Skip to main content
SpringerLink
Log in

Optimal solutions for the double row layout problem

  • Original Paper
  • Published:
Optimization Letters Aims and scope Submit manuscript

Abstract

The double row layout problem is how to allocate a given set of n machines on both sides of a straight line corridor so that the total cost of transporting materials between machines is minimized. This is a very difficult combinatorial optimization problem with important applications in industry. We formulate the problem as a mixed-integer program. Computational tests show that the proposed formulation presents a far superior performance than that of a previously published model.

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

Similar content being viewed by others

References

  1. Amaral A.R.S.: On the exact solution of a facility layout problem. Eur. J. Oper. Res. 173(2), 508–518 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  2. Amaral A.R.S.: An exact approach for the one-dimensional facility layout problem. Oper. Res. 56, 1026–1033 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  3. Amaral A.R.S.: A new lower bound for the single row facility layout problem. Discrete Appl. Math. 157(1), 183–190 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  4. Amaral, A.R.S., Letchford, A.N.: A polyhedral approach to the single-row facility layout problem, Tech. Rep., Department of Management Science, Lancaster University (2008)

  5. Anjos M.F., Kennings A., Vannelli A.: A semidefinite optimization approach for the single-row layout problem with unequal dimensions. Discrete Optim. 2, 113–122 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  6. Anjos M.F., Vannelli A.: Computing globally optimal solutions for single-row layout problems using semidefinite programming and cutting planes. INFORMS J. Comput. 20(4), 611–617 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  7. Anjos M.F., Yen G.: Provably near-optimal solutions for very large single-row facility layout problems. Optim. Methods Softw. 24(4), 805–817 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  8. Chung J., Tanchoco J.M.A.: The double row layout problem. Int. J. Prod. Res. 48(3), 709–727 (2010)

    Article  MATH  Google Scholar 

  9. Coll P.E., Ribeiro C.C., Souza C.C.: Multiprocessor scheduling under precendence constraints: polyhedral results. Discrete Appl. Math. 154, 770–801 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  10. de Alvarenga A.G., Negreiros-Gomes F.J., Mestria M.: Metaheuristic methods for a class of the facility layout problem. J. Intell. Manuf. 11, 421–430 (2000)

    Article  Google Scholar 

  11. Grötschel M., Jünger M., Reinelt G.: A cutting plane algorithm for the linear ordering problem. Oper. Res. 32, 1195–1220 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  12. Grötschel M., Jünger M., Reinelt G.: Facets of the linear ordering polytope. Math. Progr. 33, 43–60 (1985)

    Article  MATH  Google Scholar 

  13. Grötschel M., Wakabayashi Y.: A cutting plane algorithm for a clustering problem. Math. Progr. Ser. B 45, 59–96 (1989)

    Article  MATH  Google Scholar 

  14. Grötschel M., Wakabayashi Y.: Facets of the clique partitioning polytope. Math. Progr. 47, 367–387 (1990)

    Article  MATH  Google Scholar 

  15. Heragu S.S.: Facilities Design, 2nd edn. iUniverse, Bloomington (2006)

    Google Scholar 

  16. Heragu S.S., Alfa A.S.: Experiment analysis of simulated annealing based algorithms for the layout problem. Eur. J. Oper. Res. 57(2), 190–202 (1992)

    Article  MATH  Google Scholar 

  17. Heragu S.S., Kusiak A.: Machine layout problem in flexible manufacturing systems. Oper. Res. 36(2), 258–268 (1988)

    Article  Google Scholar 

  18. Heragu S.S., Kusiak A.: Efficient models for the facility layout problem. Eur. J. Oper. Res. 53, 1–13 (1991)

    Article  MATH  Google Scholar 

  19. Kumar S., Asokan P., Kumanan S., Varma B.: Scatter search algorithm for single row layout problem in FMS. Adv. Prod. Eng. Manag. 3, 193–204 (2008)

    Google Scholar 

  20. Love R.F., Wong J.Y.: On solving a one-dimensional space allocation problem with integer programming. INFOR 14(2), 139–143 (1976)

    MATH  Google Scholar 

  21. Picard J.-C., Queyranne M.: On the one-dimensional space allocation problem. Oper. Res. 29(2), 371–391 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  22. Samarghandi H., Eshghi K.: An efficient tabu algorithm for the single row facility layout problem. Eur. J. Oper. Res. 205, 98–105 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  23. Samarghandi H., Taabayan P., Jahantigh F.F.: A particle swarm optimization for the single row facility layout problem. Comput. Ind. Eng. 58, 529–534 (2010)

    Article  Google Scholar 

  24. Sherali H.D., Fraticelli B.M.P., Meller R.D.: Enhanced model formulations for optimal facility layout. Oper. Res. 51, 629–644 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  25. Simmons D.M.: One-dimensional space allocation: an ordering algorithm. Oper. Res. 17, 812–826 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  26. Simmons D.M.: A further note on one-dimensional space allocation. Oper. Res. 19, 249 (1971)

    Article  MathSciNet  Google Scholar 

  27. Solimanpur M., Vrat P., Shankar R.: An ant algorithm for the single row layout problem in flexible manufacturing systems. Comput. Oper. Res. 32(3), 583–598 (2005)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Informática, Universidade Federal do Espírito Santo (UFES), Vitória, ES, 29060-900, Brazil

    André R. S. Amaral

Authors
  1. André R. S. Amaral
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to André R. S. Amaral.

Additional information

This work was carried out while the author was with CEG/IST - Instituto Superior Técnico, Portugal.

Rights and permissions

Reprints and permissions

About this article

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-011-0426-8

Keywords

Search

Navigation