An Exact Approach for the Combined Cell Layout Problem

Conference paper
Part of the Operations Research Proceedings book series (ORP)

Abstract

We propose an exact solution method based on semidefinite optimization for simultaneously optimizing the layout of two or more cells in a cellular manufacturing system in the presence of parts that require processing in more than one cell. To the best of our knowledge, this is the first exact method proposed for this problem. We consider single-row and directed circular (or cyclic) cell layouts but the method can in principle be extended to other layout types. Preliminary computational results suggest that optimal solutions can be obtained for instances with 2 cells and up to 60 machines.

References

  1. 1.
    Chu, C-H.: Recent advances in mathematical programming for cell formation. In: Planning, Design, and Analysis of Cellular Manufacturing Systems, number 24 in Manufacturing Research and Technology, pp. 3–46. Elsevier Science B.V. (1995)Google Scholar
  2. 2.
    Picard, J.-C., Queyranne, M.: On the one-dimensional space allocation problem. Oper. Res. 29(2), 371–391 (1981)CrossRefGoogle Scholar
  3. 3.
    Heragu, S.S., Kusiak, A.: Machine layout problem in flexible manufacturing systems. Oper. Res. 36(2), 258–268 (1988)CrossRefGoogle Scholar
  4. 4.
    Simmons, D.M.: One-dimensional space allocation: an ordering algorithm. Oper. Res. 17, 812–826 (1969)CrossRefGoogle Scholar
  5. 5.
    Suryanarayanan, J., Golden, B., Wang, Q.: A new heuristic for the linear placement problem. Comput. Oper. Res. 18(3), 255–262 (1991)CrossRefGoogle Scholar
  6. 6.
    Hungerländer, P.: A semidefinite optimization approach to the directed circular facility layout problem. Technical report, submitted (2012)Google Scholar
  7. 7.
    Tucker, A.W.: On directed graphs and integer programs. Technical report, IBM Mathematical Research Project (1960)Google Scholar
  8. 8.
    Younger, D.H.: Minimum feedback arc sets for a directed graph. IEEE Trans. Circuit Theory 10(2), 238–245 (1963)CrossRefGoogle Scholar
  9. 9.
    Anjos, M.F., Kennings, A., Vannelli, A.: A semidefinite optimization approach for the single-row layout problem with unequal dimensions. Discrete Optim. 2(2), 113–122 (2005)CrossRefGoogle Scholar
  10. 10.
    Buchheim, C., Wiegele, A., Zheng, L.: Exact algorithms for the quadratic linear ordering problem. INFORMS J. Comput. 22(1), 168–177 (2010)CrossRefGoogle Scholar
  11. 11.
    M. Chimani and P. Hungerländer. Exact approaches to multi-level vertical orderings. INFORMS Journal on Computing. accepted, preprint available at www.ae.uni-jena.de/Research_Pubs/MLVO.html (2012)
  12. 12.
    Chimani, M., Hungerländer, P.: Multi-level verticality optimization: Concept, strategies, and drawing scheme. J. Graph Algorithms Appl. Accepted, preprint available at www.ae.uni-jena.de/Research_Pubs/MLVO.html (2012)
  13. 13.
    Chimani, M., Hungerländer, P., Jünger, M., Mutzel, P.: An SDP approach to multi-level crossing minimization. In: Proceedings of Algorithm Engineering and Experiments [ALENEX’2011] (2011)Google Scholar
  14. 14.
    Hungerländer, P.: Semidefinite approaches to ordering problems. PhD thesis, Alpen-Adria Universität Klagenfurt (2012)Google Scholar
  15. 15.
    Tansel, B.C., Bilen, C.: Move based heuristics for the unidirectional loop network layout problem. Eur. J. Oper. Res. 108(1), 36–48 (1998)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Institute of MathematicsAlpen-Adria Universität KlagenfurtKlagenfurtAustria
  2. 2.Canada Research Chair in Discrete Nonlinear Optimization in EngineeringGERAD and École Polytechnique de MontréalMontrealCanada

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