IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v46y1999i5p445-462.html
   My bibliography  Save this article

Worst‐case performance of approximation algorithms for tool management problems

Author

Listed:
  • Yves Crama
  • Joris van de Klundert

Abstract

Since the introduction of flexible manufacturing systems, researchers have investigated various planning and scheduling problems faced by the users of such systems. Several of these problems are not encountered in more classical production settings, and so‐called tool management problems appear to be among the more fundamental ones of these problems. Most tool management problems are hard to solve, so that numerous approximate solution techniques have been proposed to tackle them. In this paper, we investigate the quality of such algorithms by means of worst‐case analysis. We consider several polynomial‐time approximation algorithms described in the literature, and we show that all these algorithms exhibit rather poor worst‐case behavior. We also study the complexity of solving tool management problems approximately. In this respect, we investigate the interrelationships among tool management problems, as well as their relationships with other well‐known combinatorial problems such as the maximum clique problem or the set covering problem, and we prove several negative results on the approximability of various tool management problems. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 445–462, 1999

Suggested Citation

  • Yves Crama & Joris van de Klundert, 1999. "Worst‐case performance of approximation algorithms for tool management problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(5), pages 445-462, August.
    • Handle: RePEc:wly:navres:v:46:y:1999:i:5:p:445-462
    DOI: 10.1002/(SICI)1520-6750(199908)46:53.0.CO;2-R
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/(SICI)1520-6750(199908)46:53.0.CO;2-R
    Download Restriction: no
    File URL: https://libkey.io/10.1002/(SICI)1520-6750(199908)46:53.0.CO;2-R?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. Christopher S. Tang & Eric V. Denardo, 1988. "Models Arising from a Flexible Manufacturing Machine, Part II: Minimization of the Number of Switching Instants," Operations Research, INFORMS, vol. 36(5), pages 778-784, October.
    2. Crama, Yves & Oerlemans, Alwin G., 1994. "A column generation approach to job grouping for flexible manufacturing systems," European Journal of Operational Research, Elsevier, vol. 78(1), pages 58-80, October.
    3. Blazewicz, Jacek & Finke, Gerd, 1994. "Scheduling with resource management in manufacturing systems," European Journal of Operational Research, Elsevier, vol. 76(1), pages 1-14, July.
    4. Christopher S. Tang & Eric V. Denardo, 1988. "Models Arising from a Flexible Manufacturing Machine, Part I: Minimization of the Number of Tool Switches," Operations Research, INFORMS, vol. 36(5), pages 767-777, October.
    5. Crama, Yves, 1997. "Combinatorial optimization models for production scheduling in automated manufacturing systems," European Journal of Operational Research, Elsevier, vol. 99(1), pages 136-153, 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. 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.

    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. Matzliach, Barouch & Tzur, Michal, 2000. "Storage management of items in two levels of availability," European Journal of Operational Research, Elsevier, vol. 121(2), pages 363-379, March.
    2. Konak, Abdullah & Kulturel-Konak, Sadan & Azizoglu, Meral, 2008. "Minimizing the number of tool switching instants in Flexible Manufacturing Systems," International Journal of Production Economics, Elsevier, vol. 116(2), pages 298-307, December.
    3. Crama, Yves, 1997. "Combinatorial optimization models for production scheduling in automated manufacturing systems," European Journal of Operational Research, Elsevier, vol. 99(1), pages 136-153, May.
    4. Renato de Matta & Vernon Ning Hsu & Timothy J. Lowe, 1999. "Capacitated selection problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(1), pages 19-37, February.
    5. Marc Peeters & Zeger Degraeve, 2004. "The Co-Printing Problem: A Packing Problem with a Color Constraint," Operations Research, INFORMS, vol. 52(4), pages 623-638, August.
    6. M. Selim Akturk & Jay B. Ghosh & Evrim D. Gunes, 2003. "Scheduling with tool changes to minimize total completion time: A study of heuristics and their performance," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(1), pages 15-30, February.
    7. Schwerdfeger, Stefan & Boysen, Nils, 2017. "Order picking along a crane-supplied pick face: The SKU switching problem," European Journal of Operational Research, Elsevier, vol. 260(2), pages 534-545.
    8. Furrer, Martina & Mütze, Torsten, 2017. "An algorithmic framework for tool switching problems with multiple objectives," European Journal of Operational Research, Elsevier, vol. 259(3), pages 1003-1016.
    9. 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.
    10. Catanzaro, Daniele & Gouveia, Luis & Labbé, Martine, 2015. "Improved integer linear programming formulations for the job Sequencing and tool Switching Problem," European Journal of Operational Research, Elsevier, vol. 244(3), pages 766-777.
    11. Christopher S. Tang, 2017. "OM Forum—Three Simple Approaches for Young Scholars to Identify Relevant and Novel Research Topics in Operations Management," Manufacturing & Service Operations Management, INFORMS, vol. 19(3), pages 338-346, July.
    12. Nagraj Balakrishnan & Amiya K. Chakravarty, 2001. "Opportunistic retooling of a flexible machine subject to failure," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(1), pages 79-97, February.
    13. Crama Yves & Klundert Joris van de, 1996. "The approximability of tool management problems," Research Memorandum 019, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    14. Calmels, Dorothea, 2022. "An iterated local search procedure for the job sequencing and tool switching problem with non-identical parallel machines," European Journal of Operational Research, Elsevier, vol. 297(1), pages 66-85.
    15. Chakravarty, Amiya K. & Balakrishnan, Nagraj, 1997. "Job sequencing rules for minimizing the expected makespan in flexible machines," European Journal of Operational Research, Elsevier, vol. 96(2), pages 274-288, January.
    16. Dang, Quang-Vinh & van Diessen, Thijs & Martagan, Tugce & Adan, Ivo, 2021. "A matheuristic for parallel machine scheduling with tool replacements," European Journal of Operational Research, Elsevier, vol. 291(2), pages 640-660.
    17. Soares, Leonardo Cabral R. & Carvalho, Marco Antonio M., 2020. "Biased random-key genetic algorithm for scheduling identical parallel machines with tooling constraints," European Journal of Operational Research, Elsevier, vol. 285(3), pages 955-964.
    18. Moshe Dror & Mohamed Haouari, 2000. "Generalized Steiner Problems and Other Variants," Journal of Combinatorial Optimization, Springer, vol. 4(4), pages 415-436, December.
    19. Atan, Tankut S. & Pandit, Ram, 1996. "Auxiliary tool allocation in flexible manufacturing systems," European Journal of Operational Research, Elsevier, vol. 89(3), pages 642-659, March.
    20. Khadija Hadj Salem & Vincent Jost & Yann Kieffer & Luc Libralesso & Stéphane Mancini, 2022. "Minimizing makespan under data prefetching constraints for embedded vision systems: a study of optimization methods and their performance," Operational Research, Springer, vol. 22(3), pages 1639-1673, July.

    More about this item

    Statistics

    Access and download statistics

    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:wly:navres:v:46:y:1999:i:5:p:445-462. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    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.