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Scheduling under Uncertainty: Bounding the Makespan Distribution

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Computational Discrete Mathematics

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2122))

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Abstract

Deterministic models for project scheduling and control suffer from the fact that they assume complete information and neglect random influences that occur during project execution. A typical consequence is the underestimation of the expected project duration and cost frequently observed in practice. This phenomenon occurs even in the absence of resource constraints, and has been the subject of extensive research in discrete mathematics and operations research.

This article presents a survey on the reasons for this phenomenon, its complexity, and on methods how to obtain more relevant information. this end, we consider scheduling models with fixed precedence constraints, but (independent) random processing times. The objective then is to obtain information about the distribution of the project makespan. We will demonstrate that this is an #\( \mathcal{P} \) -complete problem in general, and then consider several combinatorial methods to obtain approximate information about the makespan distribution.

Supported by Deutsche Forschungsgemeinschaft under grant Mo 346/3-3 and by German Israeli Foundation under grant I-564-246.06/97

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Authors and Affiliations

  1. Technische Universität Berlin, 10623, Berlin, Germany

    Rolf H. Möhring

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  1. Rolf H. Möhring
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Editors and Affiliations

  1. Institut für Informatik, Freie Universität Berlin, Takustr. 9, 14195, Berlin, Germany

    Helmut Alt

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Möhring, R.H. (2001). Scheduling under Uncertainty: Bounding the Makespan Distribution. In: Alt, H. (eds) Computational Discrete Mathematics. Lecture Notes in Computer Science, vol 2122. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45506-X_7

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  • DOI: https://doi.org/10.1007/3-540-45506-X_7

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  • Print ISBN: 978-3-540-42775-9

  • Online ISBN: 978-3-540-45506-6

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