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Scheduling with safety distances

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Abstract

We investigate the problem of Scheduling with Safety Distances (SSD) that consists in scheduling jobs on two parallel machines without machine idle time. Every job is already assigned to its machine, and we just have to specify an ordering of the jobs for each machine. The goal is to find orderings of the jobs such that the minimum time elapsed between any two job completion times is maximized. We prove that this problem is NP-hard in general and give polynomial time algorithms for special cases. These results combined establish a sharp borderline between NP-complete and polynomial solvable versions of the problem SSD.

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Authors and Affiliations

  1. Department of Mathematics, University of Limburg, P.O. Box 616, 6200 MD, Maastricht, The Netherlands

    Frits C. R. Spieksma

  2. Institut für Theoretische Informatik, TU Graz, Klosterwiesgasse 31/II, A-8010, Graz, Austria

    Gerhard J. Woeginger

  3. Institut für Mathematik B, TU Graz, Kopernikaugasse 24, A-8010, Graz, Austria

    Zhongliang Yu

Authors
  1. Frits C. R. Spieksma
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  2. Gerhard J. Woeginger
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  3. Zhongliang Yu
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Additional information

This research was supported by the Christian Doppler Laboratorium für Diskrete Optimierung.

On leave from the Mathematics Section, Forestry University Nanjing, Nanjing, PR China.

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Spieksma, F.C.R., Woeginger, G.J. & Yu, Z. Scheduling with safety distances. Ann Oper Res 57, 251–264 (1995). https://doi.org/10.1007/BF02099701

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  • DOI: https://doi.org/10.1007/BF02099701

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