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Energetic reasoning and bin-packing problem, for bounding a parallel machine scheduling problem

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Abstract

This paper deals with an extension of energetic reasoning, using some efficient lower bounds of the bin-packing problem, to get tight lower bounds for the P|r i , q i |C max. The link between P||C max and bin-packing problem is well-known. Our purpose is to extend the use of efficient lower bounds of the bin-packing problem to P|r i , q i |C max. We focus on some time-intervals, to compute the mandatory parts of activities within this time-interval and then to deduce an associated bin-packing instance. Thus, lower bounds of the bin-packing problem are used to get new satisfiability tests for the parallel machine problem. We also propose to extend the classical time-bound adjustments of release dates and deadlines to efficiently use bin-packing lower bounds. Experimental results that prove the efficiency of our approach on several kind of instances are reported.

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Authors and Affiliations

  1. Laboratoire d’Informatique de l’Université François Rabelais de Tours, EA2101, Tours, France

    Fabrice Tercinet, Emmanuel Néron & Christophe Lenté

  2. Department of Computer Sciences, Polytech’Tours, 64 av. Jean Portalis, 37200, Tours, France

    Emmanuel Néron

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  1. Fabrice Tercinet
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  2. Emmanuel Néron
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  3. Christophe Lenté
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Correspondence to Emmanuel Néron.

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Tercinet, F., Néron, E. & Lenté, C. Energetic reasoning and bin-packing problem, for bounding a parallel machine scheduling problem. 4OR 4, 297–317 (2006). https://doi.org/10.1007/s10288-006-0017-1

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