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Lower Bounds on the Approximation Ratios of Leading Heuristics for the Single-Machine Total Tardiness Problem

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Abstract

The weakly NP-hard single-machine total tardiness scheduling problem has been extensively studied in the last decades. Various heuristics have been proposed to efficiently solve in practice a problem for which a fully polynomial time approximation scheme exists (though with complexity O(n 7/∈)). In this note, we show that all known constructive heuristics for the problem, namely AU, MDD, PSK, WI, COVERT, NBR, present arbitrarily bad approximation ratios. The same behavior is shown by the decomposition heuristics DEC/EDD, DEC/MDD, DEC/PSK, and DEC/WI.

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Authors and Affiliations

  1. D.A.I., Politecnico di Torino, Italy

    Federico Della Croce

  2. Dipartimento di Informatica, Universita` di Torino, Italy

    Andrea Grosso

  3. LAMSADE, Université Paris-Dauphine, France

    Vangelis Th. Paschos

Authors
  1. Federico Della Croce
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  2. Andrea Grosso
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  3. Vangelis Th. Paschos
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Correspondence to Federico Della Croce.

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Della Croce, F., Grosso, A. & Paschos, V.T. Lower Bounds on the Approximation Ratios of Leading Heuristics for the Single-Machine Total Tardiness Problem. Journal of Scheduling 7, 85–91 (2004). https://doi.org/10.1023/B:JOSH.0000013056.09936.fd

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  • DOI: https://doi.org/10.1023/B:JOSH.0000013056.09936.fd

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