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A two-stage mathematical-programming method for the multi-floor facility layout problem

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Journal of the Operational Research Society

Abstract

We present a two-stage method using mathematical-programming techniques for finding high-quality solutions to the multi-floor facility layout problem. The first stage is a mixed-integer linear program that assigns departments to floors such that the total of the vertical interaction costs between departments on different floors is globally minimized. The second stage finds a locally optimal layout for each floor. Two versions of the proposed approach are considered. The first solves the layout of each floor independently of the other floors, and is suitable for up to one elevator location. The second solves the layout of all floors simultaneously and can handle multiple elevator locations. Preliminary computational results show that both versions of the proposed method can efficiently provide a good variety of high-quality solutions in a short amount of time for medium and large-scale problem instances.

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References

  • Abdinnour-Helm S and Hadley SW (2000). Tabu search based heuristics for multi-floor facility layout. International Journal of Production Research 38 (2): 365–383.

    Article  Google Scholar 

  • Anjos MF and Vannelli A (2002). An attractor-repeller approach to floorplanning. Mathematical Methods of Operations Research 56 (1): 3–27.

    Article  Google Scholar 

  • Anjos MF and Vannelli A (2006). A new mathematical-programming framework for facility-layout design. INFORMS Journal on Computing 18 (1): 111–118.

    Article  Google Scholar 

  • Armour G and Buffa E (1963). A heuristic algorithm and simulation approach to relative location of facilities. Management Science 9 (1): 294–309.

    Article  Google Scholar 

  • Bozer YA, Meller RD and Erlebacher SJ (1991). An improvement-type layout algorithm for multiple-floor facilities. Technical Report 91-11, Department of Industrial & Operations Engineering, University of Michigan.

  • Bozer YA, Meller RD and Erlebacher SJ (1994). An improvement-type layout algorithm for single and multiple-floor facilities. Management Science 40 (7): 918–932.

    Article  Google Scholar 

  • Chang C-H, Lin J-L and Lin H-J (2006). Multiple-floor facility layout design with aisle construction. Industrial Engineering & Management Systems 5 (1): 1–10.

    Google Scholar 

  • Goetschalckx M and Irohara T (2007). Efficient formulations for the multi-floor facility layout problem with elevators. Georgia Institute of Technology, http://www.optimization-online.org/DB_FILE/2007/02/1598.pdf.

  • Hahn P, MacGregor Smith J and Zhu Y-R (2010). The multi-story space assignment problem. Annals of Operations Research 179 (1): 77–103.

    Article  Google Scholar 

  • Heragu SS (2006). Facilities Design. 2nd edn. iUniverse: Lincoln, NE.

    Google Scholar 

  • Johnson RV (1982). SPACECRAFT for multi-floor layout planning. Management Science 28 (4): 407–417.

    Article  Google Scholar 

  • Kaku BK, Thompson GL and Baybars I (1988). A heuristic method for the multi-story layout problem. European Journal of Operational Research 37 (3): 384–397.

    Article  Google Scholar 

  • Kusiak A (2000). Computational Intelligence in Design and Manufacturing. John Wiley & Sons: New York.

    Google Scholar 

  • Lee K-Y, Roh M-I and Jeong H-S (2005). An improved genetic algorithm for multi-floor facility layout problems having inner structure walls and passages. Computers & Operations Research 32 (4): 879–899.

    Article  Google Scholar 

  • Liggett RS and Mitchell WJ (1981). Optimal space planning in practice. Computer-aided Design 13 (5): 277–288.

    Article  Google Scholar 

  • Matsuzaki K, Irohara T and Yoshimoto K (1999). Heuristic algorithm to solve the multi-floor layout problem with the consideration of elevator utilization. Computers & Industrial Engineering 36 (2): 487–502.

    Article  Google Scholar 

  • Meller RD and Bozer YA (1992). Solving the facility layout problem with simulated annealing. Technical Report 91-20, Department of Industrial & Operations Engineering, University of Michigan.

  • Meller RD and Bozer YA (1996). A new simulated annealing algorithm for the facility layout problem. International Journal of Production Research 34 (6): 1675–1692.

    Article  Google Scholar 

  • Meller RD and Bozer YA (1997). Alternative approaches to solve the multi-floor facility layout problem. Journal of Manufacturing Systems 16 (3): 192–203.

    Article  Google Scholar 

  • Meller RD and Gau K-Y (1996). The facility layout problem: recent and emerging trends and perspectives. Journal of Manufacturing Systems 15 (5): 351–366.

    Article  Google Scholar 

  • Singh SP and Sharma RRK (2006). A review of different approaches to the facility layout problems. International Journal of Advanced Manufacturing Technology 30 (5–6): 425–433.

    Article  Google Scholar 

Download references

Acknowledgements

We thank two anonymous referees for their constructive comments that helped improve the paper.

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Authors and Affiliations

  1. University of Waterloo, Waterloo, ON, Canada

    S Bernardi

  2. GERAD & Ecole Polytechnique de Montreal, Montreal, QC, Canada

    M F Anjos

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  1. S Bernardi
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  2. M F Anjos
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Corresponding author

Correspondence to M F Anjos.

Additional information

†Research partially supported by an Ontario Graduate Scholarship.

††Research partially supported by the Natural Sciences and Engineering Research Council of Canada, and by a Humboldt Research Fellowship.

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Bernardi, S., Anjos, M. A two-stage mathematical-programming method for the multi-floor facility layout problem. J Oper Res Soc 64, 352–364 (2013). https://doi.org/10.1057/jors.2012.49

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  • DOI: https://doi.org/10.1057/jors.2012.49

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