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On the calculation of the stability radiusof an optimal or an approximate schedule

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  • Yuri Sotskov
  • Albert Wagelmans
  • Frank Werner

Abstract

The main objective of this paper is to stimulate interest in stability analysis for scheduling problems. In spite of impressive theoretical results in sequencing and scheduling, up to now the implementation of scheduling algorithms with a rather deep mathematical back-ground in production planning, scheduling and control, and in other real-life problems with sequencing aspects is limited. In classical scheduling theory, mainly deterministic systems are considered and the processing times of all operations are supposed to be given in advance. Such problems do not often arise in practice: Even if the processing times are known before applying a scheduling procedure, OR workers are forced to take into account the precision of equipment, which is used to calculate the processing times, round-off errors in the calculation of a schedule, errors within the practical realization of a schedule, machine breakdowns, additional jobs, and so on. This paper is devoted to the calculation of the stability radius of an optimal or an approximate schedule. We survey some recent results in this field and derive new results in order to make this approach more suitable for practical use. Computational results on the calculation of the stability radius for randomly generated job shop scheduling problems are presented. The extreme values of the stability radius are considered in more detail. The new results are amply illustrated with examples. Copyright Kluwer Academic Publishers 1998

Suggested Citation

  • Yuri Sotskov & Albert Wagelmans & Frank Werner, 1998. "On the calculation of the stability radiusof an optimal or an approximate schedule," Annals of Operations Research, Springer, vol. 83(0), pages 213-252, October.
    • Handle: RePEc:spr:annopr:v:83:y:1998:i:0:p:213-252:10.1023/a:1018960030420
    DOI: 10.1023/A:1018960030420
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    Cited by:

    1. Evgeny Gurevsky & Olga Battaïa & Alexandre Dolgui, 2012. "Balancing of simple assembly lines under variations of task processing times," Annals of Operations Research, Springer, vol. 201(1), pages 265-286, December.
    2. Lersteau, Charly & Rossi, André & Sevaux, Marc, 2016. "Robust scheduling of wireless sensor networks for target tracking under uncertainty," European Journal of Operational Research, Elsevier, vol. 252(2), pages 407-417.

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