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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
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    References listed on IDEAS

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    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. 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.
    5. 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.
    6. 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.
    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.
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    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.

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