A heuristic approach for the double row layout problem

Amaral, A. R. S.

doi:10.1007/s10479-020-03617-5

A heuristic approach for the double row layout problem

S.I.: CLAIO 2018
Published: 30 April 2020

Volume 316, pages 1–36, (2022)
Cite this article

Annals of Operations Research Aims and scope Submit manuscript

A. R. S. Amaral ORCID: orcid.org/0000-0001-7344-3994¹

613 Accesses
17 Citations
Explore all metrics

Abstract

In the double row layout problem, we wish to position n machines on two parallel rows in order to minimize the cost of material flow among machines. The problem is NP-hard and has applications in industry. Here, an algorithm is presented, which works in two phases: (1) applying an improvement heuristic to optimize a random double row layout of a certain type and, then, (2) adjusting the absolute position of each machine in the layout via Linear Programming. Four variants of this two-phase algorithm are proposed and their efficiency is demonstrated by computational tests on several instances from the literature with sizes up to 50 machines.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

A mixed-integer programming formulation of the double row layout problem based on a linear extension of a partial order

Article 18 November 2020

Mathematical optimization approach for facility layout on several rows

Article Open access 24 July 2020

Mathematical formulation and two-phase optimisation methodology for the constrained double-row layout problem

Article 22 January 2022

References

Ahonen, H., de Alvarenga, A. G., & Amaral, A. R. S. (2014). Simulated annealing and tabu search approaches for the Corridor Allocation Problem. European Journal of Operational Research, 232(1), 221–233. https://doi.org/10.1016/j.ejor.2013.07.01.
Article Google Scholar
Amaral, A. R. S. (2006). On the exact solution of a facility layout problem. European Journal of Operational Research, 173(2), 508–518. https://doi.org/10.1016/j.ejor.2004.12.021.
Article Google Scholar
Amaral, A. R. S. (2008a). Enhanced local search applied to the singlerow facility layout problem. In Annals of the XL SBPO - Simpósio Brasileiro de Pesquisa Operacional, João Pessoa, Brazil, pp. 1638–1647. http://www.din.uem.br/sbpo/sbpo2008/pdf/arq0026.pdf.
Amaral, A. R. S. (2008b). An exact approach to the one-dimensional facility layout problem. Operations Research, 56(4), 1026–1033. https://doi.org/10.1287/opre.1080.0548.
Article Google Scholar
Amaral, A. R. S. (2009). A new lower bound for the single row facility layout problem. Discrete Applied Mathematics, 157(1), 183–190. https://doi.org/10.1016/j.dam.2008.06.002.
Article Google Scholar
Amaral, A. R. S. (2012). The corridor allocation problem. Computers & Operations Research, 39(12), 3325–3330. https://doi.org/10.1016/j.cor.2012.04.016.
Article Google Scholar
Amaral, A. R. S. (2013a). Optimal solutions for the double row layout problem. Optimization Letters, 7, 407–413. https://doi.org/10.1007/s11590-011-0426-8.
Article Google Scholar
Amaral, A. R. S. (2013b). A parallel ordering problem in facilities layout. Computers & Operations Research, 40(12), 2930–2939. https://doi.org/10.1016/j.cor.2013.07.003.
Article Google Scholar
Amaral, A. R. S. (2018). A mixed-integer programming formulation for the double row layout of machines in manufacturing systems. International Journal of Production Research 1–14.
Amaral, A. R. S., & Letchford, A. N. (2013). A polyhedral approach to the single row facility layout problem. Mathematical Programming, 141(1–2), 453–477. https://doi.org/10.1007/s10107-012-0533-z.
Article Google Scholar
Anjos, M. F., & Vannelli, A. (2008). Computing globally optimal solutions for single-row layout problems using semidefinite programming and cutting planes. INFORMS Journal on Computing, 20(4), 611–617. https://doi.org/10.1287/ijoc.1080.0270.
Article Google Scholar
Anjos, M. F., & Yen, G. (2009). Provably near-optimal solutions for very large single-row facility layout problems. Optimization Methods and Software, 24(4), 805–817.
Article Google Scholar
Anjos, M. F., Kennings, A., & Vannelli, A. (2005). A semidefinite optimization approach for the single-row layout problem with unequal dimensions. Discrete Optimization, 2(2), 113–122. https://doi.org/10.1016/j.disopt.2005.03.001.
Article Google Scholar
Chung, J., & Tanchoco, J. M. A. (2010). The double row layout problem. International Journal of Production Research, 48(3), 709–727. https://doi.org/10.1080/00207540802192126.
Article Google Scholar
Cravo, G., & Amaral, A. (2019). A grasp algorithm for solving large-scale single row facility layout problems. Computers & Operations Research, 106, 49–61. https://doi.org/10.1016/j.cor.2019.02.009.
Article Google Scholar
Datta, D., Amaral, A. R. S., & Figueira, J. R. (2011). Single row facility layout problem using a permutation-based genetic algorithm. European Journal of Operational Research, 213(2), 388–394. https://doi.org/10.1016/j.ejor.2011.03.034.
Article Google Scholar
de Alvarenga, A. G., Negreiros-Gomes, F. J., & Mestria, M. (2000). Metaheuristic methods for a class of the facility layout problem. Journal of Intelligent Manufacturing, 11, 421–430. https://doi.org/10.1023/A:1008982420344.
Article Google Scholar
Drira, A., Pierreval, H., & Hajri-Gabouj, S. (2007). Facility layout problems: A survey. Annual Reviews in Control, 31(2), 255–267. https://doi.org/10.1016/j.arcontrol.2007.04.001.
Article Google Scholar
Guan, J., & Lin, G. (2016). Hybridizing variable neighborhood search with ant colony optimization for solving the single row facility layout problem. European Journal of Operational Research, 248(3), 899–909. https://doi.org/10.1016/j.ejor.2015.08.014.
Article Google Scholar
Heragu, S. S., & Alfa, A. S. (1992). Experimental analysis of simulated annealing based algorithms for the layout problem. European Journal of Operational Research, 57(2), 190–202. https://doi.org/10.1016/0377-2217(92)90042-8.
Article Google Scholar
Heragu, S. S., & Kusiak, A. (1988). Machine layout problem in flexible manufacturing systems. Operations Research, 36(2), 258–268. https://doi.org/10.1287/opre.36.2.258.
Article Google Scholar
Heragu, S. S., & Kusiak, A. (1991). Efficient models for the facility layout problem. European Journal of Operational Research, 53(1), 1–13. https://doi.org/10.1016/0377-2217(91)90088-D.
Article Google Scholar
Hungerländer, P., & Rendl, F. (2012). A computational study and survey of methods for the single-row facility layout problem. Computational Optimization and Applications,. https://doi.org/10.1007/s10589-012-9505-8.
Article Google Scholar
Kothari, R., & Ghosh, D. (2013a). An efficient genetic algorithm for single row facility layout. Optimization Letters,. https://doi.org/10.1007/s11590-012-0605-2.
Article Google Scholar
Kothari, R., & Ghosh, D. (2013b). Tabu search for the single row facility layout problem using exhaustive 2-opt and insertion neighborhoods. European Journal of Operational Research, 224(1), 93–100. https://doi.org/10.1016/j.ejor.2012.07.037.
Article Google Scholar
Kothari, R., & Ghosh, D. (2014). A scatter search algorithm for the single row facility layout problem. Journal of Heuristics, 20(2), 125–142. https://doi.org/10.1007/s10732-013-9234-x.
Article Google Scholar
Kumar, R. M. S., Asokan, P., Kumanan, S., & Varma, B. (2008). Scatter search algorithm for single row layout problem in fms. Advances in Production Engineering & Management, 3, 193–204.
Google Scholar
Love, R. F., & Wong, J. Y. (1976). On solving a one-dimensional space allocation problem with integer programming. INFOR, 14(2), 139–143.
Google Scholar
Murray, C. C., Smith, A. E., & Zhang, Z. (2013). An efficient local search heuristic for the double row layout problem with asymmetric material flow. International Journal of Production Research, 51(20), 6129–6139. https://doi.org/10.1080/00207543.2013.803168.
Article Google Scholar
Ozcelik, F. (2012). A hybrid genetic algorithm for the single row layout problem. International Journal of Production Research, 50(20), 5872–5886. https://doi.org/10.1080/00207543.2011.636386.
Article Google Scholar
Palubeckis, G. (2015). Fast local search for single row facility layout. European Journal of Operational Research, 246(3), 800–814. https://doi.org/10.1016/j.ejor.2015.05.055.
Article Google Scholar
Palubeckis, G. (2017). Single row facility layout using multi-start simulated annealing. Computers & Industrial Engineering, 103, 1–16. https://doi.org/10.1016/j.cie.2016.09.026.
Article Google Scholar
Picard, J. C., & Queyranne, M. (1981). On the one-dimensional space allocation problem. Operations Research, 29(2), 371–391. https://doi.org/10.1287/opre.29.2.371.
Article Google Scholar
Samarghandi, H., & Eshghi, K. (2010). An efficient tabu algorithm for the single row facility layout problem. European Journal of Operational Research, 205(1), 98–105. https://doi.org/10.1016/j.ejor.2009.11.034.
Article Google Scholar
Samarghandi, H., Taabayan, P., & Jahantigh, F. F. (2010). A particle swarm optimization for the single row facility layout problem. Computers & Industrial Engineering, 58(4), 529–534. https://doi.org/10.1016/j.cie.2009.11.015.
Article Google Scholar
Secchin, L., & Amaral, A. R. S. (2018). An improved mixed-integer programming model for the double row layout of facilities. Optimization Letters, 1–7.
Simmons, D. M. (1969). One-dimensional space allocation: An ordering algorithm. Operations Research, 17(5), 812–826. https://doi.org/10.1287/opre.17.5.812.
Article Google Scholar
Solimanpur, M., Vrat, P., & Shankar, R. (2005). An ant algorithm for the single row layout problem in flexible manufacturing systems. Computers & Operations Research, 32(3), 583–598. https://doi.org/10.1016/j.cor.2003.08.005.
Article Google Scholar
Tubaileh, A., & Siam, J. (2017). Single and multi-row layout design for flexible manufacturing systems. International Journal of Computer Integrated Manufacturing,. https://doi.org/10.1080/0951192X.2017.1314013.
Article Google Scholar
Wang, S., Zuo, X., Liu, X., Zhao, X., & Li, J. (2015). Solving dynamic double row layout problem via combining simulated annealing and mathematical programming. Applied Soft Computing, 37, 303–310. https://doi.org/10.1016/j.asoc.2015.08.023.
Article Google Scholar
Yang, X., Cheng, W., Smith, A., & Amaral, A. R. S. (2018). An improved model for the parallel row ordering problem. Journal of the Operational Research Society, 1–26.
Zhang, Z., & Murray, C. C. (2012). A corrected formulation for the double row layout problem. International Journal of Production Research, 50(15), 4220–4223. https://doi.org/10.1080/00207543.2011.603371.
Article Google Scholar
Zuo, X., Murray, C. C., & Smith, A. E. (2014). Solving an extended double row layout problem using multiobjective tabu search and linear programming. IEEE Transactions on Automation Science and Engineering, 11(4), 1122–1132.
Article Google Scholar
Zuo, X., Murray, C., & Smith, A. (2016). Sharing clearances to improve machine layout. International Journal of Production Research, 54(14), 4272–4285. https://doi.org/10.1080/00207543.2016.1142134.
Article Google Scholar

Download references

Acknowledgements

This study was financed in part by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance Code 001; and in part by Fundação de Amparo à Pesquisa e Inovação do Espírito Santo (FAPES).

Author information

Authors and Affiliations

Graduate School of Computer Science (PPGI), Federal University of Espírito Santo (UFES), Vitória, 29075-910, Brazil
A. R. S. Amaral

Authors

A. R. S. Amaral
View author publications
You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. R. S. Amaral.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix A

See Tables 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 and 20

Table 9 Average and standard deviation times and minimum, average and standard deviation solution values out of 10 runs for \({ Heuristic}1\) and \({ Heuristic}1+LP\) on DRLP instances with sizes \(9\le n\le 17\)

Full size table

Table 10 Average and standard deviation times and minimum, average and standard deviation solution values out of 10 runs for \({ Heuristic}2\) and \({ Heuristic}2+LP\) on DRLP instances with sizes \(9\le n\le 17\)

Full size table

Table 11 Average and standard deviation times and minimum, average and standard deviation solution values out of 10 runs for \({ Heuristic}3\) and \({ Heuristic}3+LP\) on DRLP instances with sizes \(9\le n\le 17\)

Full size table

Table 12 Average and standard deviation times and minimum, average and standard deviation solution values out of 10 runs for \({ Heuristic}4\) and \({ Heuristic}4+LP\) on DRLP instances with sizes \(9\le n\le 17\)

Full size table

Table 13 Average and standard deviation times and minimum, average and standard deviation solution values out of 10 runs for \({ Heuristic}1\) and \({ Heuristic}1+LP\) on DRLP instances with sizes \(n\in \{30,\,40\}\)

Full size table

Table 14 Average and standard deviation times and minimum, average and standard deviation solution values out of 10 runs for \({ Heuristic}2\) and \({ Heuristic}2+LP\) on DRLP instances with sizes \(n\in \{30,\,40\}\)

Full size table

Table 15 Average and standard deviation times and minimum, average and standard deviation solution values out of 10 runs for \({ Heuristic}3\) and \({ Heuristic}3+LP\) on DRLP instances with sizes \(n\in \{30,\,40\}\)

Full size table

Table 16 Average and standard deviation times and minimum, average and standard deviation solution values out of 10 runs for \({ Heuristic}4\) and \({ Heuristic}4+LP\) on DRLP instances with sizes \(n\in \{30,\,40\}\)

Full size table

Table 17 Average and standard deviation times and minimum, average and standard deviation solution values out of 10 runs for \({ Heuristic}1\) and \({ Heuristic}1+LP\) on DRLP instances with sizes \(n=50\)

Full size table

Table 18 Average and standard deviation times and minimum, average and standard deviation solution values out of 10 runs for \({ Heuristic}2\) and \({ Heuristic}2+LP\) on DRLP instances with sizes \(n=50\)

Full size table

Table 19 Average and standard deviation times and minimum, average and standard deviation solution values out of 10 runs for \({ Heuristic}3\) and \({ Heuristic}3+LP\) on DRLP instances with sizes \(n=50\)

Full size table

Table 20 Average and standard deviation times and minimum, average and standard deviation solution values out of 10 runs for \({ Heuristic}4\) and \({ Heuristic}4+LP\) on DRLP instances with sizes \(n=50\)

Full size table

Rights and permissions

Reprints and permissions

About this article

Cite this article

Amaral, A.R.S. A heuristic approach for the double row layout problem. Ann Oper Res 316, 1–36 (2022). https://doi.org/10.1007/s10479-020-03617-5

Download citation

Published: 30 April 2020
Issue Date: September 2022
DOI: https://doi.org/10.1007/s10479-020-03617-5

Keywords

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

A heuristic approach for the double row layout problem

Abstract

Access this article

Similar content being viewed by others

A mixed-integer programming formulation of the double row layout problem based on a linear extension of a partial order

Mathematical optimization approach for facility layout on several rows

Mathematical formulation and two-phase optimisation methodology for the constrained double-row layout problem

References

Acknowledgements

Author information

Authors and Affiliations

Corresponding author

Additional information

Publisher's Note

Appendix A

Rights and permissions

About this article

Cite this article

Keywords

Navigation

A heuristic approach for the double row layout problem

Abstract

Access this article

Similar content being viewed by others

A mixed-integer programming formulation of the double row layout problem based on a linear extension of a partial order

Mathematical optimization approach for facility layout on several rows

Mathematical formulation and two-phase optimisation methodology for the constrained double-row layout problem

References

Acknowledgements

Author information

Authors and Affiliations

Corresponding author

Additional information

Publisher's Note

Appendix A

Appendix A

Rights and permissions

About this article

Cite this article

Share this article

Keywords

Search

Navigation