R.
Romero-Conrado, Alfonso R.
Gustavo, Gatica
Tipo de recurso:
Part of book
Fecha de publicación:
2021
Institución:
Corporación Universidad de la Costa
Repositorio:
REDICUC - Repositorio CUC
Idioma:
eng
OAI Identifier:
oai:repositorio.cuc.edu.co:11323/9356
Acceso en línea:
https://hdl.handle.net/11323/9356
https://doi.org/10.1007/978-3-030-86702-7_27
https://repositorio.cuc.edu.co/
Palabra clave:
Cutting stock problem
Mixed-integer linear programming
Steel bars
Industrial application
Rights
openAccess
License
Atribución-NoComercial-CompartirIgual 4.0 Internacional (CC BY-NC-SA 4.0)
id RCUC2_fbd950db8d9a4f28abadf1737203508b
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repository_id_str
dc.title.eng.fl_str_mv A mixed-integer linear programming model for the cutting stock problem in the steel industry
title A mixed-integer linear programming model for the cutting stock problem in the steel industry
spellingShingle A mixed-integer linear programming model for the cutting stock problem in the steel industry
Cutting stock problem
Mixed-integer linear programming
Steel bars
Industrial application
title_short A mixed-integer linear programming model for the cutting stock problem in the steel industry
title_full A mixed-integer linear programming model for the cutting stock problem in the steel industry
title_fullStr A mixed-integer linear programming model for the cutting stock problem in the steel industry
title_full_unstemmed A mixed-integer linear programming model for the cutting stock problem in the steel industry
title_sort A mixed-integer linear programming model for the cutting stock problem in the steel industry
dc.creator.fl_str_mv Morillo-Torres, Daniel
Torres Baena, Mauricio
Escobar, John Wilmer
Romero-Conrado, Alfonso R.
Romero-Conrado, Alfonso R.
Gustavo, Gatica
dc.contributor.author.spa.fl_str_mv Morillo-Torres, Daniel
Torres Baena, Mauricio
Escobar, John Wilmer
Romero-Conrado, Alfonso R.
Romero-Conrado, Alfonso R.
Gustavo, Gatica
dc.subject.proposal.eng.fl_str_mv Cutting stock problem
Mixed-integer linear programming
Steel bars
Industrial application
topic Cutting stock problem
Mixed-integer linear programming
Steel bars
Industrial application
description A mixed-integer linear programming (MILP) model is proposed for solving a one dimension cutting stock problem (1D-CSP) in the steel industry. A case study of a metallurgical company is presented and the objective is to minimize waste in the cutting process of steel bars, considering inventory constraints and the potential use of the resulting leftovers. The computational results showed that an optimal solution was always found with an average improvement in waste reduction of 80%. There was no significant difference when comparing results between the complete model and the model without inventory constraints.
publishDate 2021
dc.date.issued.none.fl_str_mv 2021
dc.date.accessioned.none.fl_str_mv 2022-07-11T13:31:01Z
dc.date.available.none.fl_str_mv 2022-07-11T13:31:01Z
dc.type.spa.fl_str_mv Capítulo - Parte de Libro
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dc.identifier.citation.spa.fl_str_mv Morillo-Torres, D., Baena, M.T., Escobar, J.W., Romero-Conrado, A.R., Coronado-Hernández, J.R., Gatica, G. (2021). A Mixed-Integer Linear Programming Model for the Cutting Stock Problem in the Steel Industry. In: Figueroa-García, J.C., Díaz-Gutierrez, Y., Gaona-García, E.E., Orjuela-Cañón, A.D. (eds) Applied Computer Sciences in Engineering. WEA 2021. Communications in Computer and Information Science, vol 1431. Springer, Cham. https://doi.org/10.1007/978-3-030-86702-7_27
dc.identifier.isbn.spa.fl_str_mv 978-3-030-86701-0
dc.identifier.uri.spa.fl_str_mv https://hdl.handle.net/11323/9356
dc.identifier.url.spa.fl_str_mv https://doi.org/10.1007/978-3-030-86702-7_27
dc.identifier.doi.spa.fl_str_mv 10.1007/978-3-030-86702-7_27
dc.identifier.instname.spa.fl_str_mv Corporación Universidad de la Costa
dc.identifier.reponame.spa.fl_str_mv REDICUC - Repositorio CUC
dc.identifier.repourl.spa.fl_str_mv https://repositorio.cuc.edu.co/
dc.identifier.eisbn.spa.fl_str_mv 978-3-030-86702-7
identifier_str_mv Morillo-Torres, D., Baena, M.T., Escobar, J.W., Romero-Conrado, A.R., Coronado-Hernández, J.R., Gatica, G. (2021). A Mixed-Integer Linear Programming Model for the Cutting Stock Problem in the Steel Industry. In: Figueroa-García, J.C., Díaz-Gutierrez, Y., Gaona-García, E.E., Orjuela-Cañón, A.D. (eds) Applied Computer Sciences in Engineering. WEA 2021. Communications in Computer and Information Science, vol 1431. Springer, Cham. https://doi.org/10.1007/978-3-030-86702-7_27
978-3-030-86701-0
10.1007/978-3-030-86702-7_27
Corporación Universidad de la Costa
REDICUC - Repositorio CUC
978-3-030-86702-7
url https://hdl.handle.net/11323/9356
https://doi.org/10.1007/978-3-030-86702-7_27
https://repositorio.cuc.edu.co/
dc.language.iso.none.fl_str_mv eng
language eng
dc.relation.ispartofseries.spa.fl_str_mv Communications in Computer and Information Science;
dc.relation.ispartofbook.spa.fl_str_mv Applied Computer Sciences in Engineering
dc.relation.references.spa.fl_str_mv Benjaoran, V., Bhokha, S.: Three-step solutions for cutting stock problem of construction steel bars. KSCE J. Civ. Eng. 18(5), 1239–1247 (2014). https://doi.org/10.1007/s12205-014-0238-3
Benjaoran, V., Sooksil, N., Metham, M.: Effect of demand variations on steel bars cutting loss. Int. J. Constr. Manag. 19(2), 137–148 (2019). https://doi.org/10.1080/15623599.2017.1401258
Cheng, C.H., Feiring, B.R., Cheng, T.C.: The cutting stock problem - a survey. Int. J. Prod. Econ. 36(3), 291–305 (1994). https://doi.org/10.1016/0925-5273(94)00045-X
Cherri, A.C., Arenales, M.N., Yanasse, H.H., Poldi, K.C., Gonçalves Vianna, A.C.: The one-dimensional cutting stock problem with usable leftovers - a survey. Eur. J. Oper. Res. 236(2), 395–402 (2014). https://doi.org/10.1016/j.ejor.2013.11.026
Cui, Y., Yang, Y.: A heuristic for the one-dimensional cutting stock problem with usable leftover. Eur. J. Oper. Res. 204(2), 245–250 (2010). https://doi.org/10.1016/j.ejor.2009.10.028
Dell’Amico, M., Furini, F., Iori, M.: A branch-and-price algorithm for the temporal bin packing problem. Comput. Oper. Res. 114, 104825 (2020). https://doi.org/10.1016/j.cor.2019.104825
Delorme, M., Iori, M.: Enhanced pseudo-polynomial formulations for bin packing and cutting stock problems. INFORMS J. Comput. 32(1), 101–119 (2020). https://doi.org/10.1287/IJOC.2018.0880
Dyckhoff, H.: New linear programming approach to the cutting stock problem. Oper. Res. 29(6), 1092–1104 (1981). https://doi.org/10.1287/opre.29.6.1092
Dyckhoff, H.: A typology of cutting and packing problems. Eur. J. Oper. Res. 44(2), 145–159 (1990). https://doi.org/10.1016/0377-2217(90)90350-K
Filho, A.A., Moretti, A.C., Pato, M.V.: A comparative study of exact methods for the bi-objective integer one-dimensional cutting stock problem. J. Oper. Res. Soc. 69(1), 91–107 (2018). https://doi.org/10.1057/s41274-017-0214-7
Gilmore, P.C., Gomory, R.E.: A linear programming approach to the cutting stock problem-Part II. Oper. Res. 11(6), 863–888 (1963). https://doi.org/10.1287/opre.11.6.863
Golden, B.L.: Approaches to the cutting stock problem. AIIE Trans. 8(2), 265–274 (1976). https://doi.org/10.1080/05695557608975076
Jahromi, M.H., Tavakkoli-Moghaddam, R., Makui, A., Shamsi, A.: Solving an one-dimensional cutting stock problem by simulated annealing and tabu search. J. Ind. Eng. Int. 8(1), 24 (2012). https://doi.org/10.1186/2251-712X-8-24
Kantorovich, L.V.: Mathematical methods of organizing and planning production. Manag. Sci. 6(4), 366–422 (1960). https://doi.org/10.1287/mnsc.6.4.366
Lackes, R., Siepermann, M., Noll, T.: The problem of one-dimensionally cutting bars with alternative cutting lengths in the tubes rolling process. In: IEEE International Conference on Industrial Engineering and Engineering Management, pp. 1627–1631. IEEE Computer Society, Department of Business Information Management, Technische Universität Dortmund, Dortmund, Germany (2012). https://doi.org/10.1109/IEEM.2012.6838022
Lemos, F.K., Cherri, A.C., de Araujo, S.A.: The cutting stock problem with multiple manufacturing modes applied to a construction industry. Int. J. Prod. Res. 59(4), 1–19 (2020). https://doi.org/10.1080/00207543.2020.1720923
Maher, R.A., Melhem, N.N., Almutlaq, M.: Developing a control and management system for reinforcement steel-leftover in industrial factories. IFAC-PapersOnLine 52(13), 625–629 (2019). https://doi.org/10.1016/j.ifacol.2019.11.091
Moussavi Nadoushani, Z.S., Hammad, A.W., Xiao, J., Akbarnezhad, A.: Minimizing cutting wastes of reinforcing steel bars through optimizing lap splicing within reinforced concrete elements. Constr. Build. Mater. 185, 600–608 (2018). https://doi.org/10.1016/j.conbuildmat.2018.07.023
Pitombeira-Neto, A.R., Prata, B.d.A.: A matheuristic algorithm for the one-dimensional cutting stock and scheduling problem with heterogeneous orders. Top 28(1), 178–192 (2020). https://doi.org/10.1007/s11750-019-00531-3
Romero-Conrado, A.R., Coronado-Hernandez, J.R., Rius-Sorolla, G., García-Sabater, J.P.: A Tabu list-based algorithm for capacitated multilevel lot-sizing with alternate bills of materials and co-production environments. Appl. Sci. (Switzerland) 9(7), 1464 (2019). https://doi.org/10.3390/app9071464
Rothe, M., Reyer, M., Mathar, R.: Process optimization for cutting steel-plates. In: Liberatore, F., Parlier, G.H., Demange, M. (eds.) ICORES 2017 - Proceedings of the 6th International Conference on Operations Research and Enterprise Systems, vol. 2017-Janua, pp. 27–37. SCITEPRESS - Science and Technology Publications, Institute for Theoretical Information Technology, RWTH Aachen University, Kopernikusstraße 16, Aachen, 52074, Germany (2017). https://doi.org/10.5220/0006108400270037
Valério De Carvalho, J.M.: Exact solution of bin-packing problems using column generation and branch-and-bound. Ann. Oper. Res. 86(0), 629–659 (1999). https://doi.org/10.1023/a:1018952112615
Vance, P.H., Barnhart, C., Johnson, E.L., Nemhauser, G.L.: Solving binary cutting stock problems by column generation and branch-and-bound. Comput. Optim. Appl. 3(2), 111–130 (1994). https://doi.org/10.1007/BF01300970
Vanderbeck, F.: Computational study of a column generation algorithm for bin packing and cutting stock problems. Math. Program. Ser. B 86(3), 565–594 (1999). https://doi.org/10.1007/s101070050105
Varela, R., Vela, C.R., Puente, J., Sierra, M., González-Rodríguez, I.: An effective solution for a real cutting stock problem in manufacturing plastic rolls. Ann. Oper. Res. 166(1), 125–146 (2009). https://doi.org/10.1007/s10479-008-0407-1
Wäscher, G., Haußner, H., Schumann, H.: An improved typology of cutting and packing problems. Eur. J. Oper. Res. 183(3), 1109–1130 (2007). https://doi.org/10.1016/j.ejor.2005.12.047
Yang, C.T., Sung, T.C., Weng, W.C.: An improved tabu search approach with mixed objective function for one-dimensional cutting stock problems. Adv. Eng. Softw. 37(8), 502–513 (2006). https://doi.org/10.1016/j.advengsoft.2006.01.005
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spelling Morillo-Torres, DanielTorres Baena, MauricioEscobar, John WilmerRomero-Conrado, Alfonso R.Romero-Conrado, Alfonso R.Gustavo, Gatica2022-07-11T13:31:01Z2022-07-11T13:31:01Z2021Morillo-Torres, D., Baena, M.T., Escobar, J.W., Romero-Conrado, A.R., Coronado-Hernández, J.R., Gatica, G. (2021). A Mixed-Integer Linear Programming Model for the Cutting Stock Problem in the Steel Industry. In: Figueroa-García, J.C., Díaz-Gutierrez, Y., Gaona-García, E.E., Orjuela-Cañón, A.D. (eds) Applied Computer Sciences in Engineering. WEA 2021. Communications in Computer and Information Science, vol 1431. Springer, Cham. https://doi.org/10.1007/978-3-030-86702-7_27978-3-030-86701-0https://hdl.handle.net/11323/9356https://doi.org/10.1007/978-3-030-86702-7_2710.1007/978-3-030-86702-7_27Corporación Universidad de la CostaREDICUC - Repositorio CUChttps://repositorio.cuc.edu.co/978-3-030-86702-7A mixed-integer linear programming (MILP) model is proposed for solving a one dimension cutting stock problem (1D-CSP) in the steel industry. A case study of a metallurgical company is presented and the objective is to minimize waste in the cutting process of steel bars, considering inventory constraints and the potential use of the resulting leftovers. The computational results showed that an optimal solution was always found with an average improvement in waste reduction of 80%. There was no significant difference when comparing results between the complete model and the model without inventory constraints.1 páginaapplication/pdfengSpringer, ChamSwitzerlandCommunications in Computer and Information Science;Applied Computer Sciences in EngineeringBenjaoran, V., Bhokha, S.: Three-step solutions for cutting stock problem of construction steel bars. KSCE J. Civ. Eng. 18(5), 1239–1247 (2014). https://doi.org/10.1007/s12205-014-0238-3Benjaoran, V., Sooksil, N., Metham, M.: Effect of demand variations on steel bars cutting loss. Int. J. Constr. Manag. 19(2), 137–148 (2019). https://doi.org/10.1080/15623599.2017.1401258Cheng, C.H., Feiring, B.R., Cheng, T.C.: The cutting stock problem - a survey. Int. J. Prod. Econ. 36(3), 291–305 (1994). https://doi.org/10.1016/0925-5273(94)00045-XCherri, A.C., Arenales, M.N., Yanasse, H.H., Poldi, K.C., Gonçalves Vianna, A.C.: The one-dimensional cutting stock problem with usable leftovers - a survey. Eur. J. Oper. Res. 236(2), 395–402 (2014). https://doi.org/10.1016/j.ejor.2013.11.026Cui, Y., Yang, Y.: A heuristic for the one-dimensional cutting stock problem with usable leftover. Eur. J. Oper. Res. 204(2), 245–250 (2010). https://doi.org/10.1016/j.ejor.2009.10.028Dell’Amico, M., Furini, F., Iori, M.: A branch-and-price algorithm for the temporal bin packing problem. Comput. Oper. Res. 114, 104825 (2020). https://doi.org/10.1016/j.cor.2019.104825Delorme, M., Iori, M.: Enhanced pseudo-polynomial formulations for bin packing and cutting stock problems. INFORMS J. Comput. 32(1), 101–119 (2020). https://doi.org/10.1287/IJOC.2018.0880Dyckhoff, H.: New linear programming approach to the cutting stock problem. Oper. Res. 29(6), 1092–1104 (1981). https://doi.org/10.1287/opre.29.6.1092Dyckhoff, H.: A typology of cutting and packing problems. Eur. J. Oper. Res. 44(2), 145–159 (1990). https://doi.org/10.1016/0377-2217(90)90350-KFilho, A.A., Moretti, A.C., Pato, M.V.: A comparative study of exact methods for the bi-objective integer one-dimensional cutting stock problem. J. Oper. Res. Soc. 69(1), 91–107 (2018). https://doi.org/10.1057/s41274-017-0214-7Gilmore, P.C., Gomory, R.E.: A linear programming approach to the cutting stock problem-Part II. Oper. Res. 11(6), 863–888 (1963). https://doi.org/10.1287/opre.11.6.863Golden, B.L.: Approaches to the cutting stock problem. AIIE Trans. 8(2), 265–274 (1976). https://doi.org/10.1080/05695557608975076Jahromi, M.H., Tavakkoli-Moghaddam, R., Makui, A., Shamsi, A.: Solving an one-dimensional cutting stock problem by simulated annealing and tabu search. J. Ind. Eng. Int. 8(1), 24 (2012). https://doi.org/10.1186/2251-712X-8-24Kantorovich, L.V.: Mathematical methods of organizing and planning production. Manag. Sci. 6(4), 366–422 (1960). https://doi.org/10.1287/mnsc.6.4.366Lackes, R., Siepermann, M., Noll, T.: The problem of one-dimensionally cutting bars with alternative cutting lengths in the tubes rolling process. In: IEEE International Conference on Industrial Engineering and Engineering Management, pp. 1627–1631. IEEE Computer Society, Department of Business Information Management, Technische Universität Dortmund, Dortmund, Germany (2012). https://doi.org/10.1109/IEEM.2012.6838022Lemos, F.K., Cherri, A.C., de Araujo, S.A.: The cutting stock problem with multiple manufacturing modes applied to a construction industry. Int. J. Prod. Res. 59(4), 1–19 (2020). https://doi.org/10.1080/00207543.2020.1720923Maher, R.A., Melhem, N.N., Almutlaq, M.: Developing a control and management system for reinforcement steel-leftover in industrial factories. IFAC-PapersOnLine 52(13), 625–629 (2019). https://doi.org/10.1016/j.ifacol.2019.11.091Moussavi Nadoushani, Z.S., Hammad, A.W., Xiao, J., Akbarnezhad, A.: Minimizing cutting wastes of reinforcing steel bars through optimizing lap splicing within reinforced concrete elements. Constr. Build. Mater. 185, 600–608 (2018). https://doi.org/10.1016/j.conbuildmat.2018.07.023Pitombeira-Neto, A.R., Prata, B.d.A.: A matheuristic algorithm for the one-dimensional cutting stock and scheduling problem with heterogeneous orders. Top 28(1), 178–192 (2020). https://doi.org/10.1007/s11750-019-00531-3Romero-Conrado, A.R., Coronado-Hernandez, J.R., Rius-Sorolla, G., García-Sabater, J.P.: A Tabu list-based algorithm for capacitated multilevel lot-sizing with alternate bills of materials and co-production environments. Appl. Sci. (Switzerland) 9(7), 1464 (2019). https://doi.org/10.3390/app9071464Rothe, M., Reyer, M., Mathar, R.: Process optimization for cutting steel-plates. In: Liberatore, F., Parlier, G.H., Demange, M. (eds.) ICORES 2017 - Proceedings of the 6th International Conference on Operations Research and Enterprise Systems, vol. 2017-Janua, pp. 27–37. SCITEPRESS - Science and Technology Publications, Institute for Theoretical Information Technology, RWTH Aachen University, Kopernikusstraße 16, Aachen, 52074, Germany (2017). https://doi.org/10.5220/0006108400270037Valério De Carvalho, J.M.: Exact solution of bin-packing problems using column generation and branch-and-bound. Ann. Oper. Res. 86(0), 629–659 (1999). https://doi.org/10.1023/a:1018952112615Vance, P.H., Barnhart, C., Johnson, E.L., Nemhauser, G.L.: Solving binary cutting stock problems by column generation and branch-and-bound. Comput. Optim. Appl. 3(2), 111–130 (1994). https://doi.org/10.1007/BF01300970Vanderbeck, F.: Computational study of a column generation algorithm for bin packing and cutting stock problems. Math. Program. Ser. B 86(3), 565–594 (1999). https://doi.org/10.1007/s101070050105Varela, R., Vela, C.R., Puente, J., Sierra, M., González-Rodríguez, I.: An effective solution for a real cutting stock problem in manufacturing plastic rolls. Ann. Oper. Res. 166(1), 125–146 (2009). https://doi.org/10.1007/s10479-008-0407-1Wäscher, G., Haußner, H., Schumann, H.: An improved typology of cutting and packing problems. Eur. J. Oper. Res. 183(3), 1109–1130 (2007). https://doi.org/10.1016/j.ejor.2005.12.047Yang, C.T., Sung, T.C., Weng, W.C.: An improved tabu search approach with mixed objective function for one-dimensional cutting stock problems. Adv. Eng. Softw. 37(8), 502–513 (2006). https://doi.org/10.1016/j.advengsoft.2006.01.005326315Atribución-NoComercial-CompartirIgual 4.0 Internacional (CC BY-NC-SA 4.0)© 2021 Springer Nature Switzerland AGhttps://creativecommons.org/licenses/by-nc-sa/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2A mixed-integer linear programming model for the cutting stock problem in the steel industryCapítulo - Parte de Librohttp://purl.org/coar/resource_type/c_3248Textinfo:eu-repo/semantics/bookParthttp://purl.org/redcol/resource_type/CAP_LIBhttp://purl.org/coar/version/c_b1a7d7d4d402bccehttps://link.springer.com/chapter/10.1007/978-3-030-86702-7_27Cutting stock problemMixed-integer linear programmingSteel barsIndustrial applicationPublicationORIGINALA Mixed-Integer Linear Programming Model for the Cutting Stock Problem in the Steel Industry.pdfA Mixed-Integer Linear Programming Model for the Cutting Stock Problem in the Steel 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