IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v265y2018i1p26-38.html
   My bibliography  Save this article

A β-accurate linearization method of Euclidean distance for the facility layout problem with heterogeneous distance metrics

Author

Listed:
  • Xie, Yue
  • Zhou, Shenghan
  • Xiao, Yiyong
  • Kulturel-Konak, Sadan
  • Konak, Abdullah

Abstract

Most existing research on facility layout problems (FLPs) considers a single distance metric, mainly Rectilinear distance, in the calculation of the material handling cost between departments. However, there are many industrial cases in which heterogeneous distance metrics may need to be used simultaneously to cater for different styles of material handling, such as the Euclidean distance metric for conveyor belts and the Tchebychev distance metric for overhead cranes. In this paper, we study the unequal area facility layout problem with heterogeneous distance metrics (UA-FLP-HDM), considering a hybrid use of three metrics, i.e., Rectilinear, Euclidean, and Tchebychev, as distance measures of different styles of material handling in the production system. We propose a β-accurate linearization method that uses a set of tangent planes to convert the non-linear Euclidean distance constraint into a set of linear constraints that guarantee the approximation error within a given percentage β, e.g., as small as −0.01% in our experiments, and develop linear constraints for the Tchebychev distance metric as well. Based on these contributions, we present a mixed-integer linear programming (MILP) model for the UA-FLP-HDM. Computational experiments are carried out to test the performance of the MILP model with five benchmark problems in the literature and compare the layout designs using different distance metrics. Numerical results indicate that different distance metrics may lead to significantly different solutions and a hybrid use of heterogeneous distance metrics fits better for real industrial applications.

Suggested Citation

  • Xie, Yue & Zhou, Shenghan & Xiao, Yiyong & Kulturel-Konak, Sadan & Konak, Abdullah, 2018. "A β-accurate linearization method of Euclidean distance for the facility layout problem with heterogeneous distance metrics," European Journal of Operational Research, Elsevier, vol. 265(1), pages 26-38.
  • Handle: RePEc:eee:ejores:v:265:y:2018:i:1:p:26-38
    DOI: 10.1016/j.ejor.2017.07.052
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221717306951
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.ejor.2017.07.052?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Balakrishnan, Jaydeep & Cheng, Chun Hung, 1998. "Dynamic layout algorithms: a state-of-the-art survey," Omega, Elsevier, vol. 26(4), pages 507-521, August.
    2. van Camp, Drew J. & Carter, Michael W. & Vannelli, Anthony, 1992. "A nonlinear optimization approach for solving facility layout problems," European Journal of Operational Research, Elsevier, vol. 57(2), pages 174-189, March.
    3. Gordon C. Armour & Elwood S. Buffa, 1963. "A Heuristic Algorithm and Simulation Approach to Relative Location of Facilities," Management Science, INFORMS, vol. 9(2), pages 294-309, January.
    4. Meir J. Rosenblatt, 1986. "The Dynamics of Plant Layout," Management Science, INFORMS, vol. 32(1), pages 76-86, January.
    5. Gonçalves, José Fernando & Resende, Mauricio G.C., 2015. "A biased random-key genetic algorithm for the unequal area facility layout problem," European Journal of Operational Research, Elsevier, vol. 246(1), pages 86-107.
    6. Kulturel-Konak, Sadan, 2012. "A linear programming embedded probabilistic tabu search for the unequal-area facility layout problem with flexible bays," European Journal of Operational Research, Elsevier, vol. 223(3), pages 614-625.
    7. Guan, Jian & Lin, Geng, 2016. "Hybridizing variable neighborhood search with ant colony optimization for solving the single row facility layout problem," European Journal of Operational Research, Elsevier, vol. 248(3), pages 899-909.
    8. Paes, Frederico Galaxe & Pessoa, Artur Alves & Vidal, Thibaut, 2017. "A hybrid genetic algorithm with decomposition phases for the Unequal Area Facility Layout Problem," European Journal of Operational Research, Elsevier, vol. 256(3), pages 742-756.
    9. Hanif D. Sherali & Barbara M. P. Fraticelli & Russell D. Meller, 2003. "Enhanced Model Formulations for Optimal Facility Layout," Operations Research, INFORMS, vol. 51(4), pages 629-644, August.
    10. Eugene L. Lawler, 1963. "The Quadratic Assignment Problem," Management Science, INFORMS, vol. 9(4), pages 586-599, July.
    11. Philipp Hungerländer & Franz Rendl, 2013. "A computational study and survey of methods for the single-row facility layout problem," Computational Optimization and Applications, Springer, vol. 55(1), pages 1-20, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Mariem Besbes & Marc Zolghadri & Roberta Costa Affonso & Faouzi Masmoudi & Mohamed Haddar, 2020. "A methodology for solving facility layout problem considering barriers: genetic algorithm coupled with A* search," Journal of Intelligent Manufacturing, Springer, vol. 31(3), pages 615-640, March.
    2. Mariem Besbes & Marc Zolghadri & Roberta Costa Affonso & Faouzi Masmoudi & Mohamed Haddar, 2021. "3D facility layout problem," Journal of Intelligent Manufacturing, Springer, vol. 32(4), pages 1065-1090, April.
    3. Xiao, Yiyong & Zuo, Xiaorong & Huang, Jiaoying & Konak, Abdullah & Xu, Yuchun, 2020. "The continuous pollution routing problem," Applied Mathematics and Computation, Elsevier, vol. 387(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Anjos, Miguel F. & Vieira, Manuel V.C., 2017. "Mathematical optimization approaches for facility layout problems: The state-of-the-art and future research directions," European Journal of Operational Research, Elsevier, vol. 261(1), pages 1-16.
    2. Liu, Jingfa & Wang, Dawen & He, Kun & Xue, Yu, 2017. "Combining Wang–Landau sampling algorithm and heuristics for solving the unequal-area dynamic facility layout problem," European Journal of Operational Research, Elsevier, vol. 262(3), pages 1052-1063.
    3. Minhee Kim & Junjae Chae, 2019. "Monarch Butterfly Optimization for Facility Layout Design Based on a Single Loop Material Handling Path," Mathematics, MDPI, vol. 7(2), pages 1-21, February.
    4. Mariem Besbes & Marc Zolghadri & Roberta Costa Affonso & Faouzi Masmoudi & Mohamed Haddar, 2020. "A methodology for solving facility layout problem considering barriers: genetic algorithm coupled with A* search," Journal of Intelligent Manufacturing, Springer, vol. 31(3), pages 615-640, March.
    5. Gonçalves, José Fernando & Resende, Mauricio G.C., 2015. "A biased random-key genetic algorithm for the unequal area facility layout problem," European Journal of Operational Research, Elsevier, vol. 246(1), pages 86-107.
    6. Mehmet Burak Şenol & Ekrem Alper Murat, 2023. "A sequential solution heuristic for continuous facility layout problems," Annals of Operations Research, Springer, vol. 320(1), pages 355-377, January.
    7. Asef-Vaziri, Ardavan & Jahandideh, Hossein & Modarres, Mohammad, 2017. "Loop-based facility layout design under flexible bay structures," International Journal of Production Economics, Elsevier, vol. 193(C), pages 713-725.
    8. Bozer, Yavuz A. & Wang, Chi-Tai, 2012. "A graph-pair representation and MIP-model-based heuristic for the unequal-area facility layout problem," European Journal of Operational Research, Elsevier, vol. 218(2), pages 382-391.
    9. Gintaras Palubeckis & Armantas Ostreika & Jūratė Platužienė, 2022. "A Variable Neighborhood Search Approach for the Dynamic Single Row Facility Layout Problem," Mathematics, MDPI, vol. 10(13), pages 1-27, June.
    10. Mariem Besbes & Marc Zolghadri & Roberta Costa Affonso & Faouzi Masmoudi & Mohamed Haddar, 2021. "3D facility layout problem," Journal of Intelligent Manufacturing, Springer, vol. 32(4), pages 1065-1090, April.
    11. McKendall Jr., Alan R. & Hakobyan, Artak, 2010. "Heuristics for the dynamic facility layout problem with unequal-area departments," European Journal of Operational Research, Elsevier, vol. 201(1), pages 171-182, February.
    12. Jerzy Grobelny & Rafal Michalski, 2017. "A novel version of simulated annealing based on linguistic patterns for solving facility layout problems," WORking papers in Management Science (WORMS) WORMS/17/07, Department of Operations Research and Business Intelligence, Wroclaw University of Science and Technology.
    13. Komarudin & Wong, Kuan Yew, 2010. "Applying Ant System for solving Unequal Area Facility Layout Problems," European Journal of Operational Research, Elsevier, vol. 202(3), pages 730-746, May.
    14. Balakrishnan, Jaydeep & Hung Cheng, Chun, 2009. "The dynamic plant layout problem: Incorporating rolling horizons and forecast uncertainty," Omega, Elsevier, vol. 37(1), pages 165-177, February.
    15. Bolte, Andreas & Thonemann, Ulrich Wilhelm, 1996. "Optimizing simulated annealing schedules with genetic programming," European Journal of Operational Research, Elsevier, vol. 92(2), pages 402-416, July.
    16. Balakrishnan, Jaydeep & Cheng, Chun Hung & Conway, Daniel G. & Lau, Chun Ming, 2003. "A hybrid genetic algorithm for the dynamic plant layout problem," International Journal of Production Economics, Elsevier, vol. 86(2), pages 107-120, November.
    17. Vadivel Sengazhani Murugesan & A. H. Sequeira & Deeksha Sanjay Shetty & Sunil Kumar Jauhar, 2020. "Enhancement of mail operational performance of India post facility layout using AHP," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 11(2), pages 261-273, April.
    18. Ravi Kumar, K. & Hadjinicola, George C. & Lin, Ting-li, 1995. "A heuristic procedure for the single-row facility layout problem," European Journal of Operational Research, Elsevier, vol. 87(1), pages 65-73, November.
    19. Dahlbeck, Mirko, 2021. "A mixed-integer linear programming approach for the T-row and the multi-bay facility layout problem," European Journal of Operational Research, Elsevier, vol. 295(2), pages 443-462.
    20. Scholz, Daniel & Petrick, Anita & Domschke, Wolfgang, 2009. "STaTS: A Slicing Tree and Tabu Search based heuristic for the unequal area facility layout problem," European Journal of Operational Research, Elsevier, vol. 197(1), pages 166-178, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:265:y:2018:i:1:p:26-38. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.