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Scheduling of tasks with effectiveness precedence constraints

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Abstract

We formally present the problem of scheduling tasks with effectiveness precedence relationships in order to achieve the minimum total weighted completion time. We provide the problem formulation and define the scope of the problem considered. We present computational complexity results for this problem and an approximation algorithm for it. We prove the theoretical performance of our algorithm and demonstrate its efficiency and practical performance through computational testing, which includes a comparison to the optimal results obtained with an integer programming formulation.

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Acknowledgements

The work of these authors was supported in part by the U.S. National Science Foundation under Grant Number CMMI-1314350, the U.S. National Science Foundation under Grant Number CMMI-1254258, and the Graduate Assistance in Areas of National Need (GAANN) Fellowship from the U.S. Department of Education under Grant Number P200A120055. We thank the reviewers for taking time to provide valuable contributions to this paper to improve its quality.

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Authors and Affiliations

  1. The MITRE Corporation, 202 Burlington Rd., Bedford, MA, 01739, USA

    Emily A. Heath

  2. Department of Mathematical Sciences, Rensselaer Polytechnic Institute, 110 8th St., Troy, NY, 12180, USA

    John E. Mitchell

  3. Deparment of Industrial and Systems Engineering, Rensselaer Polytechnic Institute, 110 8th St., Troy, NY, 12180, USA

    Thomas C. Sharkey

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  1. Emily A. Heath
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  2. John E. Mitchell
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  3. Thomas C. Sharkey
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Correspondence to Emily A. Heath.

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Heath, E.A., Mitchell, J.E. & Sharkey, T.C. Scheduling of tasks with effectiveness precedence constraints. Optim Lett 14, 37–49 (2020). https://doi.org/10.1007/s11590-019-01440-x

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