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.
Research partially supported by the Natural Sciences and Engineering Research Council of Canada.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
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)
Picard, J.-C., Queyranne, M.: On the one-dimensional space allocation problem. Oper. Res. 29(2), 371–391 (1981)
Heragu, S.S., Kusiak, A.: Machine layout problem in flexible manufacturing systems. Oper. Res. 36(2), 258–268 (1988)
Simmons, D.M.: One-dimensional space allocation: an ordering algorithm. Oper. Res. 17, 812–826 (1969)
Suryanarayanan, J., Golden, B., Wang, Q.: A new heuristic for the linear placement problem. Comput. Oper. Res. 18(3), 255–262 (1991)
Hungerländer, P.: A semidefinite optimization approach to the directed circular facility layout problem. Technical report, submitted (2012)
Tucker, A.W.: On directed graphs and integer programs. Technical report, IBM Mathematical Research Project (1960)
Younger, D.H.: Minimum feedback arc sets for a directed graph. IEEE Trans. Circuit Theory 10(2), 238–245 (1963)
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)
Buchheim, C., Wiegele, A., Zheng, L.: Exact algorithms for the quadratic linear ordering problem. INFORMS J. Comput. 22(1), 168–177 (2010)
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)
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)
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)
Hungerländer, P.: Semidefinite approaches to ordering problems. PhD thesis, Alpen-Adria Universität Klagenfurt (2012)
Tansel, B.C., Bilen, C.: Move based heuristics for the unidirectional loop network layout problem. Eur. J. Oper. Res. 108(1), 36–48 (1998)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Hungerländer, P., Anjos, M.F. (2014). An Exact Approach for the Combined Cell Layout Problem. In: Helber, S., et al. Operations Research Proceedings 2012. Operations Research Proceedings. Springer, Cham. https://doi.org/10.1007/978-3-319-00795-3_40
Download citation
DOI: https://doi.org/10.1007/978-3-319-00795-3_40
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-00794-6
Online ISBN: 978-3-319-00795-3
eBook Packages: Business and EconomicsBusiness and Management (R0)