no. 4
The integrated cutting and packing heterogeneous precast beams multiperiod production planning problem
RAIRO. Operations Research, Tome 55 (2021) no. 4, pp. 2491-2524

We introduce a novel variant of cutting production planning problems named Integrated Cutting and Packing Heterogeneous Precast Beams Multiperiod Production Planning (ICP-HPBMPP). We propose an integer linear programming model for the ICP-HPBMPP, as well as a lower bound for its optimal objective function value, which is empirically shown to be closer to the optimal solution value than the bound obtained from the linear relaxation of the model. We also propose a genetic algorithm approach for the ICP-HPBMPP as an alternative solution method. We discuss computational experiments and propose a parameterization for the genetic algorithm using D-optimal experimental design. We observe good performance of the exact approach when solving small-sized instances, although there are difficulties in finding optimal solutions for medium and large-sized problems, or even in finding feasible solutions for large instances. On the other hand, the genetic algorithm is shown to typically find good-quality solutions for large-sized instances within short computing times.

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Accepté le :
Première publication :
Publié le :
DOI : 10.1051/ro/2021107
Classification : 90C27, 90B30, 90C59, 62P30
Keywords: Precast beams, modular construction, integer linear programming, metaheuristics, genetic algorithms 
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     title = {The integrated cutting and packing heterogeneous precast beams multiperiod production planning problem},
     journal = {RAIRO. Operations Research},
     pages = {2491--2524},
     year = {2021},
     publisher = {EDP-Sciences},
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     mrnumber = {4303677},
     zbl = {1479.90172},
     language = {en},
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de Araújo, Kennedy Anderson Gumarães; de Oliveira e Bonates, Tibérius; de Athayde Prata, Bruno. The integrated cutting and packing heterogeneous precast beams multiperiod production planning problem. RAIRO. Operations Research, Tome 55 (2021) no. 4, pp. 2491-2524. doi: 10.1051/ro/2021107

[1] K. A. G. Araújo, T. O. Bonates, B. A. Prata and A. R. Pitombeira-Neto, Heterogeneous prestressed precast beams multiperiod production planning problem: modeling and solution methods. TOP 29 (2021) 660–693. | MR | Zbl | DOI

[2] M. N. Arenales, A. C. Cherri, D. N. Do Nascimento and A. Vianna, A new mathematical model for the cutting stock/leftover problem. Pesquisa Operacional 35 (2015) 509–522. | DOI

[3] B. Athayde Prata, A. R. Pitombeira Neto and C. J. Moraes Sales, An integer linear programming model for the multiperiod production planning of precast concrete beams. J. Constr. Eng. Manage. 141 (2015) 1–4. | DOI

[4] N. Beldiceanu and M. Carlsson, Global constraint catalog (Nov 2018).

[5] C. Börgers, Mathematics of Social Choice: Voting, Compensation, and Division. Society for Industrial and Applied Mathematics (SIAM) (2010). | MR | Zbl | DOI

[6] P. F. De Aguiar, B. Bourguignon, M. S. Khots, D. L. Massart and R. Phan-Than-Luu, D-optimal designs. Chemom. Intell. Lab. Syst. 30 (1995) 199–210. | DOI

[7] V. C. De Castilho, M. K. El Debs and M. Do Carmo Nicoletti, Using a modified genetic algorithm to minimize the production costs for slabs of precast prestressed concrete joists. Eng. App. Artif. Intell. 20 (2007) 519–530. | DOI

[8] H. Dyckhoff, A typology of cutting and packing problems. Eur. J. Oper. Res. 44 (1990) 145–159. | MR | Zbl | DOI

[9] M. Gholami, M. Zandieh and A. Alem-Tabriz, Scheduling hybrid flow shop with sequence-dependent setup times and machines with random breakdowns. Int. J. Adv. Manuf. Technol. 42 (2009) 189–201. | DOI

[10] P. C. Gilmore and R. E. Gomory, A linear programming approach to the cutting-stock problem. Oper. Res. 9 (1961) 849–859. | MR | Zbl | DOI

[11] P. C. Gilmore and R. E. Gomory, A linear programming approach to the cutting stock problem – part II. Oper. Res. 11 (1963) 863–888. | Zbl | DOI

[12] R. T. Marler and J. S. Arora, Survey of multi-objective optimization methods for engineering. Struct. Multi. Optim. 26 (2004) 369–395. | MR | Zbl | DOI

[13] G. M. Melega, S. A. De Araújo and R. Jans, Classification and literature review of integrated lot-sizing and cutting stock problems. Eur. J. Oper. Res. 271 (2018) 1–19. | MR | Zbl | DOI

[14] D. C. Montgomery, Design and Analysis of Experiments. John Wiley & Sons (2017). | MR | Zbl

[15] J. J. Pignatiello Jr, An overview of the strategy and tactics of taguchi. IIE Trans. 20 (1988) 247–254. | DOI

[16] K. C. Poldi and M. N. Arenales, O problema de corte de estoque unidimensional multiperodo. Pesquisa Operacional 30 (2010) 153–174. | DOI

[17] C. D. A. Signorini, S. A. De Araújo and G. M. Melega, One-dimensional multi-period cutting stock problems in the concrete industry. Int. J. Prod. Res. (2021) 1–18. DOI:. | DOI

[18] H. Stadtler, A one-dimensional cutting stock problem in the aluminium industry and its solution. Eur. J. Oper. Res. 44 (1990) 209–223. | Zbl | DOI

[19] F. Triefenbach, Design of experiments: the D-optimal approach and its implementation as a computer algorithm. Bachelor’s Thesis in Information and Communication Technology (2008).

[20] P. Trkman and M. Gradisar, One-dimensional cutting stock optimization in consecutive time periods. Eur. J. Oper. Res. 179 (2007) 291–301. | Zbl | DOI

[21] P. H. Vance, Branch-and-price algorithms for the one-dimensional cutting stock problem. Comput. Optim. App. 9 (1998) 211–228. | MR | Zbl | DOI

[22] A. H. D. Vassoler, S. C. Poltroniere and S. A. Araújo, Modelagem matemática para o problema de produção de vigotas na indústria de lajes treliçadas. Revista Eletrônica Paulista de Matemática 7 (2016) 68–77. | DOI

[23] Z. Wang, H. Hu and J. Gong, Framework for modeling operational uncertainty to optimize offsite production scheduling of precast components. Autom. Constr. 86 (2018) 69–80. | DOI

[24] G. Wäscher, H. Haußner and H. Schumann, An improved typology of cutting and packing problems. Eur. J. Oper. Res. 183 (2007) 1109–1130. | Zbl | DOI

[25] L. A. Wolsey, Integer Programming. John Wiley & Sons (2020). | Zbl | DOI

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