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

Pascale Bendotti (), Luca Brunod Indrigo (), Philippe Chrétienne () and Bruno Escoffier ()
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Pascale Bendotti: EDF R&D
Luca Brunod Indrigo: EDF R&D
Philippe Chrétienne: Sorbonne Université, CNRS
Bruno Escoffier: Sorbonne Université, CNRS

Journal of Scheduling, 2024, vol. 27, issue 6, No 5, 587-606

Abstract: 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.

Keywords: Scheduling; Resource leveling; Complexity; Matchings (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10951-024-00822-z

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