IDEAS home Printed from https://ideas.repec.org/a/inm/oropre/v60y2012i5p1157-1166.html
   My bibliography  Save this article

Flexible PMP Approach for Large-Size Cell Formation

Author

Listed:
  • Boris Goldengorin

    (LATNA--Laboratory of Algorithms and Technologies for Networks Analysis and Department of Higher Mathematics, The National Research University Higher School of Economics, Moscow 101000, Russia; and Department of Mathematics and Informatics, Khmelnitsky University of Economics and Business, Khmelnitsky 29000, Ukraine)

  • Dmitry Krushinsky

    (Department of Operations, University of Groningen, 9700 AV Groningen, The Netherlands)

  • Jannes Slomp

    (Department of Operations, University of Groningen, 9700 AV Groningen, The Netherlands)

Abstract

Lately, the problem of cell formation (CF) has gained a lot of attention in the industrial engineering literature. Since it was formulated (more than 50 years ago), the problem has incorporated additional industrial factors and constraints while its solution methods have been constantly improving in terms of the solution quality and CPU times. However, despite all the efforts made, the available solution methods (including those for a popular model based on the p -median problem, PMP) are prone to two major types of errors. The first error (the modeling one) occurs when the intended objective function of the CF (as a rule, verbally formulated) is substituted by the objective function of the PMP. The second error (the algorithmic one) occurs as a direct result of applying a heuristic for solving the PMP. In this paper we show that for instances that make sense in practice, the modeling error induced by the PMP is negligible. We exclude the algorithmic error completely by solving the adjusted pseudo-Boolean formulation of the PMP exactly, which takes less than one second on a general-purpose PC and software. Our experimental study shows that the PMP-based model produces high-quality cells and in most cases outperforms several contemporary approaches.

Suggested Citation

  • Boris Goldengorin & Dmitry Krushinsky & Jannes Slomp, 2012. "Flexible PMP Approach for Large-Size Cell Formation," Operations Research, INFORMS, vol. 60(5), pages 1157-1166, October.
    • Handle: RePEc:inm:oropre:v:60:y:2012:i:5:p:1157-1166
    DOI: 10.1287/opre.1120.1108
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/opre.1120.1108
    Download Restriction: no
    File URL: https://libkey.io/10.1287/opre.1120.1108?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
    ---><---

    References listed on IDEAS

    as
    1. Sourour Elloumi, 2010. "A tighter formulation of the p-median problem," Journal of Combinatorial Optimization, Springer, vol. 19(1), pages 69-83, January.
    2. Chen, Ja-Shen & Heragu, Sunderesh S., 1999. "Stepwise decomposition approaches for large scale cell formation problems," European Journal of Operational Research, Elsevier, vol. 113(1), pages 64-79, February.
    3. Mladenovic, Nenad & Brimberg, Jack & Hansen, Pierre & Moreno-Perez, Jose A., 2007. "The p-median problem: A survey of metaheuristic approaches," European Journal of Operational Research, Elsevier, vol. 179(3), pages 927-939, June.
    4. Bader F. AlBdaiwi & Diptesh Ghosh & Boris Goldengorin, 2011. "Data aggregation for p-median problems," Journal of Combinatorial Optimization, Springer, vol. 21(3), pages 348-363, April.
    5. Yang, Miin-Shen & Yang, Jenn-Hwai, 2008. "Machine-part cell formation in group technology using a modified ART1 method," European Journal of Operational Research, Elsevier, vol. 188(1), pages 140-152, July.
    6. Yin, Yong & Yasuda, Kazuhiko, 2006. "Similarity coefficient methods applied to the cell formation problem: A taxonomy and review," International Journal of Production Economics, Elsevier, vol. 101(2), pages 329-352, June.
    7. R Bhatnagar & V Saddikuti, 2010. "Models for cellular manufacturing systems design: matching processing requirements and operator capabilities," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(5), pages 827-839, 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. Julius Žilinskas & Boris Goldengorin & Panos Pardalos, 2015. "Pareto-optimal front of cell formation problem in group technology," Journal of Global Optimization, Springer, vol. 61(1), pages 91-108, January.
    2. Mohd Fahmi Bin Mad Ali & Mohd Khairol Anuar Bin Mohd Ariffin & Faizal Bin Mustapha & Eris Elianddy Bin Supeni, 2021. "An Unsupervised Machine Learning-Based Framework for Transferring Local Factories into Supply Chain Networks," Mathematics, MDPI, vol. 9(23), pages 1-31, December.

    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. Dmitry Krushinsky & Boris Goldengorin, 2012. "An exact model for cell formation in group technology," Computational Management Science, Springer, vol. 9(3), pages 323-338, August.
    2. Wu, Tai-Hsi & Chung, Shu-Hsing & Chang, Chin-Chih, 2010. "A water flow-like algorithm for manufacturing cell formation problems," European Journal of Operational Research, Elsevier, vol. 205(2), pages 346-360, September.
    3. Alcaraz, Javier & Landete, Mercedes & Monge, Juan F., 2012. "Design and analysis of hybrid metaheuristics for the Reliability p-Median Problem," European Journal of Operational Research, Elsevier, vol. 222(1), pages 54-64.
    4. Duran-Mateluna, Cristian & Ales, Zacharie & Elloumi, Sourour, 2023. "An efficient benders decomposition for the p-median problem," European Journal of Operational Research, Elsevier, vol. 308(1), pages 84-96.
    5. Sergio García & Martine Labbé & Alfredo Marín, 2011. "Solving Large p -Median Problems with a Radius Formulation," INFORMS Journal on Computing, INFORMS, vol. 23(4), pages 546-556, November.
    6. Buchheim, Christoph & Crama, Yves & Rodríguez-Heck, Elisabeth, 2019. "Berge-acyclic multilinear 0–1 optimization problems," European Journal of Operational Research, Elsevier, vol. 273(1), pages 102-107.
    7. Boutsinas, Basilis, 2013. "Machine-part cell formation using biclustering," European Journal of Operational Research, Elsevier, vol. 230(3), pages 563-572.
    8. Michael Brusco & J Dennis Cradit & Douglas Steinley, 2021. "A comparison of 71 binary similarity coefficients: The effect of base rates," PLOS ONE, Public Library of Science, vol. 16(4), pages 1-19, April.
    9. Miriam Kießling & Sascha Kurz & Jörg Rambau, 2021. "An exact column-generation approach for the lot-type design problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 741-780, October.
    10. Kenneth Carling & Mengjie Han & Johan Håkansson, 2012. "Does Euclidean distance work well when the p-median model is applied in rural areas?," Annals of Operations Research, Springer, vol. 201(1), pages 83-97, December.
    11. Mohd Fahmi Bin Mad Ali & Mohd Khairol Anuar Bin Mohd Ariffin & Aidin Delgoshaei & Faizal Bin Mustapha & Eris Elianddy Bin Supeni, 2023. "A Comprehensive 3-Phase Framework for Determining the Customer’s Product Usage in a Food Supply Chain," Mathematics, MDPI, vol. 11(5), pages 1-20, February.
    12. Chen, Liang & Chen, Sheng-Jie & Chen, Wei-Kun & Dai, Yu-Hong & Quan, Tao & Chen, Juan, 2023. "Efficient presolving methods for solving maximal covering and partial set covering location problems," European Journal of Operational Research, Elsevier, vol. 311(1), pages 73-87.
    13. Behrooz Alizadeh & Somayeh Bakhteh, 2017. "A modified firefly algorithm for general inverse p-median location problems under different distance norms," OPSEARCH, Springer;Operational Research Society of India, vol. 54(3), pages 618-636, September.
    14. Hachicha, Wafik & Masmoudi, Faouzi & Haddar, Mohamed, 2006. "Formation of machine groups and part families in cellular manufacturing systems using a correlation analysis approach," MPRA Paper 3975, University Library of Munich, Germany, revised 04 Jan 2007.
    15. Tao Zhuolin & Zheng Qingjing & Kong Hui, 2018. "A Modified Gravity p-Median Model for Optimizing Facility Locations," Journal of Systems Science and Information, De Gruyter, vol. 6(5), pages 421-434, October.
    16. Hahsler, Michael, 2017. "An experimental comparison of seriation methods for one-mode two-way data," European Journal of Operational Research, Elsevier, vol. 257(1), pages 133-143.
    17. Amir Hossein Sadeghi & Ziyuan Sun & Amirreza Sahebi-Fakhrabad & Hamid Arzani & Robert Handfield, 2023. "A Mixed-Integer Linear Formulation for a Dynamic Modified Stochastic p-Median Problem in a Competitive Supply Chain Network Design," Logistics, MDPI, vol. 7(1), pages 1-24, March.
    18. Marle, Franck & Vidal, Ludovic-Alexandre & Bocquet, Jean-Claude, 2013. "Interactions-based risk clustering methodologies and algorithms for complex project management," International Journal of Production Economics, Elsevier, vol. 142(2), pages 225-234.
    19. Sagarra, Marti & Mar-Molinero, Cecilio & Agasisti, Tommaso, 2017. "Exploring the efficiency of Mexican universities: Integrating Data Envelopment Analysis and Multidimensional Scaling," Omega, Elsevier, vol. 67(C), pages 123-133.
    20. Caballini, Claudia & Gracia, Maria D. & Mar-Ortiz, Julio & Sacone, Simona, 2020. "A combined data mining – optimization approach to manage trucks operations in container terminals with the use of a TAS: Application to an Italian and a Mexican port," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 142(C).

    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:inm:oropre:v:60:y:2012:i:5:p:1157-1166. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.