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

Author

Listed:
  • Pascale Bendotti

    (EDF R&D
    Sorbonne Université, CNRS)

  • Luca Brunod Indrigo

    (EDF R&D
    Sorbonne Université, CNRS)

  • Philippe Chrétienne

    (Sorbonne Université, CNRS)

  • Bruno Escoffier

    (Sorbonne Université, CNRS
    Institut Universitaire de France)

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.

Suggested Citation

  • Pascale Bendotti & Luca Brunod Indrigo & Philippe Chrétienne & Bruno Escoffier, 2024. "Resource leveling: complexity of a unit execution time two-processor scheduling variant and related problems," Journal of Scheduling, Springer, vol. 27(6), pages 587-606, December.
    • Handle: RePEc:spr:jsched:v:27:y:2024:i:6:d:10.1007_s10951-024-00822-z
    DOI: 10.1007/s10951-024-00822-z
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