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Resource leveling: complexity of a unit execution time two-processor scheduling variant and related problems

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Abstract

This paper mainly focuses on a resource leveling variant of a two-processor scheduling problem. The latter problem is to schedule a set of dependent UET jobs on two identical processors with minimum makespan. It is known to be polynomial-time solvable. In the variant we consider, the resource constraint on processors is relaxed and the objective is no longer to minimize makespan. Instead, a deadline is imposed on the makespan and the objective is to minimize the total resource use exceeding a threshold resource level of two. This resource leveling criterion is known as the total overload cost. Sophisticated matching arguments allow us to provide a polynomial algorithm computing the optimal solution as a function of the makespan deadline. It extends a solving method from the literature for the two-processor scheduling problem. Moreover, the complexity of related resource leveling problems sharing the same objective is studied. These results lead to polynomial or pseudo-polynomial algorithms or NP-hardness proofs, allowing for an interesting comparison with classical machine scheduling problems.

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Authors and Affiliations

  1. EDF R&D, 7 Boulevard Gaspard Monge, 91120, Palaiseau, France

    Pascale Bendotti & Luca Brunod Indrigo

  2. LIP6 UMR 7606, Sorbonne Université, CNRS, 4 Place Jussieu, 75005, Paris, France

    Pascale Bendotti, Luca Brunod Indrigo, Philippe Chrétienne & Bruno Escoffier

  3. Institut Universitaire de France, Paris, France

    Bruno Escoffier

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  1. Pascale Bendotti
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  2. Luca Brunod Indrigo
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  3. Philippe Chrétienne
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  4. Bruno Escoffier
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Correspondence to Luca Brunod Indrigo.

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Bendotti, P., Brunod Indrigo, L., Chrétienne, P. et al. Resource leveling: complexity of a unit execution time two-processor scheduling variant and related problems. J Sched 27, 587–606 (2024). https://doi.org/10.1007/s10951-024-00822-z

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