An improved mixed-integer programming model for the double row layout of facilities

Abstract

We consider the double row layout problem, which is how to allocate a given number of machines at locations on either side of a corridor so that the total cost to transport materials among these machines is minimized. We propose modifications to a mixed-integer programming model in the literature, obtaining a tighter model. Further, we describe variants of the new model that are even tighter. Computational results show that the new model and its variants perform considerably better than the one in the literature, leading to both fewer enumeration tree nodes and smaller solution times.

This is a preview of subscription content, access via your institution.

Fig. 1

References

  1. 1.

    Amaral, A.R.S.: On the exact solution of a facility layout problem. Eur. J. Oper. Res. 173(2), 508–518 (2006). https://doi.org/10.1016/j.ejor.2004.12.021

    MathSciNet  Article  MATH  Google Scholar 

  2. 2.

    Amaral, A.R.S.: An exact approach to the one-dimensional facility layout problem. Oper. Res. 56(4), 1026–1033 (2008). https://doi.org/10.1287/opre.1080.0548

    MathSciNet  Article  MATH  Google Scholar 

  3. 3.

    Amaral, A.R.S.: A mixed 0–1 linear programming formulation for the exact solution of the minimum linear arrangement problem. Optim. Lett. 3(4), 513–520 (2009a). https://doi.org/10.1007/s11590-009-0130-0

    MathSciNet  Article  MATH  Google Scholar 

  4. 4.

    Amaral, A.R.S.: A new lower bound for the single row facility layout problem. Discrete Appl. Math. 157(1), 183–190 (2009). https://doi.org/10.1016/j.dam.2008.06.002

    MathSciNet  Article  MATH  Google Scholar 

  5. 5.

    Amaral, A.R.S.: The corridor allocation problem. Comput. Oper. Res. 39(12), 3325–3330 (2012). https://doi.org/10.1016/j.cor.2012.04.016

    Article  MATH  Google Scholar 

  6. 6.

    Amaral, A.R.S.: Optimal solutions for the double row layout problem. Optim. Lett. 7, 407–413 (2013a). https://doi.org/10.1007/s11590-011-0426-8

    MathSciNet  Article  MATH  Google Scholar 

  7. 7.

    Amaral, A.R.S.: A parallel ordering problem in facilities layout. Comput. Oper. Res. 40(12), 2930–2939 (2013). https://doi.org/10.1016/j.cor.2013.07.003

    MathSciNet  Article  MATH  Google Scholar 

  8. 8.

    Amaral, A.R.S., Letchford, A.N.: A polyhedral approach to the single row facility layout problem. Math. Program. 141(1–2), 453–477 (2013). https://doi.org/10.1007/s10107-012-0533-z

    MathSciNet  Article  MATH  Google Scholar 

  9. 9.

    Bukchin, Y., Tzur, M.: A new milp approach for the facility process-layout design problem with rectangular and l/t shape departments. Int. J. Prod. Res. 52(24), 7339–7359 (2014). https://doi.org/10.1080/00207543.2014.930534

    Article  Google Scholar 

  10. 10.

    Chae, J., Regan, A.C.: Layout design problems with heterogeneous area constraints. Comput. Ind. Eng. 102, 198–207 (2016). https://doi.org/10.1016/j.cie.2016.10.016

    Article  Google Scholar 

  11. 11.

    Chung, J., Tanchoco, J.M.A.: The double row layout problem. Int. J. Prod. Res. 48(3), 709–727 (2010). https://doi.org/10.1080/00207540802192126

    Article  MATH  Google Scholar 

  12. 12.

    Hathhorn, J., Sisikoglu, E., Sir, M.Y.: A multi-objective mixed-integer programming model for a multi-floor facility layout. Int. J. Prod. Res. 51(14), 4223–4239 (2013). https://doi.org/10.1080/00207543.2012.753486

    Article  Google Scholar 

  13. 13.

    Heragu, S.S., Kusiak, A.: Machine layout problem in flexible manufacturing systems. Oper. Res. 36(2), 258–268 (1988). https://doi.org/10.1287/opre.36.2.258

    Article  Google Scholar 

  14. 14.

    Javadi, B., Jolai, F., Slomp, J., Rabbani, M., Tavakkoli-Moghaddam, R.: An integrated approach for the cell formation and layout design in cellular manufacturing systems. Int. J. Prod. Res. 51(20), 6017–6044 (2013). https://doi.org/10.1080/00207543.2013.791755

    Article  Google Scholar 

  15. 15.

    Klausnitzer, A., Lasch, R.: Extended Model Formulation of the Facility Layout Problem with Aisle Structure, pp. 89–101. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-20863-3_7

    Google Scholar 

  16. 16.

    Niroomand, S., Vizvári, B.: A mixed integer linear programming formulation of closed loop layout with exact distances. J. Ind. Prod. Eng. 30(3), 190–201 (2013). https://doi.org/10.1080/21681015.2013.805699

    Google Scholar 

  17. 17.

    Simmons, D.M.: One-dimensional space allocation: an ordering algorithm. Oper. Res. 17(5), 812–826 (1969). https://doi.org/10.1287/opre.17.5.812

    MathSciNet  Article  MATH  Google Scholar 

Download references

Acknowledgements

The second author was supported by FAP/UFES and CAPES (Grant Number 99999.002643/2015-04).

Author information

Affiliations

Authors

Corresponding author

Correspondence to A. R. S. Amaral.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Secchin, L.D., Amaral, A.R.S. An improved mixed-integer programming model for the double row layout of facilities. Optim Lett 13, 193–199 (2019). https://doi.org/10.1007/s11590-018-1263-9

Download citation

Keywords

  • Facility layout
  • Integer programming
  • Combinatorial optimization