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Worst‐case performance of approximation algorithms for tool management problems

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  • 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
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    1. 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.
    2. 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.
    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. 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.
    5. 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.
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    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.

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